From 899489958d72615adc743e5a4537b47fa7a91ad5 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Wed, 31 Dec 2025 11:44:50 -0800 Subject: [PATCH 01/42] Refactor package structure and modernize dependencies - Moved legacy 3D code to submodule `src/distmeshnd/` - Created `src/dmesh.jl` for new `DMesh` types and utilities - Updated `Project.toml`: - Bumped Julia compat to 1.10 - Added new dependencies - Updated tests to use `DistMeshND` alias for internal legacy functions --- Project.toml | 11 +- src/DistMesh.jl | 137 ++++------------- src/distfuncs.jl | 60 ++++++++ src/distmesh2d.jl | 171 ++++++++++++++++++++++ src/distmeshnd/DistMeshND.jl | 125 ++++++++++++++++ src/{ => distmeshnd}/decompositions.jl | 0 src/{ => distmeshnd}/diff.jl | 0 src/{ => distmeshnd}/distmeshnd.jl | 40 ++--- src/{ => distmeshnd}/hilbertsort.jl | 0 src/{ => distmeshnd}/pointdistribution.jl | 0 src/{ => distmeshnd}/quality.jl | 0 src/{ => distmeshnd}/tetgen.jl | 0 src/dmesh.jl | 37 +++++ src/examples.jl | 49 +++++++ src/meshutils.jl | 59 ++++++++ test/runtests.jl | 46 +++--- 16 files changed, 583 insertions(+), 152 deletions(-) create mode 100644 src/distfuncs.jl create mode 100644 src/distmesh2d.jl create mode 100644 src/distmeshnd/DistMeshND.jl rename src/{ => distmeshnd}/decompositions.jl (100%) rename src/{ => distmeshnd}/diff.jl (100%) rename src/{ => distmeshnd}/distmeshnd.jl (90%) rename src/{ => distmeshnd}/hilbertsort.jl (100%) rename src/{ => distmeshnd}/pointdistribution.jl (100%) rename src/{ => distmeshnd}/quality.jl (100%) rename src/{ => distmeshnd}/tetgen.jl (100%) create mode 100644 src/dmesh.jl create mode 100644 src/examples.jl create mode 100644 src/meshutils.jl diff --git a/Project.toml b/Project.toml index 25e2535..594836c 100644 --- a/Project.toml +++ b/Project.toml @@ -1,17 +1,22 @@ name = "DistMesh" uuid = "f7ee28b6-bfbf-11e9-3e31-8961b86f052c" -authors = ["Steve Kelly "] -version = "0.1.0" +version = "0.2.0" +authors = ["Steve Kelly and Per-Olof Persson = c2 + return norm(p - p2) + else + return norm(p - (p1 + c1 / c2 * v)) + end +end + +function inpolygon(p, pv) + cn = 0 # Crossing number counter + for i = 1:length(pv)-1 # Loop over all edges of the polygon + if pv[i][2] <= p[2] && pv[i+1][2] > p[2] || # Upward crossing + pv[i][2] > p[2] && pv[i+1][2] <= p[2] # Downward crossing + vt = (p[2] - pv[i][2]) / (pv[i+1][2] - pv[i][2]) # Intersection + if p[1] < pv[i][1] + vt * (pv[i+1][1] - pv[i][1]) + cn += 1 # A valid cross right of p[1] + end + end + end + return cn % 2 == 1 +end + +dsegment(p, pv) = (dline(p, pv[i+1], pv[i]) for i in 1:length(pv)-1) +function dpoly(p, pv) + d = minimum(dsegment(p, pv)) + inpolygon(p, pv) ? -d : d +end + +ddiff(d1, d2) = max(d1, -d2) +dunion(d1, d2) = min(d1, d2) +dintersect(d1, d2) = max(d1, d2) + +huniform(p) = 1 + +const naca_coeffs = 0.12 / 0.2 * SVector(0.2969, -0.1260, -0.3516, 0.2843, -0.1036) + +function dnaca(p) + a0, a14... = naca_coeffs + (abs(p[2]) - sum(a14 .* p[1] .^ SVector(1, 2, 3, 4))) .^ 2 - a0^2 * p[1] +end diff --git a/src/distmesh2d.jl b/src/distmesh2d.jl new file mode 100644 index 0000000..8dc0c54 --- /dev/null +++ b/src/distmesh2d.jl @@ -0,0 +1,171 @@ +######################################################################## +# StaticVector shorthands + +const SF2 = SVector{2,Float64} +const SI2 = SVector{2,Int} +const SI3 = SVector{3,Int} + +######################################################################## +# Utility functions + +extract_elements(tri::Delaunator.Triangulation{I}) where {I} = + reinterpret(SVector{3, I}, triangles(tri)) +delaunay(p) = extract_elements(triangulate(p)) + +barvectors(p, bars) = [ p[bar[1]] - p[bar[2]] for bar in bars ] + +function init_nodes(bbox, h0) + # Create initial distribution in bounding box (equilateral triangles) + xx = bbox[1][1]:h0:bbox[2][1] + yy = bbox[1][2]:h0*√3/2:bbox[2][2] + p = [ SF2(x + iseven(iy) * h0/2, y) for x in xx for (iy,y) in enumerate(yy) ] +end + +function nodes_rejection(p, pfix, dfcn, hfcn, geps) + # Remove nodes outside the region, apply the rejection method + p = p[dfcn.(p) .< geps] + r0 = [ 1 / hfcn(pp)^2 for pp in p ] + p = p[rand(length(r0)) .< r0./maximum(r0)] + p = vcat(pfix, setdiff(p, pfix)) +end + +function retriangulate(p, dfcn, geps) + # Retriangulation by the Delaunay algorithm, remove outside triangles + t = delaunay(p) + t = filter(tt -> dfcn(sum(p[tt]) / 3) < -geps, t) + # Find all bars as the unique triangle edges + bars = [ tt[ix] for tt in t for ix in SI2[(1,2),(2,3),(3,1)] ] + bars = unique(sort.(bars)) + t, bars +end + +function desiredlengths(p, bars, L, hfcn, Fscale) + # Scaled and normalized desired bar lengths + barmid = [ (p[bar[1]] + p[bar[2]]) / 2 for bar in bars ] + hbars = hfcn.(barmid) + L0 = hbars * Fscale * sqrt(sum(L .^ 2) / sum(hbars .^ 2)) +end + +function density_control(p, L, L0, bars, nfix) + # Density control - remove nodes that are too close + pkeep = trues(length(p)) + foreach(bar -> pkeep[bar] .= false, bars[L0[:].>2*L[:]]) + pkeep[1:nfix] .= true + p = p[pkeep] +end + +function total_node_forces(L, L0, barvec, bars, np, nfix) + # Find all bar forces and accumulate at all nodes + F = max.(L0 .- L, 0.0) + Fvec = F ./ L .* barvec + Ftot = [ SF2(0.0,0.0) for ip = 1:np ] + for ibar in eachindex(bars) + Ftot[bars[ibar][1]] += Fvec[ibar] + Ftot[bars[ibar][2]] -= Fvec[ibar] + end + Ftot[1:nfix] .*= 0.0 + Ftot +end + +function project_nodes!(p, dfcn, deps) + d = dfcn.(p) + ix = findall(d .> 0) + numgrad(f,x,fx) = (SF2(f(x + SF2(deps,0)), f(x + SF2(0,deps))) .- fx) / deps + dgrad = [ numgrad(dfcn, p[i], d[i]) for i in ix ] + @. p[ix] -= d[ix] * dgrad / norm(dgrad)^2 + d +end + +######################################################################## +# Main function + +""" + distmesh2d(dfcn, hfcn, h0, bbox, pfix=[]; plotting=false) + +2-D Mesh Generator using Distance Functions. + + `p`: Node positions (Vector of (x,y) coordinates) + 't': Triangle indices (Vector of (i1,i2,i3) indices) + 'dfcn': Distance function d(p) + 'hfcn': Scaled edge length function h(p) + 'h0': Initial edge length + 'bbox': Bounding box ((xmin,ymin), (xmax,ymax)) + 'pfix': Fixed node positions (Vector of (x,y) coordinates) + +# Examples + +### Example: (Uniform Mesh on Unit Circle) +```jldoctest +dfcn(p) = sqrt(sum(p.^2)) - 1 +p,t = distmesh2d(dfcn, huniform, 0.2, ((-1,-1), (1,1)), plotting=true); +``` +#### Example: (Rectangle with circular hole, refined at circle boundary) +```jldoctest +dfcn2(p) = ddiff(drectangle(p, -1, 1, -1, 1), dcircle(p, r=0.5)) +hfcn2(p) = 0.05 + 0.3 * dcircle(p, r=0.5); +bbox = ((-1,-1), (1,1)) +pfix = [(-1,-1), (-1,1), (1,-1), (1,1)] +p,t = distmesh2d(dfcn2, hfcn2, 0.05, bbox, pfix, plotting=true); +``` +""" +function distmesh2d(dfcn, hfcn, h0, bbox, pfix=SF2[]; + plotting=false, # Optional live plotting + densityctrlfreq = 30, # Frequency of density controls + maxiter = 10_000, # When to terminate if no convergence + # Algorithmic parameters, defaults are normally good + Fscale = 1.2, # Force function parameter (compression) + deltat = 0.2, # Timestep + ttol = 0.1 * h0, # Retriangulation tolerance + geps = 0.001 * h0, # dfcn(p) tolerance for in/out points + dptol = geps, # Termination tolerance + deps = sqrt(eps()) * h0 # Finite difference stepsize + ) + + # Initializations + pfix = unique(SF2.(pfix)) + nfix = length(pfix) + pold = [SF2(Inf,Inf)] + t, bars = SI3[], SI2[] + converged = false + + # Initial nodes + p = init_nodes(bbox, h0) + p = nodes_rejection(p, pfix, dfcn, hfcn, geps) + + # Main loop + for iter = 1:maxiter + # If large relative movements, retriangulate and plot + if maximum(norm.(p .- pold)) > ttol + pold = copy(p) + t, bars = retriangulate(p, dfcn, geps) + plotting && display(simpplot(p, t)) + end + + # All bars and lengths + barvec = barvectors(p, bars) + L = norm.(barvec) + L0 = desiredlengths(p, bars, L, hfcn, Fscale) + + # Density control - remove points that are too close to each other + if iter % densityctrlfreq == 0 + p = density_control(p, L, L0, bars, nfix) + pold = [SF2(Inf,Inf)] + continue + end + + # Compute forces and update nodes + dp = deltat * total_node_forces(L, L0, barvec, bars, length(p), nfix) + p .+= dp + + # Project outside points back to boundary + d = project_nodes!(p, dfcn, deps) + + # Terminate if small (interior) node movements + converged = maximum(norm.(dp[d.<-geps])) < dptol + converged && break + end + + converged || @warn "No convergence in maxiter=$maxiter iterations" + plotting && display(simpplot(p, t)) + return DMesh(p, t) +end diff --git a/src/distmeshnd/DistMeshND.jl b/src/distmeshnd/DistMeshND.jl new file mode 100644 index 0000000..ab16e54 --- /dev/null +++ b/src/distmeshnd/DistMeshND.jl @@ -0,0 +1,125 @@ +module DistMeshND + +using LinearAlgebra, + TetGen +using GeometryBasics +using GeometryBasics: Triangle, Tetrahedron, Mesh, Polytope, Point + +const tetpairs = ((1,2),(1,3),(1,4),(2,3),(2,4),(3,4)) +const tettriangles = ((1,2,3),(1,2,4),(2,3,4),(1,3,4)) + +abstract type AbstractDistMeshAlgorithm end + +""" + DistMeshSetup + +Takes Keyword arguments as follows: + + iso (default: 0): Value of which to extract the isosurface, inside surface is negative + deltat (default: 0.1): the fraction of edge displacement to apply each iteration + sort (default:false): If true and no fixed points, sort points using a hilbert sort. + sort_interval (default:20) Use hilbert sort after the specified retriangulations + distribution (default: :regular) Initial point distribution, either :regular or :packed. +""" +struct DistMeshSetup{T} <: AbstractDistMeshAlgorithm + iso::T + deltat::T + ttol::T + ptol::T + sort::Bool # use hilbert sort to cache-localize points + sort_interval::Int # retriangulations before resorting + nonlinear::Bool # uses nonlinear edge force + distribution::Symbol # intial point distribution +end + +function DistMeshSetup(;iso=0, + ptol=.001, + deltat=0.05, + ttol=0.02, + sort=false, + sort_interval=20, + nonlinear=false, + distribution=:regular) + T = promote_type(typeof(iso),typeof(ptol),typeof(deltat), typeof(ttol)) + DistMeshSetup{T}(iso, + deltat, + ttol, + ptol, + sort, + sort_interval, + nonlinear, + distribution) +end + +""" + DistMeshQuality + +Use Tetrahedral quality analysis to control the meshing process + + iso (default: 0): Value of which to extract the iso surface, inside negative + deltat (default: 0.1): the fraction of edge displacement to apply each iteration +""" +struct DistMeshQuality{T} <: AbstractDistMeshAlgorithm + iso::T + deltat::T + filter_less_than::T # Remove tets less than the given quality + #allow_n_regressions::Int # Might want this + termination_quality::T # Once achieved, terminate + sort::Bool # use hilbert sort to cache-localize points + sort_interval::Int # retriangulations before resorting + nonlinear::Bool # uses nonlinear edge force + distribution::Symbol # intial point distribution +end + +function DistMeshQuality(;iso=0, + deltat=0.05, + filter_less_than=0.02, + termination_quality=0.3, + sort=false, + sort_interval=20, + nonlinear=true, + distribution=:regular) + DistMeshQuality(iso, + deltat, + filter_less_than, + termination_quality, + sort, + sort_interval, + nonlinear, + distribution) +end + +""" + DistMeshStatistics + + Statistics about the convergence between iterations +""" +struct DistMeshStatistics{T} + maxmove::Vector{T} # max point move in an iteration + maxdp::Vector{T} # max displacmeent induced by an edge + min_volume_edge_ratio::Vector{T} + max_volume_edge_ratio::Vector{T} + average_volume_edge_ratio::Vector{T} + retriangulations::Vector{Int} # Iteration num where retriangulation occured +end + +DistMeshStatistics() = DistMeshStatistics{Float64}([],[],[],[],[],[]) + +""" +Uniform edge length function. +""" +struct HUniform end + + +include("diff.jl") +include("pointdistribution.jl") +include("distmeshnd.jl") +include("tetgen.jl") +include("quality.jl") +include("decompositions.jl") +include("hilbertsort.jl") + +#export distmeshsurface +export distmeshnd, DistMeshSetup, DistMeshStatistics, HUniform + +end # module diff --git a/src/decompositions.jl b/src/distmeshnd/decompositions.jl similarity index 100% rename from src/decompositions.jl rename to src/distmeshnd/decompositions.jl diff --git a/src/diff.jl b/src/distmeshnd/diff.jl similarity index 100% rename from src/diff.jl rename to src/distmeshnd/diff.jl diff --git a/src/distmeshnd.jl b/src/distmeshnd/distmeshnd.jl similarity index 90% rename from src/distmeshnd.jl rename to src/distmeshnd/distmeshnd.jl index 251c44d..ca0a55b 100644 --- a/src/distmeshnd.jl +++ b/src/distmeshnd/distmeshnd.jl @@ -1,5 +1,5 @@ """ - distmesh + distmeshnd 3D Mesh Generator using Signed Distance Functions. Arguments: fdist: Distance function @@ -15,14 +15,14 @@ d(p) = sqrt(sum(p.^2))-1 p,t = distmeshnd(d,huniform,0.2) """ -function distmesh(fdist::Function, - fh::Union{Function,HUniform}, - h::Number, - setup::AbstractDistMeshAlgorithm=DistMeshSetup(); - origin=GeometryBasics.Point{3,Float64}(-1,-1,-1), - widths=GeometryBasics.Point{3,Float64}(2,2,2), - fix=nothing, - stats=false) where {VertType} +function distmeshnd(fdist::Function, + fh::Union{Function,HUniform}, + h::Number, + setup::AbstractDistMeshAlgorithm=DistMeshSetup(); + origin=GeometryBasics.Point{3,Float64}(-1,-1,-1), + widths=GeometryBasics.Point{3,Float64}(2,2,2), + fix=nothing, + stats=false) # TODO: tetgen only handles Float64 VT = GeometryBasics.Point{3,Float64} if isa(fix, Nothing) @@ -32,13 +32,13 @@ function distmesh(fdist::Function, end o = VT(origin...) w = VT(widths...) - distmesh(fdist, fh, h, setup, o, w, fp, Val(stats), VT) + distmeshnd(fdist, fh, h, setup, o, w, fp, Val(stats), VT) end """ DistMeshResult -A struct returned from the `distmesh` function that includes point, simplex, +A struct returned from the `distmeshnd` function that includes point, simplex, and interation statistics. """ struct DistMeshResult{PT, TT, STATS} @@ -47,15 +47,15 @@ struct DistMeshResult{PT, TT, STATS} stats::STATS end -function distmesh(fdist::Function, - fh, - h::Number, - setup::DistMeshSetup, - origin, - widths, - fix, - ::Val{stats}, - ::Type{VertType}) where {VertType, stats} +function distmeshnd(fdist::Function, + fh, + h::Number, + setup::DistMeshSetup, + origin, + widths, + fix, + ::Val{stats}, + ::Type{VertType}) where {VertType, stats} geps=1e-1*h+setup.iso # parameter for filtering tets outside bounds and considering for max displacment of a node diff --git a/src/hilbertsort.jl b/src/distmeshnd/hilbertsort.jl similarity index 100% rename from src/hilbertsort.jl rename to src/distmeshnd/hilbertsort.jl diff --git a/src/pointdistribution.jl b/src/distmeshnd/pointdistribution.jl similarity index 100% rename from src/pointdistribution.jl rename to src/distmeshnd/pointdistribution.jl diff --git a/src/quality.jl b/src/distmeshnd/quality.jl similarity index 100% rename from src/quality.jl rename to src/distmeshnd/quality.jl diff --git a/src/tetgen.jl b/src/distmeshnd/tetgen.jl similarity index 100% rename from src/tetgen.jl rename to src/distmeshnd/tetgen.jl diff --git a/src/dmesh.jl b/src/dmesh.jl new file mode 100644 index 0000000..4b5b3b6 --- /dev/null +++ b/src/dmesh.jl @@ -0,0 +1,37 @@ +# ------------------------------------------------------------------------- +# Mesh Data Structures and Helpers +# ------------------------------------------------------------------------- + +""" + DMesh{D, T, N, I} + +A lightweight container for mesh data. +- `D`: Spatial dimension (e.g., 2 for 2D coordinates). +- `T`: Floating point type for coordinates (e.g., Float64). +- `N`: Number of vertices per element (e.g., 3 for triangles). +- `I`: Integer type for indices (e.g., Int, Int32). +""" +struct DMesh{D, T, N, I <: Integer} + p::Vector{SVector{D, T}} + t::Vector{SVector{N, I}} +end + +# Make DMesh iterable so it acts like (p, t) +Base.iterate(m::DMesh, state=1) = iterate((m.p, m.t), state) +Base.eltype(::Type{DMesh{D,T,N,I}}) where {D,T,N,I} = Union{Vector{SVector{D,T}}, Vector{SVector{N,I}}} +Base.length(::DMesh) = 2 + +""" + p_view, t_view = as_arrays(m::DMesh) + +Return zero-copy views of the mesh nodes and elements. + +Note: The shape is `(D x NumPoints)` and `(N x NumElements)`. +This corresponds to Julia's column-major memory layout (columns are points). +Modifying these arrays will modify the underlying `DMesh`. +""" +function as_arrays(m::DMesh{D,T,N,I}) where {D,T,N,I} + p_view = reinterpret(reshape, T, m.p) + t_view = reinterpret(reshape, I, m.t) + return p_view, t_view +end diff --git a/src/examples.jl b/src/examples.jl new file mode 100644 index 0000000..f0132cc --- /dev/null +++ b/src/examples.jl @@ -0,0 +1,49 @@ +include("distmesh.jl") + +function ex5polygon(; h0=0.1) + pv = SF2[(-0.4, -0.5), (0.4, -0.2), (0.4, -0.7), (1.5, -0.4), + (0.9, 0.1), (1.6, 0.8), (0.5, 0.5), (0.2, 1.0), + (0.1, 0.4), (-0.7, 0.7), (-0.4, -0.5)] + dfcn(p) = dpoly(p, pv) + dfcn, huniform, h0, [(-1, -1), (2, 1)], pv +end + +function hnaca(p; hlead=0.01, htrail=0.04, hmax=2.0) + minimum((hlead + 0.3 * dcircle(p, c=(0, 0), r=0), + htrail + 0.3 * dcircle(p, c=(1, 0), r=0), + hmax)) +end + +function fixnaca(; htrail=0.04) + a0, a14... = naca_coeffs + fixx = 1 .- htrail * cumsum(1.3 .^ (0:4)) + fixy = a0 * sqrt.(fixx) .+ fixx .^ (1:4)' * a14 + fix = vcat(SF2[(0,0),(1,0)], [ SF2[(x,y),(x,-y)] for (x,y) in zip(fixx,fixy) ]...) +end + +function ex6naca(; hlead=0.01, htrail=0.04, hmax=2.0, circx=2.0, circr=4.0) + dfcn(p) = ddiff(dcircle(p, c=(circx, 0), r=circr), dnaca(p)) + hfcn(p) = hnaca(p; hlead=hlead, htrail=htrail, hmax=hmax) + + fix = SF2[(1,0),(0,1),(-1,0),(0,-1)] .* circr .+ SF2[(circx,0)] + fix = vcat(fix, fixnaca(htrail=htrail)) + bbox = [(circx - circr, -circr), (circx + circr, circr)] + h0 = minimum((hlead, htrail, hmax)) + dfcn, hfcn, h0, bbox, fix +end + +for ex in (ex5polygon, ex6naca) + p, t = distmesh2d(ex()...) + display(simpplot(p, t)) +end + +using Random +#for s = 1:1000 +# @show s +# Random.seed!(s) +# p,t = distmesh2d(ex6naca()...); +# @show minimum(simpqual(p,t)) +#end + +#Random.seed!(9) +#distmesh2d(ex6naca()...) diff --git a/src/meshutils.jl b/src/meshutils.jl new file mode 100644 index 0000000..4003145 --- /dev/null +++ b/src/meshutils.jl @@ -0,0 +1,59 @@ +#import Plots + +#= +function simpplot(p, t, tdata=nothing; args...) + pxy(d) = [ tix==0 ? NaN : p[tt[tix]][d] for tix in (1,2,3,1,0), tt in t ] + args = (args..., seriestype=:shape, aspect_ratio=:equal, leg=false) + if isnothing(tdata) + args = (args..., fillcolor=Plots.RGB(0.8, 0.9, 1.0)) + else + # todo + #data = vcat(tdata[t], fill(NaN, 1, size(t, 2)))[:] + #args = (args..., fillcolor=:viridis, fill_z=data, colorbar=:right) + end + h = Plots.plot(vec(pxy(1)), vec(pxy(2)); args...) +end +=# + +function simplex_area(el) + if length(el) == 3 # Triangle + p12 = el[2] - el[1] + p13 = el[3] - el[1] + return (p12[1] * p13[2] - p12[2] * p13[1]) / 2 + else + @assert "Dimension not implemented" + end +end + + +function simplex_qual(el) + if length(el) == 3 # Triangle + norm(vec) = sqrt(sum(vec.^2)) + a,b,c = ( norm(el[ix[2]] - el[ix[1]]) for ix in ((1,2),(2,3),(3,1)) ) + r = 0.5*sqrt((b+c-a) * (c+a-b) * (a+b-c) / (a+b+c)) + R = a*b*c / sqrt((a+b+c) * (b+c-a) * (c+a-b) * (a+b-c)) + return 2*r/R + else + @assert "Dimension not implemented" + end +end + +elemwise_feval(p,t,f) = [ f(p[tt]) for tt in t ] +simpqual(p, t, fqual=simplex_qual) = elemwise_feval(p, t, fqual) +simpvol(p,t) = elemwise_feval(p, t, simplex_area) + +snap(x::T, scaling=1) where {T <: Real} = x +snap(x::T, scaling=1, tol=sqrt(eps(T))) where {T <: AbstractFloat} = + scaling*tol*round(x/scaling/tol) + zero(T) # Adding zero to uniquify -0.0 and 0.0 + +function fixmesh(p, t; output_ix=false) + scaling = maximum(norm.(p)) + pp = [ snap.(p1,scaling) for p1 in p ] + ppp = unique(pp) + ix = Int.(indexin(ppp, pp)) + jx = Int.(indexin(pp, ppp)) + p = p[ix] + t = [jx[tt] for tt in t] + return output_ix ? (p,t,ix) : (p,t) +end + diff --git a/test/runtests.jl b/test/runtests.jl index 221afb4..0db5f6c 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -4,7 +4,7 @@ using GeometryBasics include("vals.jl") - +const DistMeshND = DistMesh.DistMeshND @testset "point distributions" begin vlen(a,b) = sqrt(sum((a-b).^2)) @@ -12,7 +12,7 @@ include("vals.jl") pts = [] dists = [] f(x) = -1 - DistMesh.simplecubic!(f, pts, dists, 0.5, 0, Point{3,Float64}(0),Point{3,Float64}(1),Point{3,Float64}) + DistMeshND.simplecubic!(f, pts, dists, 0.5, 0, Point{3,Float64}(0),Point{3,Float64}(1),Point{3,Float64}) @test length(pts) == 27 @test length(dists) == 27 @test isapprox(vlen(pts[1],pts[2]),0.5) @@ -23,7 +23,7 @@ include("vals.jl") pts = [] dists = [] f(x) = -1 - DistMesh.facecenteredcubic!(f, pts, dists, 0.5, 0, Point{3,Float64}(0),Point{3,Float64}(1),Point{3,Float64}) + DistMeshND.facecenteredcubic!(f, pts, dists, 0.5, 0, Point{3,Float64}(0),Point{3,Float64}(1),Point{3,Float64}) @test length(pts) == 216 @test length(dists) == 216 @test isapprox(vlen(pts[1],pts[2]),0.5) @@ -34,22 +34,22 @@ end @testset "quality analysis" begin @testset "triangles" begin - @test DistMesh.triqual([0,0,0],[1,0,0],[0,1,0]) == DistMesh.triqual([0,0,0],[2,0,0],[0,2,0]) - @test DistMesh.triqual([0,0,0],[1,0,1],[0,1,1]) == DistMesh.triqual([0,0,0],[2,0,2],[0,2,2]) - @test DistMesh.triqual([0,0,0],[2,0,0],[1,sqrt(3),0]) ≈ 1 - @test DistMesh.triqual([0,0,0],[1,sqrt(3),0],[2,0,0]) ≈ 1 + @test DistMeshND.triqual([0,0,0],[1,0,0],[0,1,0]) == DistMeshND.triqual([0,0,0],[2,0,0],[0,2,0]) + @test DistMeshND.triqual([0,0,0],[1,0,1],[0,1,1]) == DistMeshND.triqual([0,0,0],[2,0,2],[0,2,2]) + @test DistMeshND.triqual([0,0,0],[2,0,0],[1,sqrt(3),0]) ≈ 1 + @test DistMeshND.triqual([0,0,0],[1,sqrt(3),0],[2,0,0]) ≈ 1 end @testset "volume-length" begin pts = ([1,0,-1/sqrt(2)], [-1,0,-1/sqrt(2)], [0,1,1/sqrt(2)], [0,-1,1/sqrt(2)]) pts2 = ([1,1,1], [1,-1,-1], [-1,1,-1], [-1,-1,1]) pts_degenerate = ([1,1,1], [1,1,1], [-1,1,-1], [-1,-1,1]) - @test DistMesh.volume_edge_ratio(pts...) ≈ 1 - @test DistMesh.volume_edge_ratio((pts.*2)...) ≈ 1 - @test DistMesh.volume_edge_ratio((pts.*1e-6)...) ≈ 1 - @test isnan(DistMesh.volume_edge_ratio((pts.*0)...)) - @test DistMesh.volume_edge_ratio(pts2...) ≈ 1 - @test DistMesh.volume_edge_ratio((pts2.*2)...) ≈ 1 - @test DistMesh.volume_edge_ratio(pts_degenerate...) == 0 + @test DistMeshND.volume_edge_ratio(pts...) ≈ 1 + @test DistMeshND.volume_edge_ratio((pts.*2)...) ≈ 1 + @test DistMeshND.volume_edge_ratio((pts.*1e-6)...) ≈ 1 + @test isnan(DistMeshND.volume_edge_ratio((pts.*0)...)) + @test DistMeshND.volume_edge_ratio(pts2...) ≈ 1 + @test DistMeshND.volume_edge_ratio((pts2.*2)...) ≈ 1 + @test DistMeshND.volume_edge_ratio(pts_degenerate...) == 0 end end @@ -58,7 +58,7 @@ end @testset "tets to triangles" begin simps = [[4,3,2,1],[5,4,3,2],[1,2,3,4]] tris = Tuple{Int,Int,Int}[] - DistMesh.tets_to_tris!(tris,simps) + DistMeshND.tets_to_tris!(tris,simps) @test tris == [(1, 2, 3), (1, 2, 4), (1, 3, 4), (2, 3, 4), (2, 3, 5), (2, 4, 5), (3, 4, 5)] end end @@ -71,26 +71,26 @@ end a[i] = [xi,yi,zi] i += 1 end - DistMesh.hilbertsort!(a) + DistMeshND.hilbertsort!(a) @test a == hilbert_a end @testset "distmesh 3D" begin d(p) = sqrt(sum(p.^2))-1 - result = distmesh(d,HUniform(),0.2) + result = distmeshnd(d,HUniform(),0.2) @test length(result.points) == 485 @test length(result.tetrahedra) == 2207 - result = distmesh(d,HUniform(),0.2, DistMeshSetup(distribution=:packed)) + result = distmeshnd(d,HUniform(),0.2, DistMeshSetup(distribution=:packed)) @test length(result.points) == 742 @test length(result.tetrahedra) == 3472 # test stats is not messing - result = distmesh(d,HUniform(),0.2, stats=true) + result = distmeshnd(d,HUniform(),0.2, stats=true) @test length(result.points) == 485 @test length(result.tetrahedra) == 2207 - result = distmesh(d,HUniform(),0.4, stats=true) + result = distmeshnd(d,HUniform(),0.4, stats=true) @test length(result.points) == 56 @test length(result.tetrahedra) == 186 #for fn in fieldnames(typeof(result.stats)) @@ -100,11 +100,11 @@ end @testset "dihedral metrics" begin d(p) = sqrt(sum(p.^2))-1 - result = distmesh(d,HUniform(),0.2) + result = distmeshnd(d,HUniform(),0.2) p = result.points t = result.tetrahedra - all_angs = DistMesh.dihedral_angles(p,t) - min_angs = DistMesh.min_dihedral_angles(p,t) + all_angs = DistMeshND.dihedral_angles(p,t) + min_angs = DistMeshND.min_dihedral_angles(p,t) ax = extrema(all_angs) mx = extrema(min_angs) @test ax[1] == mx[1] From 9e4858fb47d93cfbc2c8d27f332a2566b77a0744 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Wed, 31 Dec 2025 12:32:29 -0800 Subject: [PATCH 02/42] show function for DMesh --- src/dmesh.jl | 18 ++++++++++++++++++ 1 file changed, 18 insertions(+) diff --git a/src/dmesh.jl b/src/dmesh.jl index 4b5b3b6..a3ab356 100644 --- a/src/dmesh.jl +++ b/src/dmesh.jl @@ -35,3 +35,21 @@ function as_arrays(m::DMesh{D,T,N,I}) where {D,T,N,I} t_view = reinterpret(reshape, I, m.t) return p_view, t_view end + + +# --- Helper for element names --- +element_name(::Val{3}) = "triangle" +element_name(::Val{4}) = "tetrahedron" +element_name(::Val{N}) where N = "$N-simplex" + +# 1. Compact Show (Standard) +function Base.show(io::IO, m::DMesh{D,T,N,I}) where {D,T,N,I} + print(io, "DMesh{$D,$T}($(length(m.p))n, $(length(m.t))e)") +end + +# 2. Rich Show (MIME) +function Base.show(io::IO, ::MIME"text/plain", m::DMesh{D,T,N,I}) where {D,T,N,I} + print(io, "DMesh: $(D)D, ") + print(io, "$(length(m.p)) nodes, ") + print(io, "$(length(m.t)) $(element_name(Val(N))) elements") +end From 7ba3fa33e56ab4c50e66fa6c09f73273fbb57686 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Wed, 31 Dec 2025 12:32:48 -0800 Subject: [PATCH 03/42] Default Int32 --- src/distmesh2d.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/distmesh2d.jl b/src/distmesh2d.jl index 8dc0c54..c8c7e16 100644 --- a/src/distmesh2d.jl +++ b/src/distmesh2d.jl @@ -2,8 +2,8 @@ # StaticVector shorthands const SF2 = SVector{2,Float64} -const SI2 = SVector{2,Int} -const SI3 = SVector{3,Int} +const SI2 = SVector{2,Int32} +const SI3 = SVector{3,Int32} ######################################################################## # Utility functions From 0ba197b4f2d096f6ee26f9de4ffee772b0ba4e9f Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Wed, 31 Dec 2025 14:54:13 -0800 Subject: [PATCH 04/42] Major documentation update: New file structure, automated scripts for examples/, and Literate.jl. --- .gitignore | 4 +- README.md | 44 ++++++++++++++++++++-- docs/Project.toml | 1 + docs/make.jl | 73 ++++++++++++++++++++++++++++++++---- docs/src/api.md | 8 ++++ docs/src/distmeshnd.md | 55 +++++++++++++++++++++++++++ docs/src/index.md | 60 ++++++++++++----------------- examples/001-polygon.jl | 31 +++++++++++++++ examples/002-naca_airfoil.jl | 36 ++++++++++++++++++ src/distmesh2d.jl | 4 +- 10 files changed, 267 insertions(+), 49 deletions(-) create mode 100644 docs/src/api.md create mode 100644 docs/src/distmeshnd.md create mode 100644 examples/001-polygon.jl create mode 100644 examples/002-naca_airfoil.jl diff --git a/.gitignore b/.gitignore index 8007493..4fb1ff7 100644 --- a/.gitignore +++ b/.gitignore @@ -3,7 +3,9 @@ *.jl.mem *.jl.*.mem .DS_Store -/Manifest.toml +Manifest.toml /dev/ /docs/build/ /docs/site/ +/docs/src/examples.md +/docs/src/*.jl diff --git a/README.md b/README.md index 85d5afc..cc1aa13 100644 --- a/README.md +++ b/README.md @@ -1,10 +1,48 @@ -# DistMesh +# DistMesh.jl [![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://distmesh.juliageometry.org/dev) [![Codecov](https://codecov.io/gh/juliageometry/DistMesh.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/juliageometry/DistMesh.jl) -The package provides a Julia port of the [DistMesh](http://persson.berkeley.edu/distmesh/) algorithm developed by [Per-Olof Persson](http://persson.berkeley.edu/). +**DistMesh.jl** is a Julia package for generating unstructured triangular and tetrahedral meshes using Signed Distance Functions (SDFs). -There have been several improvements made to improve performance and output quality from the original Matlab version. +It is designed for simplicity and interactive visualization, making it easy to generate high-quality meshes for finite element analysis or geometric modeling. + +## Quick Start (2D) + +The core function `distmesh2d` generates a mesh based on a distance function (negative inside, positive outside). + +```julia +using DistMesh +using GLMakie # Optional, for plotting + +# 1. Define the geometry +# (Here we use the built-in 'dcircle' and 'huniform' size function) +# Region: Box from (-1,-1) to (1,1) +# Initial edge length: 0.2 +msh = distmesh2d(dcircle, huniform, 0.2, ((-1,-1), (1,1))) + +# 2. Visualize +# DistMesh automatically plots correctly with Makie or Plots.jl +plot(msh) + +``` + +### Key Features + +* **Simple API:** Define geometry using standard Julia functions. +* **Robust:** Uses a physical force-equilibrium model to optimize node locations. +* **Visual:** Built-in `show` methods and plotting recipes for instant feedback. + +--- + +## Legacy & 3D Support + +### N-Dimensional Generation + +The package includes the original N-dimensional implementation (supporting 3D and higher) via the internal `DistMeshND` module. This implementation closely mirrors the original MATLAB source. + +### Background + +This package is a Julia port of the [DistMesh](http://persson.berkeley.edu/distmesh/) algorithm developed by [Per-Olof Persson](http://persson.berkeley.edu/). Several improvements have been made to performance and type stability compared to the original version. [Technical Report](https://sjkellyorg.files.wordpress.com/2020/11/distmesh_sjkelly.pdf) diff --git a/docs/Project.toml b/docs/Project.toml index eed229d..e120dba 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -1,3 +1,4 @@ [deps] +DistMesh = "f7ee28b6-bfbf-11e9-3e31-8961b86f052c" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" diff --git a/docs/make.jl b/docs/make.jl index 3d25b72..746c4bb 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -1,15 +1,74 @@ -using Documenter, DistMesh +using Documenter +using DistMesh +using Literate + +# --- 1. Automation Script: Build the "Examples" Page --- + +# Define paths +examples_dir = joinpath(@__DIR__, "..", "examples") +docs_src = joinpath(@__DIR__, "src") +master_file = joinpath(docs_src, "examples.md") + +# Initialize the master "Examples" page +open(master_file, "w") do io + write(io, "# Examples\n\nA collection of 2D meshing examples.\n\n") +end + +# Find all .jl files and sort them +jl_files = sort(filter(f -> endswith(f, ".jl"), readdir(examples_dir))) + +for file in jl_files + source_path = joinpath(examples_dir, file) + dest_path = joinpath(docs_src, file) # Copy directly to docs/src/ + + # 1. Copy the .jl file to docs/src/ + # This satisfies Documenter, which looks for the source file next to examples.md + cp(source_path, dest_path, force=true) + + # 2. Run Literate + # We output the .md file to the same folder (docs/src/) to keep paths simple. + # We use name=... to ensure unique scope. + Literate.markdown(dest_path, docs_src; + documenter=true, + credit=false, + name=replace(file, ".jl"=>"") + ) + + # 3. Read the generated markdown + md_file = replace(file, ".jl" => ".md") + generated_md_path = joinpath(docs_src, md_file) + content = read(generated_md_path, String) + + # 4. Append it to the master examples.md file + open(master_file, "a") do io + write(io, "\n\n" * content) + end + + # 5. Cleanup the individual .md file (we don't need it anymore, it's in examples.md) + # Note: We KEEP the .jl file in docs/src/ so the "Source" links work. + rm(generated_md_path) +end + +# --- 2. Build Documentation --- makedocs( - modules=[DistMesh], - format=Documenter.HTML(), - pages=[ + sitename = "DistMesh.jl", + modules = [DistMesh], + authors = "Steve Kelly and Per-Olof Persson ", + pages = [ "Home" => "index.md", + "Examples" => "examples.md", + "API Reference" => "api.md", + "Legacy (N-D & Theory)" => "distmeshnd.md", ], - sitename="DistMesh.jl", - authors="Steve Kelly ", + warnonly = [:missing_docs], + format = Documenter.HTML( + prettyurls = get(ENV, "CI", nothing) == "true" + ) ) deploydocs( - repo="github.com/JuliaGeometry/DistMesh.jl", + repo = "github.com/JuliaGeometry/DistMesh.jl.git", + push_preview = true ) + diff --git a/docs/src/api.md b/docs/src/api.md new file mode 100644 index 0000000..5fa359f --- /dev/null +++ b/docs/src/api.md @@ -0,0 +1,8 @@ +## API Reference + +```@docs +distmesh2d +distmesh +DMesh +as_arrays +``` diff --git a/docs/src/distmeshnd.md b/docs/src/distmeshnd.md new file mode 100644 index 0000000..8c51d17 --- /dev/null +++ b/docs/src/distmeshnd.md @@ -0,0 +1,55 @@ +# Legacy & Theory + +The `DistMeshND` module preserves the original N-dimensional algorithm structure, closely mirroring the original MATLAB implementation. + +## Background & Theory + +DistMesh.jl implements **simplex refinement** on signed distance functions. The algorithm was first presented in 2004 by Per-Olof Persson and assumes the geometry is defined by any function that returns a signed distance (negative inside, positive outside). + +### What is Simplex Refinement? + +In layman's terms, a **simplex** is a triangle in 2D or a tetrahedron in 3D. When simulating physics, you often want a mesh of simplices that offers: + +* **Accurate approximation** of boundaries and features. +* **Adaptive mesh sizes** to improve accuracy where needed. +* **High Element Quality** (Near-regular simplices). + +DistMesh is designed to address these needs using a physical analogy: it treats the mesh nodes as particles connected by springs (edges). The nodes "relax" into a configuration that balances the internal spring forces with the geometric constraints of the Signed Distance Function. + +### Algorithm Overview + +1. **Initial Distribution:** Nodes are distributed stochastically or on a grid inside the bounding box. +2. **Delaunay Triangulation:** Nodes are connected to form a mesh topology. +3. **Force Equilibrium:** Edges act as springs. Nodes move to minimize energy. +4. **Boundary Projection:** Nodes that move outside the geometry are projected back onto the zero-level set (the boundary) using the SDF gradient. +5. **Refinement:** Triangles that are too large (according to your size function) are split; edges that are too short are collapsed. + +### Comparison to Other Methods + +DistMesh generally has a very low memory footprint and avoids complex boundary patching logic found in advancing front methods. Since the global state of simplex qualities is optimized in each iteration, this often leads to very high-quality meshes for smooth geometries. + +Unlike surface-based meshing tools (which require Piecewise Linear Complexes/STLs as input), DistMesh works directly on mathematical functions or volumetric data, making it ideal for topology optimization, level-set methods, and image-based meshing. + +### Differences from MATLAB + +Given the same parameters, the Julia implementation of DistMesh will generally perform significantly faster than the original MATLAB implementation. + +* **Memory:** Reduced allocation overhead. +* **Triangulation:** While MATLAB uses QHull, Julia's ecosystem (and this package's legacy N-D modules) often leverages `VoronoiDelaunay.jl` or `MiniQhull` for efficiency. + +### Working with Signed Distance Functions + +You can define SDFs manually (as shown in the examples), or generate them from data. Useful libraries for turning gridded/level-set data into SDFs include: + +* [Interpolations.jl](https://github.com/JuliaMath/Interpolations.jl) +* AdaptiveDistanceFields.jl + +--- + +## Legacy API + +These functions belong to the internal `DistMeshND` module. + +```@autodocs +Modules = [DistMesh.DistMeshND] +``` diff --git a/docs/src/index.md b/docs/src/index.md index c80d268..8f67ec1 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -1,53 +1,41 @@ # DistMesh.jl +**DistMesh.jl** is a Julia generator for unstructured triangular and tetrahedral meshes. It uses [Signed Distance Functions](https://en.wikipedia.org/wiki/Signed_distance_function) (SDFs) to define geometries, allowing for clean mesh generation of complex shapes using simple mathematical functions. -DistMesh.jl implements simplex refinement on signed distance functions, or anything that -has a sign, distance, and called like a function. The algorithm was first presented -in 2004 by Per-Olof Persson, and was initially a port of the corresponding Matlab Code. - -## What is Simplex Refinement? - -In layman's terms, a simplex is either a triangle in the 2D case, or a tetrahedra in the 3D case. - -When simulating, you other want a few things from a mesh of simplices: - - Accurate approximation of boundaries and features - - Adaptive mesh sizes to improve accuracy - - Near-Regular Simplicies - -DistMesh is designed to address the above. - -## Algorithm Overview - -The basic processes is as follows: +## Installation +```julia +using Pkg +Pkg.add("DistMesh") +``` -## Comparison to other refinements +## Quick Start (2D) -DistMesh generally has a very low memory footprint, and can refine without additional -memory allocation. Similarly, since the global state of simplex qualities is accounted for -in each refinement iteration, this leads to very high quality meshes. +The primary entry point for 2D meshing is `distmesh2d`. -Aside from the above, since DistMesh works on signed distance functions it can handle -complex and varied input data that are not in the form of surface meshes (Piecewise Linear Complicies). +First, we generate the mesh. -## Difference from the MatLab implementation +```@example quickstart +using DistMesh #, CairoMakie -Given the same parameters, the Julia implementation of DistMesh will generally perform -4-60 times faster than the MatLab implementation. Delaunay Triangulation in MatLab uses -QHull, whereas DistMesh.jl uses TetGen. +msh = distmesh2d(dcircle, huniform, 0.15, ((-1,-1), (1,1))) +``` -## How do I get a Signed Distance Function? +Now we can visualize the result using `plot`. -Here are some libraries that turn gridded and level set data into an approximate signed -distance function: +```@example quickstart +# plot(msh) +``` -- Interpolations.jl -- AdaptiveDistanceFields.jl +Finally, if you need the raw coordinate and topology arrays for a solver, you can access the fields directly. -```@index +```@example quickstart +# Access the points and connectivity as matrices +p,t = as_arrays(msh) +p ``` -```@autodocs -Modules = [DistMesh] +```@example quickstart +t ``` diff --git a/examples/001-polygon.jl b/examples/001-polygon.jl new file mode 100644 index 0000000..d016e2c --- /dev/null +++ b/examples/001-polygon.jl @@ -0,0 +1,31 @@ +# ## Polygon Mesh +# +# This example demonstrates how to mesh a custom polygon using `dpoly`. + +using DistMesh +#using Plots + +# ### 1. Define Vertices +pv = [(-0.4, -0.5), (0.4, -0.2), (0.4, -0.7), (1.5, -0.4), + (0.9, 0.1), (1.6, 0.8), (0.5, 0.5), (0.2, 1.0), + (0.1, 0.4), (-0.7, 0.7), (-0.4, -0.5)] + +# ### 2. Create Distance Function +# `dpoly` computes the distance from points `p` to the polygon defined by `pv`. +# We wrap it in a new function because `distmesh2d` expects a function of `p`. +fd(p) = dpoly(p, pv) + +# ### 3. Generate Mesh +# We use a uniform mesh size of h0 = 0.1. +# The bounding box must enclose the polygon. + +bbox = ((-1,-1), (2,1)) +h0 = 0.15 + +msh = distmesh2d(fd, huniform, h0, bbox, pv) + +# ### 4. Visualize +# Plot the resulting mesh. + +#plot(msh) + diff --git a/examples/002-naca_airfoil.jl b/examples/002-naca_airfoil.jl new file mode 100644 index 0000000..db18b39 --- /dev/null +++ b/examples/002-naca_airfoil.jl @@ -0,0 +1,36 @@ +# ## NACA Airfoil Mesh + + +using DistMesh +using StaticArrays + +const SF2 = SVector{2,Float64} + +function hnaca(p; hlead=0.01, htrail=0.04, hmax=2.0) + minimum((hlead + 0.3 * dcircle(p, c=(0, 0), r=0), + htrail + 0.3 * dcircle(p, c=(1, 0), r=0), + hmax)) +end + +function fixnaca(; htrail=0.04) + a0, a14... = naca_coeffs + fixx = 1 .- htrail * cumsum(1.3 .^ (0:4)) + fixy = a0 * sqrt.(fixx) .+ fixx .^ (1:4)' * a14 + fix = vcat(SF2[(0,0),(1,0)], [ SF2[(x,y),(x,-y)] for (x,y) in zip(fixx,fixy) ]...) +end + +function dm_naca(; hlead=0.01, htrail=0.04, hmax=2.0, circx=2.0, circr=4.0) + dfcn(p) = ddiff(dcircle(p, c=(circx, 0), r=circr), dnaca(p)) + hfcn(p) = hnaca(p; hlead=hlead, htrail=htrail, hmax=hmax) + + fix = SF2[(1,0),(0,1),(-1,0),(0,-1)] .* circr .+ SF2[(circx,0)] + fix = vcat(fix, fixnaca(htrail=htrail)) + bbox = [(circx - circr, -circr), (circx + circr, circr)] + h0 = minimum((hlead, htrail, hmax)) + dfcn, hfcn, h0, bbox, fix +end + +msh = distmesh2d(dm_naca()...) + +#plot(msh) + diff --git a/src/distmesh2d.jl b/src/distmesh2d.jl index c8c7e16..273326b 100644 --- a/src/distmesh2d.jl +++ b/src/distmesh2d.jl @@ -95,12 +95,12 @@ end # Examples ### Example: (Uniform Mesh on Unit Circle) -```jldoctest +```julia dfcn(p) = sqrt(sum(p.^2)) - 1 p,t = distmesh2d(dfcn, huniform, 0.2, ((-1,-1), (1,1)), plotting=true); ``` #### Example: (Rectangle with circular hole, refined at circle boundary) -```jldoctest +```julia dfcn2(p) = ddiff(drectangle(p, -1, 1, -1, 1), dcircle(p, r=0.5)) hfcn2(p) = 0.05 + 0.3 * dcircle(p, r=0.5); bbox = ((-1,-1), (1,1)) From 07770b5050bc17e76c280897c82b0ba02a8da8df Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Wed, 31 Dec 2025 15:51:54 -0800 Subject: [PATCH 05/42] Plots extension, updated examples and docs. --- Project.toml | 10 +++++++++ docs/src/index.md | 4 ++-- examples/001-polygon.jl | 5 ++--- examples/002-naca_airfoil.jl | 4 ++-- ext/DistMeshGLMakieExt.jl | 40 ++++++++++++++++++++++++++++++++++++ ext/DistMeshPlotsExt.jl | 18 ++++++++++++++++ 6 files changed, 74 insertions(+), 7 deletions(-) create mode 100644 ext/DistMeshGLMakieExt.jl create mode 100644 ext/DistMeshPlotsExt.jl diff --git a/Project.toml b/Project.toml index 594836c..9f9ecaa 100644 --- a/Project.toml +++ b/Project.toml @@ -10,6 +10,14 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" TetGen = "c5d3f3f7-f850-59f6-8a2e-ffc6dc1317ea" +[weakdeps] +GLMakie = "e9467ef8-e4e7-5192-8a1a-b1aee30e663a" +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" + +[extensions] +DistMeshGLMakieExt = "GLMakie" +DistMeshPlotsExt = "Plots" + [compat] Delaunator = "0.1" GeometryBasics = "0.4" @@ -17,6 +25,8 @@ LinearAlgebra = "1" StaticArrays = "1.9" TetGen = "1" julia = "1.10" +Plots = "1" +GLMakie = "0.11, 0.13" [extras] GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" diff --git a/docs/src/index.md b/docs/src/index.md index 8f67ec1..352e6d8 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -17,7 +17,7 @@ The primary entry point for 2D meshing is `distmesh2d`. First, we generate the mesh. ```@example quickstart -using DistMesh #, CairoMakie +using DistMesh, Plots msh = distmesh2d(dcircle, huniform, 0.15, ((-1,-1), (1,1))) ``` @@ -25,7 +25,7 @@ msh = distmesh2d(dcircle, huniform, 0.15, ((-1,-1), (1,1))) Now we can visualize the result using `plot`. ```@example quickstart -# plot(msh) +plot(msh) ``` Finally, if you need the raw coordinate and topology arrays for a solver, you can access the fields directly. diff --git a/examples/001-polygon.jl b/examples/001-polygon.jl index d016e2c..cb9d4f2 100644 --- a/examples/001-polygon.jl +++ b/examples/001-polygon.jl @@ -3,7 +3,7 @@ # This example demonstrates how to mesh a custom polygon using `dpoly`. using DistMesh -#using Plots +using Plots # ### 1. Define Vertices pv = [(-0.4, -0.5), (0.4, -0.2), (0.4, -0.7), (1.5, -0.4), @@ -27,5 +27,4 @@ msh = distmesh2d(fd, huniform, h0, bbox, pv) # ### 4. Visualize # Plot the resulting mesh. -#plot(msh) - +plot(msh) diff --git a/examples/002-naca_airfoil.jl b/examples/002-naca_airfoil.jl index db18b39..652fc42 100644 --- a/examples/002-naca_airfoil.jl +++ b/examples/002-naca_airfoil.jl @@ -2,6 +2,7 @@ using DistMesh +using Plots using StaticArrays const SF2 = SVector{2,Float64} @@ -32,5 +33,4 @@ end msh = distmesh2d(dm_naca()...) -#plot(msh) - +plot(msh) diff --git a/ext/DistMeshGLMakieExt.jl b/ext/DistMeshGLMakieExt.jl new file mode 100644 index 0000000..e93fe25 --- /dev/null +++ b/ext/DistMeshGLMakieExt.jl @@ -0,0 +1,40 @@ +module DistMeshGLMakieExt + +using DistMesh +using GLMakie + +const meshgreen = Plots.RGBX(0.8, 1, 0.8) + +function GLMakie.plot(m::DMesh{2,T,N,I}; + labels=(), reltol=1e-3, abstol=Inf, maxref=6, + colors=(meshgreen, :black, :blue, :darkgray, :darkblue) + # colors: elements, int edges, bnd edges, ho-nodes, vertices +) where {T,N,I} + + # elem_lines, int_lines, bnd_lines, elem_mid = + # viz_mesh(m, reltol=reltol, abstol=abstol, maxref=maxref) + + # h = Plots.plot(aspect_ratio=:equal, leg=false) + # Plots.plot!(elem_lines[:, 1], elem_lines[:, 2], seriestype=:shape, + # linecolor=nothing, fillcolor=colors[1]) + # Plots.plot!(int_lines[:, 1], int_lines[:, 2], linewidth=1, color=colors[2]) + # Plots.plot!(bnd_lines[:, 1], bnd_lines[:, 2], linewidth=2, color=colors[3]) + + # if isa(labels, Symbol) + # labels = (labels,) + # end + + # if :nodes in labels + # scatter!(m.x[:,1], m.x[:,2], marker=(:circle, 2, 1.0, colors[4])) + # end + + # if :elements in labels + # for (iel,mid) in enumerate(eachrow(elem_mid)) + # annotate!(mid[1], mid[2], text("$iel", 8, :center)) + # end + # end + + # return h +end + +end diff --git a/ext/DistMeshPlotsExt.jl b/ext/DistMeshPlotsExt.jl new file mode 100644 index 0000000..e470df5 --- /dev/null +++ b/ext/DistMeshPlotsExt.jl @@ -0,0 +1,18 @@ +module DistMeshPlotsExt + +using DistMesh +using Plots + +const meshgreen = Plots.RGBX(0.8, 1, 0.8) + +function Plots.plot(m::DMesh{2,T,N,I}; args...) where {T,N,I} + pxy(d) = [ tix==0 ? NaN : m.p[tt[tix]][d] for tix in (1,2,3,1,0), tt in m.t ] + args = (args..., + seriestype=:shape, + aspect_ratio=:equal, + leg=false, + fillcolor=Plots.RGB(0.8, 0.9, 1.0)) + h = Plots.plot(vec(pxy(1)), vec(pxy(2)); args...) +end + +end From 6645d26b4f99e2b0bd850beb0365891983e337a7 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Wed, 31 Dec 2025 17:21:42 -0800 Subject: [PATCH 06/42] examples moved to the examples/ directory --- src/examples.jl | 49 ------------------------------------------------- 1 file changed, 49 deletions(-) delete mode 100644 src/examples.jl diff --git a/src/examples.jl b/src/examples.jl deleted file mode 100644 index f0132cc..0000000 --- a/src/examples.jl +++ /dev/null @@ -1,49 +0,0 @@ -include("distmesh.jl") - -function ex5polygon(; h0=0.1) - pv = SF2[(-0.4, -0.5), (0.4, -0.2), (0.4, -0.7), (1.5, -0.4), - (0.9, 0.1), (1.6, 0.8), (0.5, 0.5), (0.2, 1.0), - (0.1, 0.4), (-0.7, 0.7), (-0.4, -0.5)] - dfcn(p) = dpoly(p, pv) - dfcn, huniform, h0, [(-1, -1), (2, 1)], pv -end - -function hnaca(p; hlead=0.01, htrail=0.04, hmax=2.0) - minimum((hlead + 0.3 * dcircle(p, c=(0, 0), r=0), - htrail + 0.3 * dcircle(p, c=(1, 0), r=0), - hmax)) -end - -function fixnaca(; htrail=0.04) - a0, a14... = naca_coeffs - fixx = 1 .- htrail * cumsum(1.3 .^ (0:4)) - fixy = a0 * sqrt.(fixx) .+ fixx .^ (1:4)' * a14 - fix = vcat(SF2[(0,0),(1,0)], [ SF2[(x,y),(x,-y)] for (x,y) in zip(fixx,fixy) ]...) -end - -function ex6naca(; hlead=0.01, htrail=0.04, hmax=2.0, circx=2.0, circr=4.0) - dfcn(p) = ddiff(dcircle(p, c=(circx, 0), r=circr), dnaca(p)) - hfcn(p) = hnaca(p; hlead=hlead, htrail=htrail, hmax=hmax) - - fix = SF2[(1,0),(0,1),(-1,0),(0,-1)] .* circr .+ SF2[(circx,0)] - fix = vcat(fix, fixnaca(htrail=htrail)) - bbox = [(circx - circr, -circr), (circx + circr, circr)] - h0 = minimum((hlead, htrail, hmax)) - dfcn, hfcn, h0, bbox, fix -end - -for ex in (ex5polygon, ex6naca) - p, t = distmesh2d(ex()...) - display(simpplot(p, t)) -end - -using Random -#for s = 1:1000 -# @show s -# Random.seed!(s) -# p,t = distmesh2d(ex6naca()...); -# @show minimum(simpqual(p,t)) -#end - -#Random.seed!(9) -#distmesh2d(ex6naca()...) From 22ad02261f3621b584a6cfa0ec182b2a3a988b92 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 6 Jan 2026 12:54:59 -0800 Subject: [PATCH 07/42] Rename obscure vector short-hands to more common Point2, Index2, Index3 --- docs/Project.toml | 1 + examples/002-naca_airfoil.jl | 6 +++--- src/distmesh2d.jl | 26 +++++++++++++------------- 3 files changed, 17 insertions(+), 16 deletions(-) diff --git a/docs/Project.toml b/docs/Project.toml index e120dba..8819c63 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -2,3 +2,4 @@ DistMesh = "f7ee28b6-bfbf-11e9-3e31-8961b86f052c" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" +Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" diff --git a/examples/002-naca_airfoil.jl b/examples/002-naca_airfoil.jl index 652fc42..9f3aeca 100644 --- a/examples/002-naca_airfoil.jl +++ b/examples/002-naca_airfoil.jl @@ -5,7 +5,7 @@ using DistMesh using Plots using StaticArrays -const SF2 = SVector{2,Float64} +const Point2 = SVector{2, Float64} function hnaca(p; hlead=0.01, htrail=0.04, hmax=2.0) minimum((hlead + 0.3 * dcircle(p, c=(0, 0), r=0), @@ -17,14 +17,14 @@ function fixnaca(; htrail=0.04) a0, a14... = naca_coeffs fixx = 1 .- htrail * cumsum(1.3 .^ (0:4)) fixy = a0 * sqrt.(fixx) .+ fixx .^ (1:4)' * a14 - fix = vcat(SF2[(0,0),(1,0)], [ SF2[(x,y),(x,-y)] for (x,y) in zip(fixx,fixy) ]...) + fix = vcat(Point2[(0,0),(1,0)], [ Point2[(x,y),(x,-y)] for (x,y) in zip(fixx,fixy) ]...) end function dm_naca(; hlead=0.01, htrail=0.04, hmax=2.0, circx=2.0, circr=4.0) dfcn(p) = ddiff(dcircle(p, c=(circx, 0), r=circr), dnaca(p)) hfcn(p) = hnaca(p; hlead=hlead, htrail=htrail, hmax=hmax) - fix = SF2[(1,0),(0,1),(-1,0),(0,-1)] .* circr .+ SF2[(circx,0)] + fix = Point2[(1,0),(0,1),(-1,0),(0,-1)] .* circr .+ Point2[(circx,0)] fix = vcat(fix, fixnaca(htrail=htrail)) bbox = [(circx - circr, -circr), (circx + circr, circr)] h0 = minimum((hlead, htrail, hmax)) diff --git a/src/distmesh2d.jl b/src/distmesh2d.jl index 273326b..e4bac8a 100644 --- a/src/distmesh2d.jl +++ b/src/distmesh2d.jl @@ -1,9 +1,9 @@ ######################################################################## -# StaticVector shorthands +# Internal Type Aliases -const SF2 = SVector{2,Float64} -const SI2 = SVector{2,Int32} -const SI3 = SVector{3,Int32} +const Point2 = SVector{2, Float64} +const Index2 = SVector{2, Int32} # For Edges +const Index3 = SVector{3, Int32} # For Triangles ######################################################################## # Utility functions @@ -18,7 +18,7 @@ function init_nodes(bbox, h0) # Create initial distribution in bounding box (equilateral triangles) xx = bbox[1][1]:h0:bbox[2][1] yy = bbox[1][2]:h0*√3/2:bbox[2][2] - p = [ SF2(x + iseven(iy) * h0/2, y) for x in xx for (iy,y) in enumerate(yy) ] + p = [ Point2(x + iseven(iy) * h0/2, y) for x in xx for (iy,y) in enumerate(yy) ] end function nodes_rejection(p, pfix, dfcn, hfcn, geps) @@ -34,7 +34,7 @@ function retriangulate(p, dfcn, geps) t = delaunay(p) t = filter(tt -> dfcn(sum(p[tt]) / 3) < -geps, t) # Find all bars as the unique triangle edges - bars = [ tt[ix] for tt in t for ix in SI2[(1,2),(2,3),(3,1)] ] + bars = [ tt[ix] for tt in t for ix in Index2[(1,2),(2,3),(3,1)] ] bars = unique(sort.(bars)) t, bars end @@ -58,7 +58,7 @@ function total_node_forces(L, L0, barvec, bars, np, nfix) # Find all bar forces and accumulate at all nodes F = max.(L0 .- L, 0.0) Fvec = F ./ L .* barvec - Ftot = [ SF2(0.0,0.0) for ip = 1:np ] + Ftot = [ Point2(0.0,0.0) for ip = 1:np ] for ibar in eachindex(bars) Ftot[bars[ibar][1]] += Fvec[ibar] Ftot[bars[ibar][2]] -= Fvec[ibar] @@ -70,7 +70,7 @@ end function project_nodes!(p, dfcn, deps) d = dfcn.(p) ix = findall(d .> 0) - numgrad(f,x,fx) = (SF2(f(x + SF2(deps,0)), f(x + SF2(0,deps))) .- fx) / deps + numgrad(f,x,fx) = (Point2(f(x + Point2(deps,0)), f(x + Point2(0,deps))) .- fx) / deps dgrad = [ numgrad(dfcn, p[i], d[i]) for i in ix ] @. p[ix] -= d[ix] * dgrad / norm(dgrad)^2 d @@ -108,7 +108,7 @@ pfix = [(-1,-1), (-1,1), (1,-1), (1,1)] p,t = distmesh2d(dfcn2, hfcn2, 0.05, bbox, pfix, plotting=true); ``` """ -function distmesh2d(dfcn, hfcn, h0, bbox, pfix=SF2[]; +function distmesh2d(dfcn, hfcn, h0, bbox, pfix=Point2[]; plotting=false, # Optional live plotting densityctrlfreq = 30, # Frequency of density controls maxiter = 10_000, # When to terminate if no convergence @@ -122,10 +122,10 @@ function distmesh2d(dfcn, hfcn, h0, bbox, pfix=SF2[]; ) # Initializations - pfix = unique(SF2.(pfix)) + pfix = unique(Point2.(pfix)) nfix = length(pfix) - pold = [SF2(Inf,Inf)] - t, bars = SI3[], SI2[] + pold = [Point2(Inf,Inf)] + t, bars = Index3[], Index2[] converged = false # Initial nodes @@ -149,7 +149,7 @@ function distmesh2d(dfcn, hfcn, h0, bbox, pfix=SF2[]; # Density control - remove points that are too close to each other if iter % densityctrlfreq == 0 p = density_control(p, L, L0, bars, nfix) - pold = [SF2(Inf,Inf)] + pold = [Point2(Inf,Inf)] continue end From 86a9e07b821b1e89237a0b210dca09bdbc799686 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 6 Jan 2026 13:16:36 -0800 Subject: [PATCH 08/42] Fixed live-plotting with internal do-nothing function and warning. --- ext/DistMeshPlotsExt.jl | 2 ++ src/distmesh2d.jl | 8 +++++--- src/dmesh.jl | 12 ++++++++++++ 3 files changed, 19 insertions(+), 3 deletions(-) diff --git a/ext/DistMeshPlotsExt.jl b/ext/DistMeshPlotsExt.jl index e470df5..ac5a32b 100644 --- a/ext/DistMeshPlotsExt.jl +++ b/ext/DistMeshPlotsExt.jl @@ -15,4 +15,6 @@ function Plots.plot(m::DMesh{2,T,N,I}; args...) where {T,N,I} h = Plots.plot(vec(pxy(1)), vec(pxy(2)); args...) end +DistMesh.live_plot(m::DMesh; args...) = display(plot(m)) + end diff --git a/src/distmesh2d.jl b/src/distmesh2d.jl index e4bac8a..4aedd2c 100644 --- a/src/distmesh2d.jl +++ b/src/distmesh2d.jl @@ -138,7 +138,7 @@ function distmesh2d(dfcn, hfcn, h0, bbox, pfix=Point2[]; if maximum(norm.(p .- pold)) > ttol pold = copy(p) t, bars = retriangulate(p, dfcn, geps) - plotting && display(simpplot(p, t)) + plotting && live_plot(DMesh(p,t)) end # All bars and lengths @@ -166,6 +166,8 @@ function distmesh2d(dfcn, hfcn, h0, bbox, pfix=Point2[]; end converged || @warn "No convergence in maxiter=$maxiter iterations" - plotting && display(simpplot(p, t)) - return DMesh(p, t) + + msh = DMesh(p, t) + plotting && live_plot(msh) + return msh end diff --git a/src/dmesh.jl b/src/dmesh.jl index a3ab356..2eb8485 100644 --- a/src/dmesh.jl +++ b/src/dmesh.jl @@ -53,3 +53,15 @@ function Base.show(io::IO, ::MIME"text/plain", m::DMesh{D,T,N,I}) where {D,T,N,I print(io, "$(length(m.p)) nodes, ") print(io, "$(length(m.t)) $(element_name(Val(N))) elements") end + + +# Global flag to track if we have warned the user yet +const _has_warned_plot = Ref(false) + +function live_plot(args...) + if !_has_warned_plot[] + @warn "Live plotting was requested, but no plotting backend is loaded. Try `using Plots`." + _has_warned_plot[] = true + end + return nothing +end From 7f11857eabaf274a809451c69e1fdb9462a0919a Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 6 Jan 2026 16:16:58 -0800 Subject: [PATCH 09/42] CairoMakie and GLMakie support. Live plotting support. --- Project.toml | 11 ++-- docs/Project.toml | 2 +- docs/make.jl | 9 ++- examples/001-polygon.jl | 2 +- examples/002-naca_airfoil.jl | 3 +- ext/DistMeshCairoMakieExt.jl | 30 ++++++++++ ext/DistMeshGLMakieExt.jl | 110 +++++++++++++++++++++++++++-------- ext/DistMeshPlotsExt.jl | 4 +- 8 files changed, 135 insertions(+), 36 deletions(-) create mode 100644 ext/DistMeshCairoMakieExt.jl diff --git a/Project.toml b/Project.toml index 9f9ecaa..9818f8f 100644 --- a/Project.toml +++ b/Project.toml @@ -11,22 +11,25 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" TetGen = "c5d3f3f7-f850-59f6-8a2e-ffc6dc1317ea" [weakdeps] +CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" GLMakie = "e9467ef8-e4e7-5192-8a1a-b1aee30e663a" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" [extensions] +DistMeshCairoMakieExt = "CairoMakie" DistMeshGLMakieExt = "GLMakie" DistMeshPlotsExt = "Plots" [compat] +CairoMakie = "0.15" Delaunator = "0.1" -GeometryBasics = "0.4" +GLMakie = "0.11, 0.13" +GeometryBasics = "0.5" LinearAlgebra = "1" +Plots = "1" StaticArrays = "1.9" -TetGen = "1" +TetGen = "2" julia = "1.10" -Plots = "1" -GLMakie = "0.11, 0.13" [extras] GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" diff --git a/docs/Project.toml b/docs/Project.toml index 8819c63..46a38f3 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -2,4 +2,4 @@ DistMesh = "f7ee28b6-bfbf-11e9-3e31-8961b86f052c" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" -Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" +CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" diff --git a/docs/make.jl b/docs/make.jl index 746c4bb..58cd63c 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -9,6 +9,12 @@ examples_dir = joinpath(@__DIR__, "..", "examples") docs_src = joinpath(@__DIR__, "src") master_file = joinpath(docs_src, "examples.md") +# Define a preprocessing function +function replace_gl_with_cairo(content) + # Replace the specific line "using GLMakie" with "using CairoMakie" + return replace(content, "using GLMakie" => "using CairoMakie") +end + # Initialize the master "Examples" page open(master_file, "w") do io write(io, "# Examples\n\nA collection of 2D meshing examples.\n\n") @@ -31,7 +37,8 @@ for file in jl_files Literate.markdown(dest_path, docs_src; documenter=true, credit=false, - name=replace(file, ".jl"=>"") + name=replace(file, ".jl"=>""), + preprocess = replace_gl_with_cairo ) # 3. Read the generated markdown diff --git a/examples/001-polygon.jl b/examples/001-polygon.jl index cb9d4f2..95587f3 100644 --- a/examples/001-polygon.jl +++ b/examples/001-polygon.jl @@ -3,7 +3,7 @@ # This example demonstrates how to mesh a custom polygon using `dpoly`. using DistMesh -using Plots +using GLMakie # ### 1. Define Vertices pv = [(-0.4, -0.5), (0.4, -0.2), (0.4, -0.7), (1.5, -0.4), diff --git a/examples/002-naca_airfoil.jl b/examples/002-naca_airfoil.jl index 9f3aeca..689ca2e 100644 --- a/examples/002-naca_airfoil.jl +++ b/examples/002-naca_airfoil.jl @@ -1,8 +1,7 @@ # ## NACA Airfoil Mesh - using DistMesh -using Plots +using GLMakie using StaticArrays const Point2 = SVector{2, Float64} diff --git a/ext/DistMeshCairoMakieExt.jl b/ext/DistMeshCairoMakieExt.jl new file mode 100644 index 0000000..c9d98a3 --- /dev/null +++ b/ext/DistMeshCairoMakieExt.jl @@ -0,0 +1,30 @@ +module DistMeshCairoMakieExt + +using DistMesh +using CairoMakie + +const MESH_COLOR = "#DDEEFF" + +function CairoMakie.plot(m::DMesh{2}; args...) + f = Figure(size=(800, 800)) + ax = Axis(f[1,1], aspect=DataAspect()) + + p, t = as_arrays(m) + poly!(ax, p', t', color=MESH_COLOR, strokewidth=1) + return f +end + +const _has_warned_live = Ref(false) + +function DistMesh.live_plot(m::DMesh) + if !_has_warned_live[] + @warn "Live plotting disabled for CairoMakie. \n" * + "CairoMakie is for static plots (PDF/PNG). \n" * + "Switch to `using GLMakie` for animations." + _has_warned_live[] = true + end + return nothing +end + +end + diff --git a/ext/DistMeshGLMakieExt.jl b/ext/DistMeshGLMakieExt.jl index e93fe25..a9c6a57 100644 --- a/ext/DistMeshGLMakieExt.jl +++ b/ext/DistMeshGLMakieExt.jl @@ -2,39 +2,99 @@ module DistMeshGLMakieExt using DistMesh using GLMakie +using GeometryBasics -const meshgreen = Plots.RGBX(0.8, 1, 0.8) +const MESH_COLOR = "#DDEEFF" -function GLMakie.plot(m::DMesh{2,T,N,I}; - labels=(), reltol=1e-3, abstol=Inf, maxref=6, - colors=(meshgreen, :black, :blue, :darkgray, :darkblue) - # colors: elements, int edges, bnd edges, ho-nodes, vertices -) where {T,N,I} +# --------------------------------------------------------- +# 1. Helpers +# --------------------------------------------------------- - # elem_lines, int_lines, bnd_lines, elem_mid = - # viz_mesh(m, reltol=reltol, abstol=abstol, maxref=maxref) +""" + get_canvas(; aspect=DataAspect()) - # h = Plots.plot(aspect_ratio=:equal, leg=false) - # Plots.plot!(elem_lines[:, 1], elem_lines[:, 2], seriestype=:shape, - # linecolor=nothing, fillcolor=colors[1]) - # Plots.plot!(int_lines[:, 1], int_lines[:, 2], linewidth=1, color=colors[2]) - # Plots.plot!(bnd_lines[:, 1], bnd_lines[:, 2], linewidth=2, color=colors[3]) +Gets the current figure/axis if they exist, or creates new ones. +""" +function get_canvas(; aspect=DataAspect()) + fig = current_figure() + if isnothing(fig) + fig = Figure(size=(800, 800)) + ax = Axis(fig[1,1], aspect=aspect) + return fig, ax + else + ax = current_axis() + if isnothing(ax) + ax = Axis(fig[1,1], aspect=aspect) + end + return fig, ax + end +end + +""" + to_gl_mesh(m::DMesh) - # if isa(labels, Symbol) - # labels = (labels,) - # end +Converts a DistMesh DMesh object into a GeometryBasics.normal_mesh +suitable for high-performance GLMakie plotting and updates. +""" +function to_gl_mesh(m::DMesh{2}) + p, t = as_arrays(m) + + # 1. strict conversion to Float32 Points (GL standard) + pts = Point2f[Point2f(col) for col in eachcol(p)] + + # 2. strict conversion to standard Triangle Faces + faces = GLTriangleFace[GLTriangleFace(col...) for col in eachcol(t)] + + # 3. Create Mesh and compute Normals + # (Required because Makie initializes with normals by default; + # we must match that type for updates to work) + return GeometryBasics.normal_mesh(GeometryBasics.Mesh(pts, faces)) +end + +# --------------------------------------------------------- +# 2. Standard Plot (Static) +# --------------------------------------------------------- + +function GLMakie.plot(m::DMesh{2}; args...) + f, ax = get_canvas() + + # Standard plot: Clear the axis and draw fresh + empty!(ax) + + gl_mesh = to_gl_mesh(m) + poly!(ax, gl_mesh, color=MESH_COLOR, strokewidth=1) + + return f +end - # if :nodes in labels - # scatter!(m.x[:,1], m.x[:,2], marker=(:circle, 2, 1.0, colors[4])) - # end +# --------------------------------------------------------- +# 3. Live Plot (Dynamic / Animation) +# --------------------------------------------------------- - # if :elements in labels - # for (iel,mid) in enumerate(eachrow(elem_mid)) - # annotate!(mid[1], mid[2], text("$iel", 8, :center)) - # end - # end +function DistMesh.live_plot(m::DMesh{2}) + f, ax = get_canvas() + + # Always convert the incoming data to the strict GL mesh format + gl_mesh = to_gl_mesh(m) - # return h + if isempty(ax.scene.plots) + # --- INITIALIZATION --- + # If axis is empty, draw for the first time + poly!(ax, gl_mesh, color=MESH_COLOR, strokewidth=1) + autolimits!(ax) + else + # --- UPDATE --- + # If plot exists, update the Observable in place (Zero Allocation on GPU) + plt = ax.scene.plots[1] + + # We update the first argument of the plot object + plt[1][] = gl_mesh + end + + # Yield to the event loop so the window redraws + sleep(0.01) + + return f end end diff --git a/ext/DistMeshPlotsExt.jl b/ext/DistMeshPlotsExt.jl index ac5a32b..4028396 100644 --- a/ext/DistMeshPlotsExt.jl +++ b/ext/DistMeshPlotsExt.jl @@ -3,7 +3,7 @@ module DistMeshPlotsExt using DistMesh using Plots -const meshgreen = Plots.RGBX(0.8, 1, 0.8) +const meshblue = Plots.RGBX(0.8, 0.9, 1.0) function Plots.plot(m::DMesh{2,T,N,I}; args...) where {T,N,I} pxy(d) = [ tix==0 ? NaN : m.p[tt[tix]][d] for tix in (1,2,3,1,0), tt in m.t ] @@ -11,7 +11,7 @@ function Plots.plot(m::DMesh{2,T,N,I}; args...) where {T,N,I} seriestype=:shape, aspect_ratio=:equal, leg=false, - fillcolor=Plots.RGB(0.8, 0.9, 1.0)) + fillcolor=meshblue) h = Plots.plot(vec(pxy(1)), vec(pxy(2)); args...) end From 040ce743ed7ae85f729761610dcf94ac8a61e0dc Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 6 Jan 2026 16:31:40 -0800 Subject: [PATCH 10/42] Rename Point2 -> Point2d to be consistent with GeometryBasics --- examples/002-naca_airfoil.jl | 6 +++--- src/distmesh2d.jl | 16 ++++++++-------- 2 files changed, 11 insertions(+), 11 deletions(-) diff --git a/examples/002-naca_airfoil.jl b/examples/002-naca_airfoil.jl index 689ca2e..de1b49e 100644 --- a/examples/002-naca_airfoil.jl +++ b/examples/002-naca_airfoil.jl @@ -4,7 +4,7 @@ using DistMesh using GLMakie using StaticArrays -const Point2 = SVector{2, Float64} +const Point2d = SVector{2, Float64} function hnaca(p; hlead=0.01, htrail=0.04, hmax=2.0) minimum((hlead + 0.3 * dcircle(p, c=(0, 0), r=0), @@ -16,14 +16,14 @@ function fixnaca(; htrail=0.04) a0, a14... = naca_coeffs fixx = 1 .- htrail * cumsum(1.3 .^ (0:4)) fixy = a0 * sqrt.(fixx) .+ fixx .^ (1:4)' * a14 - fix = vcat(Point2[(0,0),(1,0)], [ Point2[(x,y),(x,-y)] for (x,y) in zip(fixx,fixy) ]...) + fix = vcat(Point2d[(0,0),(1,0)], [ Point2d[(x,y),(x,-y)] for (x,y) in zip(fixx,fixy) ]...) end function dm_naca(; hlead=0.01, htrail=0.04, hmax=2.0, circx=2.0, circr=4.0) dfcn(p) = ddiff(dcircle(p, c=(circx, 0), r=circr), dnaca(p)) hfcn(p) = hnaca(p; hlead=hlead, htrail=htrail, hmax=hmax) - fix = Point2[(1,0),(0,1),(-1,0),(0,-1)] .* circr .+ Point2[(circx,0)] + fix = Point2d[(1,0),(0,1),(-1,0),(0,-1)] .* circr .+ Point2d[(circx,0)] fix = vcat(fix, fixnaca(htrail=htrail)) bbox = [(circx - circr, -circr), (circx + circr, circr)] h0 = minimum((hlead, htrail, hmax)) diff --git a/src/distmesh2d.jl b/src/distmesh2d.jl index 4aedd2c..f8864d5 100644 --- a/src/distmesh2d.jl +++ b/src/distmesh2d.jl @@ -1,7 +1,7 @@ ######################################################################## # Internal Type Aliases -const Point2 = SVector{2, Float64} +const Point2d = SVector{2, Float64} const Index2 = SVector{2, Int32} # For Edges const Index3 = SVector{3, Int32} # For Triangles @@ -18,7 +18,7 @@ function init_nodes(bbox, h0) # Create initial distribution in bounding box (equilateral triangles) xx = bbox[1][1]:h0:bbox[2][1] yy = bbox[1][2]:h0*√3/2:bbox[2][2] - p = [ Point2(x + iseven(iy) * h0/2, y) for x in xx for (iy,y) in enumerate(yy) ] + p = [ Point2d(x + iseven(iy) * h0/2, y) for x in xx for (iy,y) in enumerate(yy) ] end function nodes_rejection(p, pfix, dfcn, hfcn, geps) @@ -58,7 +58,7 @@ function total_node_forces(L, L0, barvec, bars, np, nfix) # Find all bar forces and accumulate at all nodes F = max.(L0 .- L, 0.0) Fvec = F ./ L .* barvec - Ftot = [ Point2(0.0,0.0) for ip = 1:np ] + Ftot = [ Point2d(0.0,0.0) for ip = 1:np ] for ibar in eachindex(bars) Ftot[bars[ibar][1]] += Fvec[ibar] Ftot[bars[ibar][2]] -= Fvec[ibar] @@ -70,7 +70,7 @@ end function project_nodes!(p, dfcn, deps) d = dfcn.(p) ix = findall(d .> 0) - numgrad(f,x,fx) = (Point2(f(x + Point2(deps,0)), f(x + Point2(0,deps))) .- fx) / deps + numgrad(f,x,fx) = (Point2d(f(x + Point2d(deps,0)), f(x + Point2d(0,deps))) .- fx) / deps dgrad = [ numgrad(dfcn, p[i], d[i]) for i in ix ] @. p[ix] -= d[ix] * dgrad / norm(dgrad)^2 d @@ -108,7 +108,7 @@ pfix = [(-1,-1), (-1,1), (1,-1), (1,1)] p,t = distmesh2d(dfcn2, hfcn2, 0.05, bbox, pfix, plotting=true); ``` """ -function distmesh2d(dfcn, hfcn, h0, bbox, pfix=Point2[]; +function distmesh2d(dfcn, hfcn, h0, bbox, pfix=Point2d[]; plotting=false, # Optional live plotting densityctrlfreq = 30, # Frequency of density controls maxiter = 10_000, # When to terminate if no convergence @@ -122,9 +122,9 @@ function distmesh2d(dfcn, hfcn, h0, bbox, pfix=Point2[]; ) # Initializations - pfix = unique(Point2.(pfix)) + pfix = unique(Point2d.(pfix)) nfix = length(pfix) - pold = [Point2(Inf,Inf)] + pold = [Point2d(Inf,Inf)] t, bars = Index3[], Index2[] converged = false @@ -149,7 +149,7 @@ function distmesh2d(dfcn, hfcn, h0, bbox, pfix=Point2[]; # Density control - remove points that are too close to each other if iter % densityctrlfreq == 0 p = density_control(p, L, L0, bars, nfix) - pold = [Point2(Inf,Inf)] + pold = [Point2d(Inf,Inf)] continue end From dde65ad7b9ea19d20919ad39ac580c7faf01d72a Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 6 Jan 2026 16:42:52 -0800 Subject: [PATCH 11/42] Minor plotting tweaks. --- ext/DistMeshGLMakieExt.jl | 8 ++------ ext/DistMeshPlotsExt.jl | 4 ++-- 2 files changed, 4 insertions(+), 8 deletions(-) diff --git a/ext/DistMeshGLMakieExt.jl b/ext/DistMeshGLMakieExt.jl index a9c6a57..cc6fc6f 100644 --- a/ext/DistMeshGLMakieExt.jl +++ b/ext/DistMeshGLMakieExt.jl @@ -79,21 +79,17 @@ function DistMesh.live_plot(m::DMesh{2}) if isempty(ax.scene.plots) # --- INITIALIZATION --- - # If axis is empty, draw for the first time poly!(ax, gl_mesh, color=MESH_COLOR, strokewidth=1) autolimits!(ax) + display(f) else # --- UPDATE --- - # If plot exists, update the Observable in place (Zero Allocation on GPU) plt = ax.scene.plots[1] - - # We update the first argument of the plot object plt[1][] = gl_mesh + # autolimits!(ax) # technically needed, but makes animation non-smooth end - # Yield to the event loop so the window redraws sleep(0.01) - return f end diff --git a/ext/DistMeshPlotsExt.jl b/ext/DistMeshPlotsExt.jl index 4028396..7f7793e 100644 --- a/ext/DistMeshPlotsExt.jl +++ b/ext/DistMeshPlotsExt.jl @@ -3,7 +3,7 @@ module DistMeshPlotsExt using DistMesh using Plots -const meshblue = Plots.RGBX(0.8, 0.9, 1.0) +const MESH_COLOR = Plots.RGBX(0.8, 0.9, 1.0) function Plots.plot(m::DMesh{2,T,N,I}; args...) where {T,N,I} pxy(d) = [ tix==0 ? NaN : m.p[tt[tix]][d] for tix in (1,2,3,1,0), tt in m.t ] @@ -11,7 +11,7 @@ function Plots.plot(m::DMesh{2,T,N,I}; args...) where {T,N,I} seriestype=:shape, aspect_ratio=:equal, leg=false, - fillcolor=meshblue) + fillcolor=MESH_COLOR) h = Plots.plot(vec(pxy(1)), vec(pxy(2)); args...) end From 9344bb3a9bff4f8723dcb8184582820d3df5e943 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 6 Jan 2026 17:12:40 -0800 Subject: [PATCH 12/42] Major Gemini pass on the doc strings --- docs/src/api.md | 58 +++++++++++++++++++++++++++- src/distfuncs.jl | 97 +++++++++++++++++++++++++++++++++++++++++++++-- src/distmesh2d.jl | 65 ++++++++++++++++++++++--------- src/meshutils.jl | 22 +++-------- 4 files changed, 205 insertions(+), 37 deletions(-) diff --git a/docs/src/api.md b/docs/src/api.md index 5fa359f..91d43f9 100644 --- a/docs/src/api.md +++ b/docs/src/api.md @@ -1,8 +1,64 @@ -## API Reference +# API Reference + +## Core Meshing & Types + +The primary interface for generating meshes and handling the resulting data structures. ```@docs distmesh2d distmesh DMesh as_arrays + +``` + +## Distance Functions: Basic Shapes + +Pre-defined signed distance functions for common primitives in 2D and 3D. + +```@docs +dcircle +drectangle +dhypersphere +dsphere +dblock + +``` + +## Distance Functions: Polygons & Lines + +Utilities for working with polygonal boundaries and line segments. + +```@docs +dpoly +dline +DistMesh.inpolygon + +``` + +## Distance Functions: Boolean Operations (CSG) + +Constructive Solid Geometry operations to combine multiple distance functions. + +```@docs +ddiff +dunion +dintersect + +``` + +## Distance Functions: Special Functions + +Helper functions for element sizing and specific test cases (like airfoils). + +```@docs +dnaca + +``` + +## Mesh utilities: Sizing functions + +```@docs +huniform + ``` diff --git a/src/distfuncs.jl b/src/distfuncs.jl index 32221e0..b7801fe 100644 --- a/src/distfuncs.jl +++ b/src/distfuncs.jl @@ -1,15 +1,59 @@ -#using StaticArrays -#using LinearAlgebra +################################################################################ +### 1. Basic Shapes (Circles, Rectangles) +################################################################################ +""" + dhypersphere(p, c, r) + +Signed distance function for a hypersphere of radius `r` centered at `c`. +Works for any dimension, provided `p` and `c` have matching lengths. +""" dhypersphere(p, c, r) = norm(p - c) - r + +""" + dcircle(p; c=(0, 0), r=1.0) + +Signed distance function for a 2D circle. +Wrapper around `dhypersphere` that enforces 2D inputs. +""" dcircle(p; c=(0, 0), r=1) = dhypersphere(SVector{2}(p), SVector{2}(c), r) + +""" + dsphere(p; c=(0, 0, 0), r=1.0) + +Signed distance function for a 3D sphere. +Wrapper around `dhypersphere` that enforces 3D inputs. +""" dsphere(p; c=(0, 0, 0), r=1) = dhypersphere(SVector{3}(p), SVector{3}(c), r) +""" + drectangle(p, x1, x2, y1, y2) + +Signed distance function for a 2D axis-aligned rectangle. +Returns negative values inside the region `[x1, x2] × [y1, y2]`. +""" drectangle(p, x1, x2, y1, y2) = -minimum((-y1 + p[2], y2 - p[2], -x1 + p[1], x2 - p[1])) + +""" + dblock(p, x1, x2, y1, y2, z1, z2) + +Signed distance function for a 3D axis-aligned block (cuboid). +Returns negative values inside the region `[x1, x2] × [y1, y2] × [z1, z2]`. +""" dblock(p, x1, x2, y1, y2, z1, z2) = -minimum((-z1 + p[3], z2 - p[3], -y1 + p[2], y2 - p[2], -x1 + p[1], x2 - p[1])) +################################################################################ +### 2. Polygons & Lines +################################################################################ + +""" + dline(p, p1, p2) + +Distance from point `p` to the finite line segment defined by endpoints `p1` and `p2`. +Returns the Euclidean distance (always non-negative). +""" function dline(p, p1, p2) p,p1,p2 = SVector{2}.((p,p1,p2)) @@ -26,6 +70,12 @@ function dline(p, p1, p2) end end +""" + inpolygon(p, pv) + +Point-in-polygon test using the Ray Casting algorithm. +Returns `true` if `p` is inside the polygon defined by vertices `pv`. +""" function inpolygon(p, pv) cn = 0 # Crossing number counter for i = 1:length(pv)-1 # Loop over all edges of the polygon @@ -40,20 +90,61 @@ function inpolygon(p, pv) return cn % 2 == 1 end +# Internal helper (not typically exported, so no docstring needed unless you want one) dsegment(p, pv) = (dline(p, pv[i+1], pv[i]) for i in 1:length(pv)-1) + +""" + dpoly(p, pv) + +Signed distance function for a polygon defined by vertices `pv`. +**Note:** `pv` must be a closed loop (i.e., `pv[end] == pv[1]`). +Returns negative values inside, positive outside. +""" function dpoly(p, pv) d = minimum(dsegment(p, pv)) inpolygon(p, pv) ? -d : d end +################################################################################ +### 3. Boolean Operations (CSG) +################################################################################ + +""" + ddiff(d1, d2) + +Difference of two regions (Region 1 minus Region 2). +`d1` and `d2` are signed distances. +""" ddiff(d1, d2) = max(d1, -d2) + +""" + dunion(d1, d2) + +Union of two regions. +`d1` and `d2` are signed distances. +""" dunion(d1, d2) = min(d1, d2) + +""" + dintersect(d1, d2) + +Intersection of two regions. +`d1` and `d2` are signed distances. +""" dintersect(d1, d2) = max(d1, d2) -huniform(p) = 1 +################################################################################ +### 4. Special Functions +################################################################################ const naca_coeffs = 0.12 / 0.2 * SVector(0.2969, -0.1260, -0.3516, 0.2843, -0.1036) +""" + dnaca(p) + +Implicit level-set function for a NACA 0012 airfoil. +Zero contour defines the airfoil boundary. +""" function dnaca(p) a0, a14... = naca_coeffs (abs(p[2]) - sum(a14 .* p[1] .^ SVector(1, 2, 3, 4))) .^ 2 - a0^2 * p[1] diff --git a/src/distmesh2d.jl b/src/distmesh2d.jl index f8864d5..dea8704 100644 --- a/src/distmesh2d.jl +++ b/src/distmesh2d.jl @@ -80,32 +80,63 @@ end # Main function """ - distmesh2d(dfcn, hfcn, h0, bbox, pfix=[]; plotting=false) + distmesh2d(dfcn, hfcn, h0, bbox, pfix=[]; kwargs...) -> (p, t) -2-D Mesh Generator using Distance Functions. +Generate a 2D unstructured triangular mesh using a signed distance function. - `p`: Node positions (Vector of (x,y) coordinates) - 't': Triangle indices (Vector of (i1,i2,i3) indices) - 'dfcn': Distance function d(p) - 'hfcn': Scaled edge length function h(p) - 'h0': Initial edge length - 'bbox': Bounding box ((xmin,ymin), (xmax,ymax)) - 'pfix': Fixed node positions (Vector of (x,y) coordinates) +This function implements the DistMesh algorithm (Persson/Strang), which treats the mesh generation +as a physical equilibrium problem. A system of truss bars (edges) is relaxed until the force +equilibrium is reached, constrained by the signed distance function `dfcn` to stay within the domain. + +# Arguments +- `dfcn::Function`: Signed distance function `d(p)`. Returns negative values inside the region, + positive outside. Input `p` is an `(N,2)` array. +- `hfcn::Function`: Element size function `h(p)`. Returns target edge length at point `p`. +- `h0::Real`: Initial nominal edge length (scaling factor for `hfcn`). +- `bbox`: Bounding box tuple `((xmin, ymin), (xmax, ymax))` defining the initial grid generation area. +- `pfix::Vector`: (Optional) List of fixed node positions that must be part of the mesh (e.g., corners). + +# Keywords +- `plotting::Bool = false`: Enable live visualization of the relaxation process (requires GLMakie). +- `maxiter::Int = 1000`: Maximum number of relaxation iterations. +- `ttol::Real`: Tolerance for retriangulation (defaults to `0.1 * h0`). +- `dptol::Real`: Termination tolerance for node movement (defaults to `0.001 * h0`). + +# Returns +- `p::Vector{Point2d}`: The node positions. +- `t::Vector{Index3}`: The triangle connectivity indices. # Examples -### Example: (Uniform Mesh on Unit Circle) +**Uniform Mesh on a Unit Circle** ```julia -dfcn(p) = sqrt(sum(p.^2)) - 1 -p,t = distmesh2d(dfcn, huniform, 0.2, ((-1,-1), (1,1)), plotting=true); +using DistMesh +# Distance function for a circle of radius 1 +fd = p -> sqrt.(sum(p.^2, dims=2)) .- 1.0 +# Uniform mesh size +fh = p -> ones(size(p,1)) + +p, t = distmesh2d(fd, fh, 0.2, ((-1,-1), (1,1)), plotting=false) ``` -#### Example: (Rectangle with circular hole, refined at circle boundary) + +**Rectangle with Circular Hole (Refined at Boundary)** ```julia -dfcn2(p) = ddiff(drectangle(p, -1, 1, -1, 1), dcircle(p, r=0.5)) -hfcn2(p) = 0.05 + 0.3 * dcircle(p, r=0.5); +using DistMesh + +# Define distance function: Rectangle minus Circle +function fd_hole(p) + d_rect = drectangle(p, -1, 1, -1, 1) + d_circ = dcircle(p, 0, 0, 0.5) + return ddiff(d_rect, d_circ) +end + +# Size function: Refine near the hole +fh_hole(p) = 0.05 .+ 0.3 * dcircle(p, 0, 0, 0.5) + bbox = ((-1,-1), (1,1)) -pfix = [(-1,-1), (-1,1), (1,-1), (1,1)] -p,t = distmesh2d(dfcn2, hfcn2, 0.05, bbox, pfix, plotting=true); +pfix = [(-1,-1), (-1,1), (1,-1), (1,1)] # Fix corners + +p, t = distmesh2d(fd_hole, fh_hole, 0.05, bbox, pfix) ``` """ function distmesh2d(dfcn, hfcn, h0, bbox, pfix=Point2d[]; diff --git a/src/meshutils.jl b/src/meshutils.jl index 4003145..703aea5 100644 --- a/src/meshutils.jl +++ b/src/meshutils.jl @@ -1,19 +1,9 @@ -#import Plots - -#= -function simpplot(p, t, tdata=nothing; args...) - pxy(d) = [ tix==0 ? NaN : p[tt[tix]][d] for tix in (1,2,3,1,0), tt in t ] - args = (args..., seriestype=:shape, aspect_ratio=:equal, leg=false) - if isnothing(tdata) - args = (args..., fillcolor=Plots.RGB(0.8, 0.9, 1.0)) - else - # todo - #data = vcat(tdata[t], fill(NaN, 1, size(t, 2)))[:] - #args = (args..., fillcolor=:viridis, fill_z=data, colorbar=:right) - end - h = Plots.plot(vec(pxy(1)), vec(pxy(2)); args...) -end -=# +""" + huniform(p) + +Returns `1.0`. Default sizing function for uniform meshes. +""" +huniform(p) = 1 function simplex_area(el) if length(el) == 3 # Triangle From c35ba9e4d70a1f7bb8f1fbd4e66ee9fb3f17b7e1 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Wed, 7 Jan 2026 10:29:22 -0800 Subject: [PATCH 13/42] Various improvements of meshutils. Fix triangule orientation of Delaunator's delaunay. --- src/distmesh2d.jl | 4 -- src/meshutils.jl | 94 ++++++++++++++++++++++++++++++++++++++++++----- 2 files changed, 84 insertions(+), 14 deletions(-) diff --git a/src/distmesh2d.jl b/src/distmesh2d.jl index dea8704..8b0862f 100644 --- a/src/distmesh2d.jl +++ b/src/distmesh2d.jl @@ -8,10 +8,6 @@ const Index3 = SVector{3, Int32} # For Triangles ######################################################################## # Utility functions -extract_elements(tri::Delaunator.Triangulation{I}) where {I} = - reinterpret(SVector{3, I}, triangles(tri)) -delaunay(p) = extract_elements(triangulate(p)) - barvectors(p, bars) = [ p[bar[1]] - p[bar[2]] for bar in bars ] function init_nodes(bbox, h0) diff --git a/src/meshutils.jl b/src/meshutils.jl index 703aea5..eb9fea9 100644 --- a/src/meshutils.jl +++ b/src/meshutils.jl @@ -1,3 +1,31 @@ +################################################################################ +### Delaunator wrappers +################################################################################ + +extract_elements(tri::Delaunator.Triangulation{I}) where {I} = + reinterpret(SVector{3, I}, triangles(tri)) + +function fix_winding!(tri::Delaunator.Triangulation{I}) where {I} + tris = triangles(tri) + mat = reinterpret(reshape, I, tris) + + # Swap rows 2 and 3 (in-place) + @inbounds for c in axes(mat, 2) + mat[2, c], mat[3, c] = mat[3, c], mat[2, c] + end + return nothing +end + +function delaunay(p) + t = triangulate(p) + fix_winding!(t) + return extract_elements(t) +end + +################################################################################ +### Size function utilities +################################################################################ + """ huniform(p) @@ -5,6 +33,10 @@ Returns `1.0`. Default sizing function for uniform meshes. """ huniform(p) = 1 +################################################################################ +### Element properties +################################################################################ + function simplex_area(el) if length(el) == 3 # Triangle p12 = el[2] - el[1] @@ -15,7 +47,6 @@ function simplex_area(el) end end - function simplex_qual(el) if length(el) == 3 # Triangle norm(vec) = sqrt(sum(vec.^2)) @@ -28,22 +59,65 @@ function simplex_qual(el) end end -elemwise_feval(p,t,f) = [ f(p[tt]) for tt in t ] -simpqual(p, t, fqual=simplex_qual) = elemwise_feval(p, t, fqual) -simpvol(p,t) = elemwise_feval(p, t, simplex_area) +elemwise_feval(m::DMesh, f) = [ f(m.p[tt]) for tt in m.t ] + +simpqual(m::DMesh, fqual=simplex_qual) = elemwise_feval(m, fqual) +simpvol(m::DMesh) = elemwise_feval(m, simplex_area) + +################################################################################ +### General mesh utilities +################################################################################ snap(x::T, scaling=1) where {T <: Real} = x snap(x::T, scaling=1, tol=sqrt(eps(T))) where {T <: AbstractFloat} = scaling*tol*round(x/scaling/tol) + zero(T) # Adding zero to uniquify -0.0 and 0.0 -function fixmesh(p, t; output_ix=false) + +""" + fixmesh(msh::DMesh) -> (msh::DMesh, ix::Vector{Int}) + +Remove duplicate nodes from the mesh `msh` and re-index the connectivity. + +This function identifies nodes that are coincident (or within a very small tolerance relative to the mesh size) +and merges them. This is useful after mesh generation or modification operations that might create +overlapping vertices. + +# Arguments +- `msh::DMesh`: The input mesh containing nodes `p` and connectivity `t`. + +# Returns +A `NamedTuple` `(msh, ix)` where: +- `msh`: The cleaned `DMesh` with duplicate nodes removed. +- `ix`: An index vector mapping the **new** nodes to the **old** nodes (i.e., `new_p = old_p[ix]`). + +# Example +```julia +clean_msh, = fixmesh(dirty_msh) # Ignoring the index output (ix) + +``` + +""" +function fixmesh(msh::DMesh) + p, t = msh + + # 1. Snap nodes to a grid to identify duplicates (relative tolerance) scaling = maximum(norm.(p)) - pp = [ snap.(p1,scaling) for p1 in p ] + pp = [snap.(p1, scaling) for p1 in p] + + # 2. Find unique nodes ppp = unique(pp) + + # 3. Create mappings + # ix: Mapping from New -> Old (which old node did this new node come from?) ix = Int.(indexin(ppp, pp)) + # jx: Mapping from Old -> New (where did this old node go?) jx = Int.(indexin(pp, ppp)) - p = p[ix] - t = [jx[tt] for tt in t] - return output_ix ? (p,t,ix) : (p,t) -end + + # 4. Rebuild Mesh + new_p = p[ix] + # Broadcast the index lookup to preserve SVector/Tuple structure of triangles + new_t = [map(idx -> jx[idx], tri) for tri in t] + return (msh=DMesh(new_p, new_t), ix=ix) + +end From ed82a6ae6e3fdbcbd4688aceea41b49511a838da Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Wed, 7 Jan 2026 17:42:50 -0800 Subject: [PATCH 14/42] Rewriting of README and first section of docs. Default fig size 600x600 instead of 800x800. --- README.md | 58 ++++++++++++++--------- circle_mesh.png | Bin 0 -> 63922 bytes docs/src/index.md | 87 ++++++++++++++++++++++++++++------- ext/DistMeshCairoMakieExt.jl | 2 +- ext/DistMeshGLMakieExt.jl | 2 +- 5 files changed, 109 insertions(+), 40 deletions(-) create mode 100644 circle_mesh.png diff --git a/README.md b/README.md index cc1aa13..2249500 100644 --- a/README.md +++ b/README.md @@ -3,46 +3,62 @@ [![Dev](https://img.shields.io/badge/docs-dev-blue.svg)](https://distmesh.juliageometry.org/dev) [![Codecov](https://codecov.io/gh/juliageometry/DistMesh.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/juliageometry/DistMesh.jl) -**DistMesh.jl** is a Julia package for generating unstructured triangular and tetrahedral meshes using Signed Distance Functions (SDFs). +**DistMesh.jl** is a Julia generator for unstructured triangular and tetrahedral meshes. It uses [Signed Distance Functions](https://en.wikipedia.org/wiki/Signed_distance_function) (SDFs) to define geometries, enabling the generation of high-quality, isotropic meshes for complex shapes defined by simple mathematical functions. -It is designed for simplicity and interactive visualization, making it easy to generate high-quality meshes for finite element analysis or geometric modeling. +Primary use cases include Finite Element Analysis (FEA), computational fluid dynamics, and geometric modeling. + +--- ## Quick Start (2D) -The core function `distmesh2d` generates a mesh based on a distance function (negative inside, positive outside). +The core function `distmesh2d` generates a mesh based on a distance function, a relative size function, an initial edge length, and a bounding box. + +The code below generates a mesh of the unit circle: ```julia using DistMesh -using GLMakie # Optional, for plotting -# 1. Define the geometry -# (Here we use the built-in 'dcircle' and 'huniform' size function) -# Region: Box from (-1,-1) to (1,1) -# Initial edge length: 0.2 +# Generate mesh: Distance function, size function, resolution, bounding box msh = distmesh2d(dcircle, huniform, 0.2, ((-1,-1), (1,1))) +``` -# 2. Visualize -# DistMesh automatically plots correctly with Makie or Plots.jl -plot(msh) +```text +DMesh: 2D, 88 nodes, 143 triangle elements +``` + +Optionally, the mesh can be visualized using various plotting packages: + +```julia +using GLMakie # or Plots, or CairoMakie +plot(msh) ``` -### Key Features +![Triangular mesh of the unit circle](circle_mesh.png) + +For more details and extensive examples, please see the [DistMesh documentation](https://distmesh.juliageometry.org). + +--- + +## 3D Support & Legacy Code + +The original versions of this package featured an N-dimensional implementation (`distmeshnd`) which supports 3D generation. This functionality is still available via the internal `DistMeshND` module. -* **Simple API:** Define geometry using standard Julia functions. -* **Robust:** Uses a physical force-equilibrium model to optimize node locations. -* **Visual:** Built-in `show` methods and plotting recipes for instant feedback. +Please note that the modern 2D functionality has been rewritten independently to prioritize performance and type stability. Consequently, the API style for 3D generation differs from the 2D interface. Future work will focus on harmonizing these implementations. --- -## Legacy & 3D Support +## Background -### N-Dimensional Generation +This package is a Julia port of the [DistMesh](http://persson.berkeley.edu/distmesh/) algorithm developed by [Per-Olof Persson](http://persson.berkeley.edu/). Significant improvements have been made to performance and type stability compared to the original MATLAB implementation. The algorithm is described in the following publications: -The package includes the original N-dimensional implementation (supporting 3D and higher) via the internal `DistMeshND` module. This implementation closely mirrors the original MATLAB source. +* P.-O. Persson, G. Strang, *[A Simple Mesh Generator in MATLAB](https://persson.berkeley.edu/distmesh/persson04mesh.pdf)*. SIAM Review, Volume 46 (2), pp. 329-345, June 2004. +* P.-O. Persson, *[Mesh Generation for Implicit Geometries](https://persson.berkeley.edu/thesis/persson-thesis-color.pdf)*. Ph.D. thesis, Department of Mathematics, MIT, Dec 2004. -### Background +Details on the implementation of the legacy N-dimensional generator can be found in this [technical report](https://sjkellyorg.files.wordpress.com/2020/11/distmesh_sjkelly.pdf). + +--- -This package is a Julia port of the [DistMesh](http://persson.berkeley.edu/distmesh/) algorithm developed by [Per-Olof Persson](http://persson.berkeley.edu/). Several improvements have been made to performance and type stability compared to the original version. +## Related Packages -[Technical Report](https://sjkellyorg.files.wordpress.com/2020/11/distmesh_sjkelly.pdf) +Several other implementations of the DistMesh algorithm exist in the Julia ecosystem, including [DistMesh-Julia](https://github.com/precise-simulation/distmesh-julia) and [DistMesh2D.jl](https://juliapackages.com/p/distmesh2d). 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unstructured triangular and tetrahedral meshes. It uses [Signed Distance Functions](https://en.wikipedia.org/wiki/Signed_distance_function) (SDFs) to define geometries, allowing for clean mesh generation of complex shapes using simple mathematical functions. +**DistMesh.jl** is a Julia generator for unstructured triangular and tetrahedral meshes. It uses [Signed Distance Functions](https://en.wikipedia.org/wiki/Signed_distance_function) (SDFs) to define geometries, enabling the generation of high-quality, isotropic meshes for complex shapes defined by simple mathematical functions. ## Installation ```julia using Pkg Pkg.add("DistMesh") - ``` -## Quick Start (2D) +## Introduction + +### A Simple Example Mesh + +The primary entry point for 2D meshing is `distmesh2d`. It generates a mesh based on: -The primary entry point for 2D meshing is `distmesh2d`. +* A distance function (negative inside, positive outside). In this example, + we represent the unit circle by $d(x,y) = \sqrt{x^2+y^2} - 1$ + +* A relative size function. For a uniform mesh, we can simply set $h(x,y) = 1$ -First, we generate the mesh. +* An initial, or minimum, element edge length. Since our size function is + uniform, this will also be roughly the size of the generated elements. + +* A bounding box for the domain. For the unit circle, we use the coordinates + (-1,-1) and (1,1). + +The code below demonstrates how to implement this using DistMesh in Julia. -```@example quickstart -using DistMesh, Plots +```@example introduction +using DistMesh +using GLMakie # or Plots, or CairoMakie (optional) -msh = distmesh2d(dcircle, huniform, 0.15, ((-1,-1), (1,1))) +fd(p) = sqrt(sum(p.^2)) - 1 # or dcircle(p) - unit circle geometry +fh(p) = 1.0 # or huniform(p) - uniform size function +hmin = 0.2 # initial edge lengths +bbox = ((-1,-1), (1,1)) # bounding box for unit circle + +msh = distmesh2d(fd, fh, hmin, bbox) ``` -Now we can visualize the result using `plot`. +The resulting mesh can be visualized with the `plot` command. -```@example quickstart +```@example introduction plot(msh) ``` -Finally, if you need the raw coordinate and topology arrays for a solver, you can access the fields directly. +### Accessing the generated mesh + +The `msh` object contains the node coordinates `p` and the triangle indices `t`, stored as vectors of static vectors (for efficiency) + +```@example introduction +# Access the nodes and connectivity as vectors of static vectors +p,t = msh +p[1:3] # First 3 nodes +``` + +```@example introduction +t[1:3] # First 3 triangles +``` + +If you prefer a matrix-based representation (similar to the original MATLAB DistMesh, except transposed), the utility function `as_arrays` creates a zero-allocation view for this. Note that if you modify these matrices, the original versions in `msh` will also be changed! -```@example quickstart -# Access the points and connectivity as matrices -p,t = as_arrays(msh) -p +```@example introduction +# Access the nodes and connectivity as matrices +p_mat,t_mat = as_arrays(msh) +p_mat[:,1:3] # First 3 nodes ``` -```@example quickstart -t +```@example introduction +t_mat[:,1:3] # First 3 triangles ``` + +If you want separate re-allocated versions of these matrices, use `collect`. + +### Fixed points + +An optional argument to `distmesh2d` is `pfix` - a vector of frozen points that are part of the generated mesh. These are typically required for boundaries with sharp corners, since the implicit geometry representation as a signed distance function does not explicitly provide them. Here is a simple example of a mesh of a rectangle, where we include the four corner points in `pfix1`. +```@example introduction +fd(p) = drectangle(p, -1, 1, -1, 1) +pfix = ((-1,-1), (1,-1), (-1,1), (1,1)) +# fh, hmin, bbox same as before +msh = distmesh2d(fd, fh, hmin, bbox, pfix) +``` + +```@example introduction +plot(msh) +``` + +## Distance Functions + +## Size Functions + diff --git a/ext/DistMeshCairoMakieExt.jl b/ext/DistMeshCairoMakieExt.jl index c9d98a3..0b46a58 100644 --- a/ext/DistMeshCairoMakieExt.jl +++ b/ext/DistMeshCairoMakieExt.jl @@ -6,7 +6,7 @@ using CairoMakie const MESH_COLOR = "#DDEEFF" function CairoMakie.plot(m::DMesh{2}; args...) - f = Figure(size=(800, 800)) + f = Figure(size=(600, 600)) ax = Axis(f[1,1], aspect=DataAspect()) p, t = as_arrays(m) diff --git a/ext/DistMeshGLMakieExt.jl b/ext/DistMeshGLMakieExt.jl index cc6fc6f..4f50efb 100644 --- a/ext/DistMeshGLMakieExt.jl +++ b/ext/DistMeshGLMakieExt.jl @@ -18,7 +18,7 @@ Gets the current figure/axis if they exist, or creates new ones. function get_canvas(; aspect=DataAspect()) fig = current_figure() if isnothing(fig) - fig = Figure(size=(800, 800)) + fig = Figure(size=(600, 600)) ax = Axis(fig[1,1], aspect=aspect) return fig, ax else From 418025e5aea592413327f4a330b5bedec9dcfa2a Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Thu, 8 Jan 2026 09:49:30 -0800 Subject: [PATCH 15/42] Minor docs update. Revert Makie figure size to default. --- docs/src/api.md | 9 ++++++++- docs/src/index.md | 12 ++++++++++-- ext/DistMeshCairoMakieExt.jl | 2 +- ext/DistMeshGLMakieExt.jl | 2 +- 4 files changed, 20 insertions(+), 5 deletions(-) diff --git a/docs/src/api.md b/docs/src/api.md index 91d43f9..330b418 100644 --- a/docs/src/api.md +++ b/docs/src/api.md @@ -56,9 +56,16 @@ dnaca ``` -## Mesh utilities: Sizing functions +## Mesh utilities: Size functions ```@docs huniform ``` + +## Mesh utilities: General + +```@docs +DistMesh.fixmesh + +``` diff --git a/docs/src/index.md b/docs/src/index.md index 8a7fc2a..1f643d8 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -57,7 +57,11 @@ p[1:3] # First 3 nodes ``` ```@example introduction -t[1:3] # First 3 triangles +t[1:3] # First 3 triangles (indices) +``` + +```@example introduction +p[t[1]] # x,y-coordinates of the first triangle ``` If you prefer a matrix-based representation (similar to the original MATLAB DistMesh, except transposed), the utility function `as_arrays` creates a zero-allocation view for this. Note that if you modify these matrices, the original versions in `msh` will also be changed! @@ -69,7 +73,11 @@ p_mat[:,1:3] # First 3 nodes ``` ```@example introduction -t_mat[:,1:3] # First 3 triangles +t_mat[:,1:3] # First 3 triangles (indices) +``` + +```@example introduction +p_mat[:,t_mat[:,1]] # x,y-coordinates of the first triangle ``` If you want separate re-allocated versions of these matrices, use `collect`. diff --git a/ext/DistMeshCairoMakieExt.jl b/ext/DistMeshCairoMakieExt.jl index 0b46a58..7d4c41c 100644 --- a/ext/DistMeshCairoMakieExt.jl +++ b/ext/DistMeshCairoMakieExt.jl @@ -6,7 +6,7 @@ using CairoMakie const MESH_COLOR = "#DDEEFF" function CairoMakie.plot(m::DMesh{2}; args...) - f = Figure(size=(600, 600)) + f = Figure() # size=(600, 600) ax = Axis(f[1,1], aspect=DataAspect()) p, t = as_arrays(m) diff --git a/ext/DistMeshGLMakieExt.jl b/ext/DistMeshGLMakieExt.jl index 4f50efb..e1a2447 100644 --- a/ext/DistMeshGLMakieExt.jl +++ b/ext/DistMeshGLMakieExt.jl @@ -18,7 +18,7 @@ Gets the current figure/axis if they exist, or creates new ones. function get_canvas(; aspect=DataAspect()) fig = current_figure() if isnothing(fig) - fig = Figure(size=(600, 600)) + fig = Figure() # size=(600, 600) ax = Axis(fig[1,1], aspect=aspect) return fig, ax else From 7d72ef1c82afa95e78df5d343518c6a3075decb5 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Thu, 8 Jan 2026 10:51:45 -0800 Subject: [PATCH 16/42] Fix inconsistent figure sizes in docs. --- docs/make.jl | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index 58cd63c..b95b995 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -11,8 +11,8 @@ master_file = joinpath(docs_src, "examples.md") # Define a preprocessing function function replace_gl_with_cairo(content) - # Replace the specific line "using GLMakie" with "using CairoMakie" - return replace(content, "using GLMakie" => "using CairoMakie") + setup_cmd = "using CairoMakie; CairoMakie.activate!(type=\"png\", px_per_unit=1); # update_theme!(size=(600, 450))" + return replace(content, "using GLMakie" => setup_cmd) end # Initialize the master "Examples" page From a27569c5515cf5d1d699be8eba20e8d85f2d2469 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Thu, 8 Jan 2026 10:51:58 -0800 Subject: [PATCH 17/42] New subsection outlines. --- docs/src/index.md | 16 ++++++++++++++++ 1 file changed, 16 insertions(+) diff --git a/docs/src/index.md b/docs/src/index.md index 1f643d8..df197c1 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -2,6 +2,8 @@ **DistMesh.jl** is a Julia generator for unstructured triangular and tetrahedral meshes. It uses [Signed Distance Functions](https://en.wikipedia.org/wiki/Signed_distance_function) (SDFs) to define geometries, enabling the generation of high-quality, isotropic meshes for complex shapes defined by simple mathematical functions. +--- + ## Installation ```julia @@ -9,6 +11,8 @@ using Pkg Pkg.add("DistMesh") ``` +--- + ## Introduction ### A Simple Example Mesh @@ -96,7 +100,19 @@ msh = distmesh2d(fd, fh, hmin, bbox, pfix) plot(msh) ``` +### Implicit Geometry vs Distance Function + +### Non-uniform size function + +### Randomness and reproducability + +### Save/export meshes + +--- + ## Distance Functions +--- + ## Size Functions From 70ffd4e490157264cda5fcc9a3d3074c8fe51c91 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 20 Jan 2026 09:38:24 -0800 Subject: [PATCH 18/42] Added implicit function example. --- docs/src/index.md | 12 +++++++++--- 1 file changed, 9 insertions(+), 3 deletions(-) diff --git a/docs/src/index.md b/docs/src/index.md index df197c1..f5e0681 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -88,20 +88,26 @@ If you want separate re-allocated versions of these matrices, use `collect`. ### Fixed points -An optional argument to `distmesh2d` is `pfix` - a vector of frozen points that are part of the generated mesh. These are typically required for boundaries with sharp corners, since the implicit geometry representation as a signed distance function does not explicitly provide them. Here is a simple example of a mesh of a rectangle, where we include the four corner points in `pfix1`. +An optional argument to `distmesh2d` is `pfix` - a vector of frozen points that are part of the generated mesh. These are typically required for boundaries with sharp corners, since the implicit geometry representation as a signed distance function does not explicitly provide them. Here is a simple example of a mesh of a rectangle, where we include the four corner points in `pfix`. ```@example introduction fd(p) = drectangle(p, -1, 1, -1, 1) pfix = ((-1,-1), (1,-1), (-1,1), (1,1)) # fh, hmin, bbox same as before msh = distmesh2d(fd, fh, hmin, bbox, pfix) +plot(msh) ``` +### Implicit Geometry vs Distance Function + +Although the original version of DistMesh required actual signed distance functions for the geometry, this condition was relaxed in later versions and the algorithm actually accepts any smooth function with an implicitly defined zero level-set. This can be very convenient when defining non-trivial geometries, e.g. an ellipse with semi-axes 2,1 can now be represented as the zero level-set of $d(x,y)=(x/2)^2 + (y/1)^2 -1$. Note that this is not the actual distance function for the ellipse. + ```@example introduction +fd(p) = (p[1]/2)^2 + (p[2]/1)^2 - 1 +bbox = ((-2,-1), (2,1)) +msh = distmesh2d(fd, huniform, 0.2, bbox) plot(msh) ``` -### Implicit Geometry vs Distance Function - ### Non-uniform size function ### Randomness and reproducability From a6ed80b3e67573c8e2eff400379910c59cecf872 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 20 Jan 2026 09:38:36 -0800 Subject: [PATCH 19/42] Remove CairoMakie from doc build. --- docs/make.jl | 9 +-------- 1 file changed, 1 insertion(+), 8 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index b95b995..746c4bb 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -9,12 +9,6 @@ examples_dir = joinpath(@__DIR__, "..", "examples") docs_src = joinpath(@__DIR__, "src") master_file = joinpath(docs_src, "examples.md") -# Define a preprocessing function -function replace_gl_with_cairo(content) - setup_cmd = "using CairoMakie; CairoMakie.activate!(type=\"png\", px_per_unit=1); # update_theme!(size=(600, 450))" - return replace(content, "using GLMakie" => setup_cmd) -end - # Initialize the master "Examples" page open(master_file, "w") do io write(io, "# Examples\n\nA collection of 2D meshing examples.\n\n") @@ -37,8 +31,7 @@ for file in jl_files Literate.markdown(dest_path, docs_src; documenter=true, credit=false, - name=replace(file, ".jl"=>""), - preprocess = replace_gl_with_cairo + name=replace(file, ".jl"=>"") ) # 3. Read the generated markdown From d8be8e45e2e0ddeb41e837d16baaa80ef5b6125f Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 20 Jan 2026 14:18:20 -0800 Subject: [PATCH 20/42] Run all scripts in examples/ as part of the unit tests. --- Project.toml | 3 ++- test/runtests.jl | 36 ++++++++++++++++++++++++++++++++++++ 2 files changed, 38 insertions(+), 1 deletion(-) diff --git a/Project.toml b/Project.toml index 9818f8f..83a331f 100644 --- a/Project.toml +++ b/Project.toml @@ -35,6 +35,7 @@ julia = "1.10" GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" TetGen = "c5d3f3f7-f850-59f6-8a2e-ffc6dc1317ea" +CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" [targets] -test = ["Test", "GeometryBasics", "TetGen"] +test = ["Test", "GeometryBasics", "TetGen", "CairoMakie"] diff --git a/test/runtests.jl b/test/runtests.jl index 0db5f6c..7ec7293 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -1,6 +1,42 @@ using DistMesh using Test using GeometryBasics +using CairoMakie + +# ------------------------------------------------------------------------------ +# DistMesh 2D Tests +# ------------------------------------------------------------------------------ + +const EXAMPLES_DIR = joinpath(@__DIR__, "..", "examples") + +@testset "Examples" begin + # Get all .jl files + files = filter(f -> endswith(f, ".jl"), readdir(EXAMPLES_DIR)) + + for file in files + @testset "$file" begin + # Read the example file + path = joinpath(EXAMPLES_DIR, file) + content = read(path, String) + + # Swap GLMakie -> CairoMakie (for Headless tests) + content = replace(content, "using GLMakie" => "using CairoMakie") + + # Run the code + try + include_string(Main, content, path) + @test true + catch e + @error "Example $file failed to run" exception=(e, catch_backtrace()) + @test false + end + end + end +end + +# ------------------------------------------------------------------------------ +# DistMesh ND Tests +# ------------------------------------------------------------------------------ include("vals.jl") From 9a8bcfd16156ffe0c4ee03ffc36569043288fcd3 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 20 Jan 2026 14:22:22 -0800 Subject: [PATCH 21/42] Relicense project from GPL to MIT Updates the LICENSE file to the standard MIT License and adds the license metadata to Project.toml. This change is part of the package modernization to align DistMesh.jl with the broader Julia ecosystem. Note: This re-licensing covers legacy code copyrighted by Steve Kelly; the change is being coordinated with the authors and is pending final confirmation. --- LICENSE | 320 ++++----------------------------------------------- Project.toml | 3 +- 2 files changed, 25 insertions(+), 298 deletions(-) diff --git a/LICENSE b/LICENSE index 81ced2c..9f59c10 100644 --- a/LICENSE +++ b/LICENSE @@ -1,297 +1,23 @@ -Copyright (C) 2004-2012 Per-Olof Persson, 2019 Steve Kelly - -This program is free software; you can redistribute it and/or modify -it under the terms of the GNU General Public License as published by -the Free Software Foundation; either version 2 of the License, or -(at your option) any later version. - -This program is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. 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For software which is copyrighted by the Free -Software Foundation, write to the Free Software Foundation; we sometimes -make exceptions for this. Our decision will be guided by the two goals -of preserving the free status of all derivatives of our free software and -of promoting the sharing and reuse of software generally. - - NO WARRANTY - - 11. BECAUSE THE PROGRAM IS LICENSED FREE OF CHARGE, THERE IS NO WARRANTY -FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN -OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES -PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED -OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF -MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS -TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE -PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, -REPAIR OR CORRECTION. - - 12. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING -WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MAY MODIFY AND/OR -REDISTRIBUTE THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, -INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING -OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED -TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY -YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER -PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE -POSSIBILITY OF SUCH DAMAGES. - - END OF TERMS AND CONDITIONS +MIT License + +Copyright (c) 2004-2012 Per-Olof Persson +Copyright (c) 2019 Steve Kelly +Copyright (c) 2026 Per-Olof Persson + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/Project.toml b/Project.toml index 83a331f..a2991de 100644 --- a/Project.toml +++ b/Project.toml @@ -1,7 +1,8 @@ name = "DistMesh" uuid = "f7ee28b6-bfbf-11e9-3e31-8961b86f052c" version = "0.2.0" -authors = ["Steve Kelly and Per-Olof Persson ", "Per-Olof Persson "] +license = "MIT" [deps] Delaunator = "466f8f70-d5e3-4806-ac0b-a54b75a91218" From eb385350d62002e9099119bc38af0a6790d5ba12 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 20 Jan 2026 17:02:31 -0800 Subject: [PATCH 22/42] Added more unit tests for distmesh2d --- test/runtests.jl | 51 ++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 51 insertions(+) diff --git a/test/runtests.jl b/test/runtests.jl index 7ec7293..561a6ed 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -7,6 +7,57 @@ using CairoMakie # DistMesh 2D Tests # ------------------------------------------------------------------------------ +""" + check_mesh(p, t; np, nt, area, areatol, minqual) + +Validates a 2D mesh against expected properties. +- `np`: Expected number of nodes. +- `nt`: Expected number of triangles. +- `area`: Expected total area of the domain. +- `areatol`: Tolerance for total area check. +- `minqual`: Minimum allowable triangle quality (0.0 to 1.0). +""" +function check_mesh(msh::DMesh; np::Int=0, nt::Int=0, area::Real=0.0, areatol::Real=1e-6, minqual::Real=0.1) + @testset "Mesh Validation" begin + + # 1. Check Counts + np > 0 && @test length(msh.p) == np + nt > 0 && @test length(msh.t) == nt + + # 2. Compute Geometric Properties + total_area = sum(simpvol(msh)) + min_q = minimum(simpqual(msh)) + has_negative_area = minimum(simpvol(msh)) < 0.0 + + # 3. Check Winding / Topology + @test !has_negative_area + + # 4. Check Total Area + area > 0.0 && @test isapprox(total_area, area, atol=areatol) + + # 5. Check Element Quality + @test min_q >= minqual + end +end + +@testset "Unit Circle Mesh" begin + msh = distmesh2d(dcircle, huniform, 0.2, ((-1,-1), (1,1))) + check_mesh(msh, np=88, nt=143) + + for h in (0.01, 0.02, 0.05, 0.10, 0.15, 0.2) + msh = distmesh2d(dcircle, huniform, h, ((-1,-1), (1,1))) + check_mesh(msh, + area=pi, + areatol=h^2, # Not an exact circle + minqual=0.6 + ) + end +end + + +# ------------------------------------------------------------------------------ +# Run all scripts in the examples/ directory + const EXAMPLES_DIR = joinpath(@__DIR__, "..", "examples") @testset "Examples" begin From a18446abb51bb26ffed80b885f39dc462f7a98d4 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 20 Jan 2026 18:38:30 -0800 Subject: [PATCH 23/42] More docs and docstring examples. --- docs/src/index.md | 84 +++++++++++++++++++++++++++++++++++++++++++++-- src/distmesh2d.jl | 73 +++++++++++++++++++++++++++------------- 2 files changed, 132 insertions(+), 25 deletions(-) diff --git a/docs/src/index.md b/docs/src/index.md index f5e0681..0a28451 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -110,15 +110,95 @@ plot(msh) ### Non-uniform size function +For non-uniform element sizes, we provide a (relative) size function $h(x,y)$. In general, it is best to make this an absolute size function that gives the actual desired edge lengths at point $x,y$. To achieve this, you set the initial edge lengths `hmin` to the smallest value of $h(x,y)$ in the domain. + +For example, to set the element sizes to $h_\mathrm{min}$ at a source and let the element sizes increase exponentially away from the source, we use a *linearly growing* size function $h(x,y) = h_\mathrm{min} + 0.3d(x,y)$ where $d(x,y)$ is the distance function of the source. + +```@example introduction +# Point source +hmin = 0.01 +fh(p) = hmin + 0.3 * dcircle(p, r=0) +msh = distmesh2d(dcircle, fh, hmin, ((-1,-1), (1,1))) +plot(msh) +``` + +Multiple size function sources can be combined using the `min` function: + +```@example introduction +# Point and line sources +fd(p) = drectangle(p, 0, 1, 0, 1) +fh(p) = min(min(0.01 + 0.3*abs(dcircle(p, r=0)), + 0.025 + 0.3*abs(dpoly(p, [(0.3,0.7), (0.7,0.5)]))), + 0.15) +msh = distmesh2d(fd, fh, 0.01, ((0,0), (1,1)), ((0,0), (1,0), (0,1), (1,1))) +plot(msh) +``` + ### Randomness and reproducability +The DistMesh algorithm is notoriously *chaotic*, or initial value sensitive. This means that very small perturbations in the mesh calculations can grow to large changes in the mesh (that is, completely different meshes). Having said that, running on the same deterministic computer, if you repeat a `distmesh2d` call twice with uniform size functions, it usually gives two identical meshes: + +```@example introduction +msh1 = distmesh2d(dcircle, huniform, 0.2, ((-1,-1), (1,1))) +msh2 = distmesh2d(dcircle, huniform, 0.2, ((-1,-1), (1,1))) +println(msh1.p == msh2.p) +println(msh1.t == msh2.t) +``` + +However, for non-uniform size functions, DistMesh uses the `rand` function for the initial point distribution. This means two meshes with identical inputs will in general not be the same: + +```@example introduction +fh(p) = 0.01 + 0.3 * dcircle(p, r=0) +msh1 = distmesh2d(dcircle, fh, 0.01, ((-1,-1), (1,1))) +msh2 = distmesh2d(dcircle, fh, 0.01, ((-1,-1), (1,1))) +display(msh1) +display(msh2) +``` + +Many times this is undesirable, e.g. for reproducability, debugging, etc. You can then seed the random number generator to make the meshes identical: + +```@example introduction +using Random +fh(p) = 0.01 + 0.3 * dcircle(p, r=0) +Random.seed!(1234) +msh1 = distmesh2d(dcircle, fh, 0.01, ((-1,-1), (1,1))) +Random.seed!(1234) +msh2 = distmesh2d(dcircle, fh, 0.01, ((-1,-1), (1,1))) +display(msh1) +display(msh2) +println(msh1.p == msh2.p) +println(msh1.t == msh2.t) +``` + ### Save/export meshes +DistMesh does not provide any mesh export functionality to external programs. However, it is easy to write specialized routines e.g. based on text files. A common format is to have an initial line with information such as number of nodes and number of elements, then comma-separated rows with all the node positions and then the element connectivities: + +```@example introduction +using DelimitedFiles +function savemesh(msh::DMesh, fname) + open(fname, "w") do io + p,t = as_arrays(msh) + println(io, "$(length(p)) $(length(t)) # nbr_nodes nbr_elems") + writedlm(io, p', ',') + writedlm(io, t', ',') + end +end + +msh = distmesh2d(dcircle, huniform, 0.2, ((-1,-1), (1,1))) +fname = tempdir() * "/mesh.dat" +savemesh(msh, fname) +println("Mesh saved to file $fname") +``` + --- -## Distance Functions +## More about Distance Functions + +TODO --- -## Size Functions +## More about Size Functions +TODO diff --git a/src/distmesh2d.jl b/src/distmesh2d.jl index 8b0862f..7004da8 100644 --- a/src/distmesh2d.jl +++ b/src/distmesh2d.jl @@ -85,18 +85,17 @@ as a physical equilibrium problem. A system of truss bars (edges) is relaxed unt equilibrium is reached, constrained by the signed distance function `dfcn` to stay within the domain. # Arguments -- `dfcn::Function`: Signed distance function `d(p)`. Returns negative values inside the region, - positive outside. Input `p` is an `(N,2)` array. +- `dfcn::Function`: Signed distance function `d(p)`. Returns negative values inside the region, + positive outside. The input `p` is a 2-element coordinate vector (e.g., `Vector`, `Tuple`, or `SVector`). - `hfcn::Function`: Element size function `h(p)`. Returns target edge length at point `p`. - `h0::Real`: Initial nominal edge length (scaling factor for `hfcn`). - `bbox`: Bounding box tuple `((xmin, ymin), (xmax, ymax))` defining the initial grid generation area. - `pfix::Vector`: (Optional) List of fixed node positions that must be part of the mesh (e.g., corners). # Keywords -- `plotting::Bool = false`: Enable live visualization of the relaxation process (requires GLMakie). -- `maxiter::Int = 1000`: Maximum number of relaxation iterations. -- `ttol::Real`: Tolerance for retriangulation (defaults to `0.1 * h0`). -- `dptol::Real`: Termination tolerance for node movement (defaults to `0.001 * h0`). +- `plotting::Bool = false`: Enable live visualization of the relaxation process (Plots or GLMakie). +- `maxiter::Int = 10_000`: Maximum number of relaxation iterations. +- Several other parameters that are rarely modified # Returns - `p::Vector{Point2d}`: The node positions. @@ -107,33 +106,61 @@ equilibrium is reached, constrained by the signed distance function `dfcn` to st **Uniform Mesh on a Unit Circle** ```julia using DistMesh -# Distance function for a circle of radius 1 -fd = p -> sqrt.(sum(p.^2, dims=2)) .- 1.0 -# Uniform mesh size -fh = p -> ones(size(p,1)) -p, t = distmesh2d(fd, fh, 0.2, ((-1,-1), (1,1)), plotting=false) +fd(p) = sqrt(sum(p.^2)) - 1 # or dcircle(p) - unit circle geometry +fh(p) = 1.0 # or huniform(p) - uniform size function +hmin = 0.2 # initial edge lengths +bbox = ((-1,-1), (1,1)) # bounding box for unit circle + +msh = distmesh2d(fd, fh, hmin, bbox) + +# Optionally, the mesh can be visualized using various plotting packages: +using GLMakie # or Plots, or CairoMakie +plot(msh) ``` **Rectangle with Circular Hole (Refined at Boundary)** ```julia using DistMesh +hmin = 0.05 +fd(p) = ddiff(drectangle(p, -1, 1, -1, 1), dcircle(p, r=0.5)) +fh(p) = hmin + 0.3*dcircle(p, r=0.5) +msh = distmesh2d(fd, fh, hmin, ((-1,-1), (1,1)), ((-1,-1), (-1,1), (1,-1), (1,1))) +``` -# Define distance function: Rectangle minus Circle -function fd_hole(p) - d_rect = drectangle(p, -1, 1, -1, 1) - d_circ = dcircle(p, 0, 0, 0.5) - return ddiff(d_rect, d_circ) -end - -# Size function: Refine near the hole -fh_hole(p) = 0.05 .+ 0.3 * dcircle(p, 0, 0, 0.5) +**Polygon** +```julia +using DistMesh +pv = [(-0.4, -0.5), (0.4, -0.2), (0.4, -0.7), (1.5, -0.4), + (0.9, 0.1), (1.6, 0.8), (0.5, 0.5), (0.2, 1.0), + (0.1, 0.4), (-0.7, 0.7), (-0.4, -0.5)] +fd(p) = dpoly(p, pv) +bbox = ((-1,-1), (2,1)) +h0 = 0.15 +msh = distmesh2d(fd, huniform, h0, bbox, pv) +``` -bbox = ((-1,-1), (1,1)) -pfix = [(-1,-1), (-1,1), (1,-1), (1,1)] # Fix corners +**Ellipse** +```julia +using DistMesh +fd(p) = (p[1]/2)^2 + (p[2]/1)^2 - 1 +bbox = ((-2,-1), (2,1)) +msh = distmesh2d(fd, huniform, 0.2, bbox) +``` -p, t = distmesh2d(fd_hole, fh_hole, 0.05, bbox, pfix) +**Square, with size function point and line sources** +```julia +using DistMesh +fd(p) = drectangle(p, 0, 1, 0, 1) +fh(p) = min(min(0.01 + 0.3*abs(dcircle(p, r=0)), + 0.025 + 0.3*abs(dpoly(p, [(0.3,0.7), (0.7,0.5)]))), + 0.15) +msh = distmesh2d(fd, fh, 0.01, ((0,0), (1,1)), ((0,0), (1,0), (0,1), (1,1))) ``` + +**NACA0012 airfoil** + +See `examples/002-naca_airfoil.jl` """ function distmesh2d(dfcn, hfcn, h0, bbox, pfix=Point2d[]; plotting=false, # Optional live plotting From 80d9f971d2f475f7de51a6c8b6c6bb7cdf21a7cd Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 20 Jan 2026 20:46:35 -0800 Subject: [PATCH 24/42] Many minor changes to docs and examples. --- docs/make.jl | 2 +- docs/src/index.md | 123 +++++++++++++++++++++++------------ examples/001-polygon.jl | 26 ++++---- examples/002-naca_airfoil.jl | 35 +++++++++- 4 files changed, 127 insertions(+), 59 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index 746c4bb..831a63d 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -11,7 +11,7 @@ master_file = joinpath(docs_src, "examples.md") # Initialize the master "Examples" page open(master_file, "w") do io - write(io, "# Examples\n\nA collection of 2D meshing examples.\n\n") + write(io, "# Examples\n\nA collection of 2D meshing examples. Note that all the codes are available in the `examples` directory.\n\n") end # Find all .jl files and sort them diff --git a/docs/src/index.md b/docs/src/index.md index 0a28451..4d927eb 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -1,6 +1,6 @@ # DistMesh.jl -**DistMesh.jl** is a Julia generator for unstructured triangular and tetrahedral meshes. It uses [Signed Distance Functions](https://en.wikipedia.org/wiki/Signed_distance_function) (SDFs) to define geometries, enabling the generation of high-quality, isotropic meshes for complex shapes defined by simple mathematical functions. +**DistMesh.jl** is a Julia package for generating unstructured triangular and tetrahedral meshes. It uses [Signed Distance Functions](https://en.wikipedia.org/wiki/Signed_distance_function) (SDFs) to define geometries, enabling the generation of high-quality, isotropic meshes for complex shapes defined by simple mathematical functions. --- @@ -9,6 +9,7 @@ ```julia using Pkg Pkg.add("DistMesh") + ``` --- @@ -19,17 +20,11 @@ Pkg.add("DistMesh") The primary entry point for 2D meshing is `distmesh2d`. It generates a mesh based on: -* A distance function (negative inside, positive outside). In this example, - we represent the unit circle by $d(x,y) = \sqrt{x^2+y^2} - 1$ - -* A relative size function. For a uniform mesh, we can simply set $h(x,y) = 1$ - -* An initial, or minimum, element edge length. Since our size function is - uniform, this will also be roughly the size of the generated elements. - -* A bounding box for the domain. For the unit circle, we use the coordinates - (-1,-1) and (1,1). - +* A **distance function** `fd(p)` (negative inside, positive outside). In this example, we represent the unit circle by $d(x,y) = \sqrt{x^2+y^2} - 1$. +* A **relative size function** `fh(p)`. For a uniform mesh, we can simply set $h(x,y)=1$. +* An **initial element edge length** `h0`. Since our size function is uniform, this will also be roughly the final size of the generated elements. +* A **bounding box** `bbox` for the domain. For the unit circle, we use the coordinates `((-1,-1), (1,1))`. + The code below demonstrates how to implement this using DistMesh in Julia. ```@example introduction @@ -42,77 +37,91 @@ hmin = 0.2 # initial edge lengths bbox = ((-1,-1), (1,1)) # bounding box for unit circle msh = distmesh2d(fd, fh, hmin, bbox) + ``` The resulting mesh can be visualized with the `plot` command. ```@example introduction plot(msh) + ``` ### Accessing the generated mesh -The `msh` object contains the node coordinates `p` and the triangle indices `t`, stored as vectors of static vectors (for efficiency) +The `msh` object contains the node coordinates `p` and the triangle indices `t`, stored as vectors of static vectors (for efficiency). ```@example introduction # Access the nodes and connectivity as vectors of static vectors -p,t = msh +p, t = msh p[1:3] # First 3 nodes + ``` ```@example introduction t[1:3] # First 3 triangles (indices) + ``` ```@example introduction p[t[1]] # x,y-coordinates of the first triangle + ``` If you prefer a matrix-based representation (similar to the original MATLAB DistMesh, except transposed), the utility function `as_arrays` creates a zero-allocation view for this. Note that if you modify these matrices, the original versions in `msh` will also be changed! ```@example introduction # Access the nodes and connectivity as matrices -p_mat,t_mat = as_arrays(msh) -p_mat[:,1:3] # First 3 nodes +p_mat, t_mat = as_arrays(msh) +p_mat[:, 1:3] # First 3 nodes + ``` ```@example introduction -t_mat[:,1:3] # First 3 triangles (indices) +t_mat[:, 1:3] # First 3 triangles (indices) + ``` ```@example introduction -p_mat[:,t_mat[:,1]] # x,y-coordinates of the first triangle +p_mat[:, t_mat[:, 1]] # x,y-coordinates of the first triangle + ``` If you want separate re-allocated versions of these matrices, use `collect`. ### Fixed points -An optional argument to `distmesh2d` is `pfix` - a vector of frozen points that are part of the generated mesh. These are typically required for boundaries with sharp corners, since the implicit geometry representation as a signed distance function does not explicitly provide them. Here is a simple example of a mesh of a rectangle, where we include the four corner points in `pfix`. +An optional argument to `distmesh2d` is `pfix` - a vector of frozen points that are forced to be part of the generated mesh. These are typically required for boundaries with sharp corners, since the implicit geometry representation as a signed distance function does not explicitly provide them. + +Here is a simple example of a mesh of a rectangle, where we include the four corner points in `pfix`. + ```@example introduction -fd(p) = drectangle(p, -1, 1, -1, 1) -pfix = ((-1,-1), (1,-1), (-1,1), (1,1)) -# fh, hmin, bbox same as before -msh = distmesh2d(fd, fh, hmin, bbox, pfix) +fd(p) = drectangle(p, 0, 1, 0, 1) +pfix = ((0,0), (1,0), (0,1), (1,1)) +msh = distmesh2d(fd, huniform, 0.1, ((0,0), (1,1)), pfix) plot(msh) + ``` ### Implicit Geometry vs Distance Function -Although the original version of DistMesh required actual signed distance functions for the geometry, this condition was relaxed in later versions and the algorithm actually accepts any smooth function with an implicitly defined zero level-set. This can be very convenient when defining non-trivial geometries, e.g. an ellipse with semi-axes 2,1 can now be represented as the zero level-set of $d(x,y)=(x/2)^2 + (y/1)^2 -1$. Note that this is not the actual distance function for the ellipse. +Although the original version of DistMesh required actual signed distance functions for the geometry, this condition was relaxed in later versions. The algorithm actually accepts any smooth function with an implicitly defined zero level-set. + +This can be very convenient when defining non-trivial geometries. For example, an ellipse with semi-axes 2 and 1 can now be represented as the zero level-set of $d(x,y)=(x/2)^2 + (y/1)^2 - 1$. Note that this is not the actual Euclidean distance function for the ellipse. ```@example introduction fd(p) = (p[1]/2)^2 + (p[2]/1)^2 - 1 bbox = ((-2,-1), (2,1)) msh = distmesh2d(fd, huniform, 0.2, bbox) plot(msh) + ``` ### Non-uniform size function -For non-uniform element sizes, we provide a (relative) size function $h(x,y)$. In general, it is best to make this an absolute size function that gives the actual desired edge lengths at point $x,y$. To achieve this, you set the initial edge lengths `hmin` to the smallest value of $h(x,y)$ in the domain. +For non-uniform element sizes, we provide a (relative) size function $h(x,y)$. In general, it is best to make this an absolute size function that gives the actual desired edge lengths at point . To achieve this, you set the initial edge lengths `hmin` to the smallest value of $h(x,y)$ in the domain. -For example, to set the element sizes to $h_\mathrm{min}$ at a source and let the element sizes increase exponentially away from the source, we use a *linearly growing* size function $h(x,y) = h_\mathrm{min} + 0.3d(x,y)$ where $d(x,y)$ is the distance function of the source. +For example, to set the element sizes to at a source and let the element sizes increase linearly away from the source, we use a size function $h(x,y)=h_\mathrm{min} + 0.3d(x,y)$ where $d(x,y)$ is the distance function of the source. ```@example introduction # Point source @@ -120,6 +129,7 @@ hmin = 0.01 fh(p) = hmin + 0.3 * dcircle(p, r=0) msh = distmesh2d(dcircle, fh, hmin, ((-1,-1), (1,1))) plot(msh) + ``` Multiple size function sources can be combined using the `min` function: @@ -130,55 +140,83 @@ fd(p) = drectangle(p, 0, 1, 0, 1) fh(p) = min(min(0.01 + 0.3*abs(dcircle(p, r=0)), 0.025 + 0.3*abs(dpoly(p, [(0.3,0.7), (0.7,0.5)]))), 0.15) -msh = distmesh2d(fd, fh, 0.01, ((0,0), (1,1)), ((0,0), (1,0), (0,1), (1,1))) +# Note: we explicitly add corners to pfix for the rectangle +pfix = ((0,0), (1,0), (0,1), (1,1)) +msh = distmesh2d(fd, fh, 0.01, ((0,0), (1,1)), pfix) plot(msh) + ``` -### Randomness and reproducability +### Randomness and Reproducibility + +The DistMesh algorithm is notoriously *chaotic*, or sensitive to initial conditions. This means that very small perturbations in the mesh calculations can grow to large changes in the mesh (resulting in completely different meshes). -The DistMesh algorithm is notoriously *chaotic*, or initial value sensitive. This means that very small perturbations in the mesh calculations can grow to large changes in the mesh (that is, completely different meshes). Having said that, running on the same deterministic computer, if you repeat a `distmesh2d` call twice with uniform size functions, it usually gives two identical meshes: +However, running on the same deterministic computer, if you repeat a `distmesh2d` call twice with uniform size functions, it usually gives two identical meshes because it uses a deterministic grid-based initialization: ```@example introduction msh1 = distmesh2d(dcircle, huniform, 0.2, ((-1,-1), (1,1))) msh2 = distmesh2d(dcircle, huniform, 0.2, ((-1,-1), (1,1))) -println(msh1.p == msh2.p) -println(msh1.t == msh2.t) +msh1.p == msh2.p && msh1.t == msh2.t + ``` -However, for non-uniform size functions, DistMesh uses the `rand` function for the initial point distribution. This means two meshes with identical inputs will in general not be the same: +For **non-uniform size functions**, DistMesh uses the `rand` function for the initial point distribution (rejection sampling). This means two meshes with identical inputs will in general not be the same: ```@example introduction fh(p) = 0.01 + 0.3 * dcircle(p, r=0) msh1 = distmesh2d(dcircle, fh, 0.01, ((-1,-1), (1,1))) + +``` + +```@example introduction msh2 = distmesh2d(dcircle, fh, 0.01, ((-1,-1), (1,1))) -display(msh1) -display(msh2) + ``` -Many times this is undesirable, e.g. for reproducability, debugging, etc. You can then seed the random number generator to make the meshes identical: +```@example introduction +# Check if they are identical (likely false) +msh1.p == msh2.p && msh1.t == msh2.t + +``` + +Many times this is undesirable (e.g., for regression testing or debugging). You can seed the random number generator to make the meshes identical: ```@example introduction using Random fh(p) = 0.01 + 0.3 * dcircle(p, r=0) + Random.seed!(1234) msh1 = distmesh2d(dcircle, fh, 0.01, ((-1,-1), (1,1))) + +``` + +Now we generate the second mesh with the same seed: + +```@example introduction Random.seed!(1234) msh2 = distmesh2d(dcircle, fh, 0.01, ((-1,-1), (1,1))) -display(msh1) -display(msh2) -println(msh1.p == msh2.p) -println(msh1.t == msh2.t) + +``` + +Finally, we verify they are identical: + +```@example introduction +msh1.p == msh2.p && msh1.t == msh2.t + ``` ### Save/export meshes -DistMesh does not provide any mesh export functionality to external programs. However, it is easy to write specialized routines e.g. based on text files. A common format is to have an initial line with information such as number of nodes and number of elements, then comma-separated rows with all the node positions and then the element connectivities: +DistMesh does not provide built-in mesh export functionality to external formats. However, it is easy to write specialized routines, e.g., based on text files. + +A common format is to have an initial line with metadata (number of nodes and elements), followed by comma-separated rows for node positions and element connectivities: ```@example introduction using DelimitedFiles + function savemesh(msh::DMesh, fname) open(fname, "w") do io - p,t = as_arrays(msh) + p, t = as_arrays(msh) println(io, "$(length(p)) $(length(t)) # nbr_nodes nbr_elems") writedlm(io, p', ',') writedlm(io, t', ',') @@ -186,9 +224,10 @@ function savemesh(msh::DMesh, fname) end msh = distmesh2d(dcircle, huniform, 0.2, ((-1,-1), (1,1))) -fname = tempdir() * "/mesh.dat" +fname = joinpath(tempdir(), "mesh.dat") savemesh(msh, fname) println("Mesh saved to file $fname") + ``` --- diff --git a/examples/001-polygon.jl b/examples/001-polygon.jl index 95587f3..cfd673f 100644 --- a/examples/001-polygon.jl +++ b/examples/001-polygon.jl @@ -1,30 +1,28 @@ # ## Polygon Mesh -# -# This example demonstrates how to mesh a custom polygon using `dpoly`. using DistMesh using GLMakie -# ### 1. Define Vertices +# First, define the vertices of the polygon as a list of points (tuples) pv = [(-0.4, -0.5), (0.4, -0.2), (0.4, -0.7), (1.5, -0.4), (0.9, 0.1), (1.6, 0.8), (0.5, 0.5), (0.2, 1.0), - (0.1, 0.4), (-0.7, 0.7), (-0.4, -0.5)] + (0.1, 0.4), (-0.7, 0.7), (-0.4, -0.5)]; -# ### 2. Create Distance Function -# `dpoly` computes the distance from points `p` to the polygon defined by `pv`. -# We wrap it in a new function because `distmesh2d` expects a function of `p`. +# Next, use the `dpoly` function and these vertices to define the distance function fd(p) = dpoly(p, pv) -# ### 3. Generate Mesh -# We use a uniform mesh size of h0 = 0.1. -# The bounding box must enclose the polygon. +# We use a uniform mesh size function, with a given desired edge length +hmin = 0.15 +fh = huniform +# DistMesh also needs a bounding box, which must enclose the polygon bbox = ((-1,-1), (2,1)) -h0 = 0.15 -msh = distmesh2d(fd, huniform, h0, bbox, pv) +# Sharp corners have to be provided in the `pfix` argument +pfix = pv -# ### 4. Visualize -# Plot the resulting mesh. +# Generate the mesh +msh = distmesh2d(fd, fh, hmin, bbox, pfix) +# Finally, plot the resulting mesh plot(msh) diff --git a/examples/002-naca_airfoil.jl b/examples/002-naca_airfoil.jl index de1b49e..786657a 100644 --- a/examples/002-naca_airfoil.jl +++ b/examples/002-naca_airfoil.jl @@ -1,4 +1,9 @@ # ## NACA Airfoil Mesh +# +# This example shows how to generate a mesh around a NACA0012 airfoil. + +# First, load the required packages and define a convenient short-hand +# for static 2D points. using DistMesh using GLMakie @@ -6,12 +11,19 @@ using StaticArrays const Point2d = SVector{2, Float64} +# First, we define the size function for the NACA airfoil. It consists of the minimum of several point sources and constants: +# * A point source at the tip of the airfoil, with size `hlead` +# * A point source at the traling edge of the airfoil, with size `htrail` +# * A maximum element size in the entire domain `hmax` + function hnaca(p; hlead=0.01, htrail=0.04, hmax=2.0) minimum((hlead + 0.3 * dcircle(p, c=(0, 0), r=0), htrail + 0.3 * dcircle(p, c=(1, 0), r=0), hmax)) end +# Next, we define the fix points. This could be as simple as just the trailing edge at `(1,0)`. However, the mesh quality is improved by providing several points along the surface, spread out consistently with the size function above. Therefore, this function also needs the edge length `htrail` from before. We also add the symmetry point `(0,0)`. + function fixnaca(; htrail=0.04) a0, a14... = naca_coeffs fixx = 1 .- htrail * cumsum(1.3 .^ (0:4)) @@ -19,17 +31,36 @@ function fixnaca(; htrail=0.04) fix = vcat(Point2d[(0,0),(1,0)], [ Point2d[(x,y),(x,-y)] for (x,y) in zip(fixx,fixy) ]...) end +# Finally, we can define a function for generating the arguments to `distmesh2d` for generating the NACA mesh. The parameters are the sizes from before, as well as a center point `(circx,0)` and a radius for the far-field circle boundary. + function dm_naca(; hlead=0.01, htrail=0.04, hmax=2.0, circx=2.0, circr=4.0) + ## Distance function: Difference between the outer circle and the NACA airfoil dfcn(p) = ddiff(dcircle(p, c=(circx, 0), r=circr), dnaca(p)) + + ## Size function: Given by `hnaca` above hfcn(p) = hnaca(p; hlead=hlead, htrail=htrail, hmax=hmax) + ## Fix points: Add symmetry points for the circle plus the once from `fixnaca` fix = Point2d[(1,0),(0,1),(-1,0),(0,-1)] .* circr .+ Point2d[(circx,0)] fix = vcat(fix, fixnaca(htrail=htrail)) + + ## Bounding box: Determined by the far-field circle bbox = [(circx - circr, -circr), (circx + circr, circr)] - h0 = minimum((hlead, htrail, hmax)) - dfcn, hfcn, h0, bbox, fix + + ## The `hmin` parameter needs to be the smallest element size in the domain + hmin = minimum((hlead, htrail, hmax)) + + dfcn, hfcn, hmin, bbox, fix end +# Now we can generate and plot the default mesh msh = distmesh2d(dm_naca()...) +plot(msh) + +# We can modify the mesh, e.g. by shrinking the farfield circle +msh = distmesh2d(dm_naca(circx=1, circr=1.5)...) +plot(msh) +# Finally, we can increase the element sizes at the sources +msh = distmesh2d(dm_naca(circx=1, circr=1.5, hlead=0.05, htrail=0.1)...) plot(msh) From e14ef73404dc35d1b4ef30408669a2e0f6eed43f Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 20 Jan 2026 23:01:18 -0800 Subject: [PATCH 25/42] Another try on CairoMakie for all docs. Version updates on Makie in Project.toml. --- Project.toml | 2 +- docs/Project.toml | 3 +++ docs/make.jl | 8 +++++++- docs/src/index.md | 2 +- 4 files changed, 12 insertions(+), 3 deletions(-) diff --git a/Project.toml b/Project.toml index a2991de..4d3a4c5 100644 --- a/Project.toml +++ b/Project.toml @@ -24,7 +24,7 @@ DistMeshPlotsExt = "Plots" [compat] CairoMakie = "0.15" Delaunator = "0.1" -GLMakie = "0.11, 0.13" +GLMakie = "0.11, 0.12, 0.13" GeometryBasics = "0.5" LinearAlgebra = "1" Plots = "1" diff --git a/docs/Project.toml b/docs/Project.toml index 46a38f3..d693dd8 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -3,3 +3,6 @@ DistMesh = "f7ee28b6-bfbf-11e9-3e31-8961b86f052c" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" + +[compat] +CairoMakie = "0.15" diff --git a/docs/make.jl b/docs/make.jl index 831a63d..d019b03 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -9,6 +9,11 @@ examples_dir = joinpath(@__DIR__, "..", "examples") docs_src = joinpath(@__DIR__, "src") master_file = joinpath(docs_src, "examples.md") +# Define a preprocessing function +function replace_gl_with_cairo(content) + return replace(content, "using GLMakie" => "using CairoMakie") +end + # Initialize the master "Examples" page open(master_file, "w") do io write(io, "# Examples\n\nA collection of 2D meshing examples. Note that all the codes are available in the `examples` directory.\n\n") @@ -31,7 +36,8 @@ for file in jl_files Literate.markdown(dest_path, docs_src; documenter=true, credit=false, - name=replace(file, ".jl"=>"") + name=replace(file, ".jl"=>""), + preprocess = replace_gl_with_cairo ) # 3. Read the generated markdown diff --git a/docs/src/index.md b/docs/src/index.md index 4d927eb..158f9e8 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -29,7 +29,7 @@ The code below demonstrates how to implement this using DistMesh in Julia. ```@example introduction using DistMesh -using GLMakie # or Plots, or CairoMakie (optional) +using CairoMakie # or Plots, or GLMakie (optional) fd(p) = sqrt(sum(p.^2)) - 1 # or dcircle(p) - unit circle geometry fh(p) = 1.0 # or huniform(p) - uniform size function From 6e9b036bbf7c65216ebb51b78d71c3e713b0ed20 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 20 Jan 2026 23:01:59 -0800 Subject: [PATCH 26/42] CI build docs on new dev branch. --- .github/workflows/ci.yml | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml index 46a19a8..5504d13 100644 --- a/.github/workflows/ci.yml +++ b/.github/workflows/ci.yml @@ -8,6 +8,7 @@ on: push: branches: - master + - 'v0.2-revamp' tags: '*' jobs: test: @@ -47,7 +48,7 @@ jobs: runs-on: ubuntu-latest steps: - uses: actions/checkout@v4 - - uses: julia-actions/setup-julia@v1 + - uses: julia-actions/setup-julia@v2 with: version: '1' - run: | From f5b09ce41a6f34e35daa901c555bd2e5ee3f39a9 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 20 Jan 2026 23:25:09 -0800 Subject: [PATCH 27/42] Add Literate.jl dependency. --- docs/Project.toml | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/docs/Project.toml b/docs/Project.toml index d693dd8..ff89df3 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -1,8 +1,9 @@ [deps] +CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" DistMesh = "f7ee28b6-bfbf-11e9-3e31-8961b86f052c" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" -CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" +Literate = "98b081ad-f1c9-55d3-8b20-4c87d4299306" [compat] CairoMakie = "0.15" From 156c907781ad5205b8a04f66f41600da04b64c67 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Tue, 20 Jan 2026 23:37:22 -0800 Subject: [PATCH 28/42] Added StaticArrays dependency. --- docs/Project.toml | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/Project.toml b/docs/Project.toml index ff89df3..d94c96e 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -4,6 +4,7 @@ DistMesh = "f7ee28b6-bfbf-11e9-3e31-8961b86f052c" Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4" GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" Literate = "98b081ad-f1c9-55d3-8b20-4c87d4299306" +StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" [compat] CairoMakie = "0.15" From c563daa44bb271c9b27e276220e5ac0f4b5a8ef3 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Wed, 21 Jan 2026 09:26:05 -0800 Subject: [PATCH 29/42] Resolve case-insensitive name conflict (for Windows/MacOS). --- src/distmeshnd/DistMeshND.jl | 2 +- src/distmeshnd/{distmeshnd.jl => core.jl} | 0 2 files changed, 1 insertion(+), 1 deletion(-) rename src/distmeshnd/{distmeshnd.jl => core.jl} (100%) diff --git a/src/distmeshnd/DistMeshND.jl b/src/distmeshnd/DistMeshND.jl index ab16e54..57df97b 100644 --- a/src/distmeshnd/DistMeshND.jl +++ b/src/distmeshnd/DistMeshND.jl @@ -113,7 +113,7 @@ struct HUniform end include("diff.jl") include("pointdistribution.jl") -include("distmeshnd.jl") +include("core.jl") include("tetgen.jl") include("quality.jl") include("decompositions.jl") diff --git a/src/distmeshnd/distmeshnd.jl b/src/distmeshnd/core.jl similarity index 100% rename from src/distmeshnd/distmeshnd.jl rename to src/distmeshnd/core.jl From 2db7d0bc3b95b33d0c1ca4574c0dc6259b8e67f9 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Wed, 21 Jan 2026 15:53:58 -0800 Subject: [PATCH 30/42] Mesh utilities: Improvements, name changes, docstrings. --- docs/src/api.md | 4 ++- src/DistMesh.jl | 2 +- src/meshutils.jl | 85 +++++++++++++++++++++++++++++++++++++++--------- test/runtests.jl | 6 ++-- 4 files changed, 76 insertions(+), 21 deletions(-) diff --git a/docs/src/api.md b/docs/src/api.md index 330b418..03981df 100644 --- a/docs/src/api.md +++ b/docs/src/api.md @@ -66,6 +66,8 @@ huniform ## Mesh utilities: General ```@docs -DistMesh.fixmesh +element_volumes +element_qualities +cleanup_mesh ``` diff --git a/src/DistMesh.jl b/src/DistMesh.jl index dbdf29d..00c8a67 100644 --- a/src/DistMesh.jl +++ b/src/DistMesh.jl @@ -28,7 +28,7 @@ export ddiff, dunion, dintersect export huniform export naca_coeffs, dnaca -export simpqual, simpvol, fixmesh +export element_qualities, element_volumes, cleanup_mesh # Legacy API (Re-exports) export distmeshnd, DistMeshSetup, DistMeshStatistics, HUniform diff --git a/src/meshutils.jl b/src/meshutils.jl index eb9fea9..3a86209 100644 --- a/src/meshutils.jl +++ b/src/meshutils.jl @@ -33,36 +33,89 @@ Returns `1.0`. Default sizing function for uniform meshes. """ huniform(p) = 1 + ################################################################################ ### Element properties ################################################################################ -function simplex_area(el) - if length(el) == 3 # Triangle +""" + element_volume(el) + +Compute the generalized volume (area in 2D, volume in 3D) of a single element. +`el` is a vector of coordinates (e.g. [[x1, y1], [x2, y2], [x3, y3]]). +""" +function element_volume(el) + # Generic simplex handling could go here later. + # For now, explicit checks for standard shapes: + + if length(el) == 3 # Triangle (2D) p12 = el[2] - el[1] p13 = el[3] - el[1] return (p12[1] * p13[2] - p12[2] * p13[1]) / 2 + + elseif length(el) == 4 # Tetrahedron (3D) + error("3D Tetrahedra not yet implemented") + + elseif length(el) == 4 && length(el[1]) == 2 # Example: Quad (2D) logic check + # Quad logic + error("2D Quadrilaterals not yet implemented") + else - @assert "Dimension not implemented" + error("Element type or dimension not supported") end end -function simplex_qual(el) +""" + element_quality(el) + +Compute a quality metric for a single element (normalized 0.0 to 1.0). +Currently implements 2*r/R (radius ratio) for triangles. +""" +function element_quality(el) if length(el) == 3 # Triangle - norm(vec) = sqrt(sum(vec.^2)) - a,b,c = ( norm(el[ix[2]] - el[ix[1]]) for ix in ((1,2),(2,3),(3,1)) ) - r = 0.5*sqrt((b+c-a) * (c+a-b) * (a+b-c) / (a+b+c)) - R = a*b*c / sqrt((a+b+c) * (b+c-a) * (c+a-b) * (a+b-c)) - return 2*r/R + # Lengths of the three edges + a = norm(el[2] - el[1]) + b = norm(el[3] - el[2]) + c = norm(el[1] - el[3]) + + # Semiperimeter + s = (a + b + c) / 2 + + # Area (Heron's formula) for inradius calculation + # area = sqrt(s * (s-a) * (s-b) * (s-c)) + # r = area / s + # R = a*b*c / (4*area) + # Quality = 2*r/R + + # Simplified equivalent formula: + denom = (a * b * c) + if denom ≈ 0 + return 0.0 + end + + numerator = (b + c - a) * (c + a - b) * (a + b - c) + return 8 * (s - a) * (s - b) * (s - c) / (a * b * c) else - @assert "Dimension not implemented" + error("Dimension not implemented") end end -elemwise_feval(m::DMesh, f) = [ f(m.p[tt]) for tt in m.t ] +# Helper to map a function over all elements +_map_elements(m::DMesh, f) = [f(m.p[indices]) for indices in m.t] + +""" + element_qualities(m::DMesh, quality_func=element_quality) + +Return a vector of quality metrics for every element in the mesh. +""" +element_qualities(m::DMesh, f=element_quality) = _map_elements(m, f) + +""" + element_volumes(m::DMesh) -simpqual(m::DMesh, fqual=simplex_qual) = elemwise_feval(m, fqual) -simpvol(m::DMesh) = elemwise_feval(m, simplex_area) +Return a vector of volumes (or areas) for every element in the mesh. +""" +element_volumes(m::DMesh) = _map_elements(m, element_volume) ################################################################################ ### General mesh utilities @@ -74,7 +127,7 @@ snap(x::T, scaling=1, tol=sqrt(eps(T))) where {T <: AbstractFloat} = """ - fixmesh(msh::DMesh) -> (msh::DMesh, ix::Vector{Int}) + cleanup_mesh(msh::DMesh) -> (msh::DMesh, ix::Vector{Int}) Remove duplicate nodes from the mesh `msh` and re-index the connectivity. @@ -92,12 +145,12 @@ A `NamedTuple` `(msh, ix)` where: # Example ```julia -clean_msh, = fixmesh(dirty_msh) # Ignoring the index output (ix) +clean_msh, = cleanup_mesh(dirty_msh) # Ignoring the index output (ix) ``` """ -function fixmesh(msh::DMesh) +function cleanup_mesh(msh::DMesh) p, t = msh # 1. Snap nodes to a grid to identify duplicates (relative tolerance) diff --git a/test/runtests.jl b/test/runtests.jl index 561a6ed..c588cb9 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -25,9 +25,9 @@ function check_mesh(msh::DMesh; np::Int=0, nt::Int=0, area::Real=0.0, areatol::R nt > 0 && @test length(msh.t) == nt # 2. Compute Geometric Properties - total_area = sum(simpvol(msh)) - min_q = minimum(simpqual(msh)) - has_negative_area = minimum(simpvol(msh)) < 0.0 + total_area = sum(element_volumes(msh)) + min_q = minimum(element_qualities(msh)) + has_negative_area = minimum(element_volumes(msh)) < 0.0 # 3. Check Winding / Topology @test !has_negative_area From ea0c1c5b9c8fe0044b1ba0afdc6041607cddf49d Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Wed, 21 Jan 2026 16:09:13 -0800 Subject: [PATCH 31/42] Figure size updates in docs. --- docs/make.jl | 5 +++-- docs/src/index.md | 1 + 2 files changed, 4 insertions(+), 2 deletions(-) diff --git a/docs/make.jl b/docs/make.jl index d019b03..0042863 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -11,9 +11,10 @@ master_file = joinpath(docs_src, "examples.md") # Define a preprocessing function function replace_gl_with_cairo(content) - return replace(content, "using GLMakie" => "using CairoMakie") + return replace(content, "using GLMakie" => "using CairoMakie\nCairoMakie.activate!(type=\"png\", px_per_unit=1.0); # hide") end - +# update_theme!(size=(600, 450)) # For setting figure size instead of px_per_unit + # Initialize the master "Examples" page open(master_file, "w") do io write(io, "# Examples\n\nA collection of 2D meshing examples. Note that all the codes are available in the `examples` directory.\n\n") diff --git a/docs/src/index.md b/docs/src/index.md index 158f9e8..ecab0c4 100644 --- a/docs/src/index.md +++ b/docs/src/index.md @@ -30,6 +30,7 @@ The code below demonstrates how to implement this using DistMesh in Julia. ```@example introduction using DistMesh using CairoMakie # or Plots, or GLMakie (optional) +CairoMakie.activate!(type="png", px_per_unit=1.0) # hide fd(p) = sqrt(sum(p.^2)) - 1 # or dcircle(p) - unit circle geometry fh(p) = 1.0 # or huniform(p) - uniform size function From c81a83378bfe9d54447e847dacd4cb6eb037128c Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Wed, 21 Jan 2026 17:53:34 -0800 Subject: [PATCH 32/42] Remove legacy N-D code and finalize v0.2.0 transition This commit officially retires the legacy `distmeshnd` module to establish a clean slate for version 0.2.0. Major Changes: - Removed `src/distmeshnd/` and `bench/` directories. - Removed legacy exports (`distmeshnd`, `HUniform`, `DistMeshSetup`) from the main module. - Cleaned `Project.toml` dependencies (removed packages used only by legacy code). - Updated `test/runtests.jl` to exclude legacy test suites. Documentation & Licensing: - Switched `LICENSE` to standard MIT (removed previous dual-copyright notices). - Updated `Project.toml` authors list. - Updated README.md with a "Legacy Support" notice advising users to pin v0.1 for old functionality. - Removed documentation pages and references related to the legacy implementation. --- LICENSE | 4 +- Project.toml | 10 +- README.md | 24 +-- bench/.gitignore | 3 - bench/benchmarks.jl | 90 ---------- bench/hilbert_perf.jl | 12 -- bench/perf.jl | 76 -------- bench/profile.jl | 12 -- bench/util.jl | 31 ---- docs/make.jl | 5 +- docs/src/api.md | 1 - docs/src/distmeshnd.md | 55 ------ src/DistMesh.jl | 28 +-- src/distmeshnd/DistMeshND.jl | 125 ------------- src/distmeshnd/core.jl | 266 ---------------------------- src/distmeshnd/decompositions.jl | 74 -------- src/distmeshnd/diff.jl | 7 - src/distmeshnd/hilbertsort.jl | 145 --------------- src/distmeshnd/pointdistribution.jl | 37 ---- src/distmeshnd/quality.jl | 137 -------------- src/distmeshnd/tetgen.jl | 22 --- test/runtests.jl | 115 ------------ test/vals.jl | 4 - 23 files changed, 21 insertions(+), 1262 deletions(-) delete mode 100644 bench/.gitignore delete mode 100644 bench/benchmarks.jl delete mode 100644 bench/hilbert_perf.jl delete mode 100644 bench/perf.jl delete mode 100644 bench/profile.jl delete mode 100644 bench/util.jl delete mode 100644 docs/src/distmeshnd.md delete mode 100644 src/distmeshnd/DistMeshND.jl delete mode 100644 src/distmeshnd/core.jl delete mode 100644 src/distmeshnd/decompositions.jl delete mode 100644 src/distmeshnd/diff.jl delete mode 100644 src/distmeshnd/hilbertsort.jl delete mode 100644 src/distmeshnd/pointdistribution.jl delete mode 100644 src/distmeshnd/quality.jl delete mode 100644 src/distmeshnd/tetgen.jl delete mode 100644 test/vals.jl diff --git a/LICENSE b/LICENSE index 9f59c10..b9b3466 100644 --- a/LICENSE +++ b/LICENSE @@ -1,8 +1,6 @@ MIT License -Copyright (c) 2004-2012 Per-Olof Persson -Copyright (c) 2019 Steve Kelly -Copyright (c) 2026 Per-Olof Persson +Copyright (c) 2004-2026 Per-Olof Persson Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal diff --git a/Project.toml b/Project.toml index 4d3a4c5..d3fa1a8 100644 --- a/Project.toml +++ b/Project.toml @@ -1,15 +1,13 @@ name = "DistMesh" uuid = "f7ee28b6-bfbf-11e9-3e31-8961b86f052c" version = "0.2.0" -authors = ["Steve Kelly ", "Per-Olof Persson "] +authors = ["Per-Olof Persson "] license = "MIT" [deps] Delaunator = "466f8f70-d5e3-4806-ac0b-a54b75a91218" -GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" -TetGen = "c5d3f3f7-f850-59f6-8a2e-ffc6dc1317ea" [weakdeps] CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" @@ -25,18 +23,14 @@ DistMeshPlotsExt = "Plots" CairoMakie = "0.15" Delaunator = "0.1" GLMakie = "0.11, 0.12, 0.13" -GeometryBasics = "0.5" LinearAlgebra = "1" Plots = "1" StaticArrays = "1.9" -TetGen = "2" julia = "1.10" [extras] -GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" -TetGen = "c5d3f3f7-f850-59f6-8a2e-ffc6dc1317ea" CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" [targets] -test = ["Test", "GeometryBasics", "TetGen", "CairoMakie"] +test = ["Test", "CairoMakie"] diff --git a/README.md b/README.md index 2249500..ca12ffc 100644 --- a/README.md +++ b/README.md @@ -9,7 +9,19 @@ Primary use cases include Finite Element Analysis (FEA), computational fluid dyn --- -## Quick Start (2D) +## Note on Version 0.2.0 + +Version 0.2.0 represents a major rewrite of `DistMesh.jl`, focusing on replicating the original 2D code but with better performance, native Julia implementations, and integration with the Makie/Plots ecosystems. **This version is now fully MIT licensed.** + +**Legacy Support:** The original N-dimensional meshing code port has been retired in this version to allow for a cleaner architecture. If you require the legacy `distmeshnd` functionality, please pin your package version to v0.1: + +```julia +] add DistMesh@0.1 +``` + +--- + +## Quick Start The core function `distmesh2d` generates a mesh based on a distance function, a relative size function, an initial edge length, and a bounding box. @@ -40,14 +52,6 @@ For more details and extensive examples, please see the [DistMesh documentation] --- -## 3D Support & Legacy Code - -The original versions of this package featured an N-dimensional implementation (`distmeshnd`) which supports 3D generation. This functionality is still available via the internal `DistMeshND` module. - -Please note that the modern 2D functionality has been rewritten independently to prioritize performance and type stability. Consequently, the API style for 3D generation differs from the 2D interface. Future work will focus on harmonizing these implementations. - ---- - ## Background This package is a Julia port of the [DistMesh](http://persson.berkeley.edu/distmesh/) algorithm developed by [Per-Olof Persson](http://persson.berkeley.edu/). Significant improvements have been made to performance and type stability compared to the original MATLAB implementation. The algorithm is described in the following publications: @@ -55,8 +59,6 @@ This package is a Julia port of the [DistMesh](http://persson.berkeley.edu/distm * P.-O. Persson, G. Strang, *[A Simple Mesh Generator in MATLAB](https://persson.berkeley.edu/distmesh/persson04mesh.pdf)*. SIAM Review, Volume 46 (2), pp. 329-345, June 2004. * P.-O. Persson, *[Mesh Generation for Implicit Geometries](https://persson.berkeley.edu/thesis/persson-thesis-color.pdf)*. Ph.D. thesis, Department of Mathematics, MIT, Dec 2004. -Details on the implementation of the legacy N-dimensional generator can be found in this [technical report](https://sjkellyorg.files.wordpress.com/2020/11/distmesh_sjkelly.pdf). - --- ## Related Packages diff --git a/bench/.gitignore b/bench/.gitignore deleted file mode 100644 index ff7ba74..0000000 --- a/bench/.gitignore +++ /dev/null @@ -1,3 +0,0 @@ -*.csv -*.json -output/* diff --git a/bench/benchmarks.jl b/bench/benchmarks.jl deleted file mode 100644 index 2b4e886..0000000 --- a/bench/benchmarks.jl +++ /dev/null @@ -1,90 +0,0 @@ -using DistMesh -using BenchmarkTools -using Plots -using Dates -using Descartes -using GeometryBasics -#using JLD -#using HDF5 - -include("util.jl") - -#= -In addition to performance we want to measure the convergence rate. -Ideally this will be somewhat smooth without many fast changes. - -- ttol (retriangulation critera) -- deltat (displacement applied per iteration) - -termination critera: -- ptol (termination critera) -- mamove delta (TBD) - -output for each trial: -- store input parameters (above) -- DistMeshStatistics -- Benchmark Stats -=# - -#= -TODO: - -- Make sure plots have equal yscale -- Consistent quality histogram bins - -Solids: -- Box -- Sphere -- Shelled Sphere -- Torus -- deadmau5 (mouse-head with sphere subtracted from sphere, bad metric distance function) -=# - -# -# Distance Functions -# - -torus(v) = (sqrt(v[1]^2+v[2]^2)-0.5)^2 + v[3]^2 - 0.25 # torus - - -# Define a parent BenchmarkGroup to contain our suite -const suite = BenchmarkGroup() - -# all solids should be in -2:2 for each axis for ease - -println("Benchmarking DistMesh.jl...") - -# -# Algorithms to benchmark -# - -timestamp = Dates.format(now(), "yyyy-mm-ddTHH_MM") -# generate an orthogonal test suite -for ttol in 0.01:0.01:0.05, deltat in 0.05:0.05:0.1, el = 0.1:0.05:0.2 - rt = time() - result = distmesh(torus, - HUniform(), - el, - DistMeshSetup(deltat=deltat,ttol=ttol,distribution=:packed), - origin = GeometryBasics.Point{3,Float64}(-2), - widths = GeometryBasics.Point{3,Float64}(4), - stats=true) - running_time = time() - rt # approximate, since we mostly care about convergence factors - item = "torus$timestamp" - folder = joinpath(@__DIR__, "output") - !isdir(folder) && mkdir(folder) - folder = joinpath(folder, "$item") - !isdir(folder) && mkdir(folder) - param_str = "_ttol=$(ttol)_deltat=$(deltat)_el=$(el)" - # save plots - plotout(result.stats, DistMesh.triangle_qualities(result.points,result.tetrahedra), folder, param_str) - # save dataset as JLD - # jldopen("$folder/$item.jld", "w") do file - # g = g_create(file, param_str) - # g["points"] = p - # g["tets"] = t - # g["stats"] = s - # g["running_time"] = running_time - # end - println(param_str) -end diff --git a/bench/hilbert_perf.jl b/bench/hilbert_perf.jl deleted file mode 100644 index a452fc0..0000000 --- a/bench/hilbert_perf.jl +++ /dev/null @@ -1,12 +0,0 @@ -using DistMesh -using BenchmarkTools -using StaticArrays - -a = [rand(SVector{3,Float64}) for i = 1:50000] - -function test_hilbert(a) - b = copy(a) - DistMesh.hilbertsort!(b) -end - -@benchmark test_hilbert(a) diff --git a/bench/perf.jl b/bench/perf.jl deleted file mode 100644 index 56e7cab..0000000 --- a/bench/perf.jl +++ /dev/null @@ -1,76 +0,0 @@ -using DistMesh -using BenchmarkTools -using GeometryBasics - -# -# DistMesh.jl Performance Benchmarks -# - -# Define a parent BenchmarkGroup to contain our suite -const suite = BenchmarkGroup() -suite["Torus"] = BenchmarkGroup() -suite["Sphere"] = BenchmarkGroup() -suite["Box"] = BenchmarkGroup() - -println("Benchmarking DistMesh.jl...") - -# -# Algorithms to benchmark -# - -algos = [DistMeshSetup(deltat=0.1, distribution=:packed), - DistMeshSetup(distribution=:packed), - DistMeshSetup(deltat=0.1, distribution=:packed,sort=true), - DistMeshSetup(distribution=:packed,sort=true)] - -fn_torus(v) = (sqrt(v[1]^2+v[2]^2)-0.5)^2 + v[3]^2 - 0.25 # torus -fn_sphere(v) = sqrt(sum(v.^2)) -1 -# -# Benchmark algorithms -# - -for algo in algos - for el in (0.15,0.2) - suite["Torus"][string(algo)*" edge="*string(el)] = - @benchmarkable distmesh(fn_torus, - HUniform(), - $el, - $algo, - origin = GeometryBasics.Point{3,Float64}(-2), - widths = GeometryBasics.Point{3,Float64}(4), - stats=false) - suite["Sphere"][string(algo)*" edge="*string(el)] = - @benchmarkable distmesh(fn_sphere, - HUniform(), - $el, - $algo, - origin = GeometryBasics.Point{3,Float64}(-1), - widths = GeometryBasics.Point{3,Float64}(2), - stats=false) - end -end - -# If a cache of tuned parameters already exists, use it, otherwise, tune and cache -# the benchmark parameters. Reusing cached parameters is faster and more reliable -# than re-tuning `suite` every time the file is included. -paramspath = joinpath(dirname(@__FILE__), "params.json") - -if isfile(paramspath) - loadparams!(suite, BenchmarkTools.load(paramspath)[1], :evals); -else - tune!(suite) - BenchmarkTools.save(paramspath, params(suite)); -end - -# -# Perform benchmarks and print results -# - -results = run(suite) - -for trial in results - ctx = IOContext(stdout, :verbose => true, :compact => false) - println(ctx) - println(ctx, trial.first) - println(ctx, trial.second) -end diff --git a/bench/profile.jl b/bench/profile.jl deleted file mode 100644 index d4c5b45..0000000 --- a/bench/profile.jl +++ /dev/null @@ -1,12 +0,0 @@ -using DistMesh -using GeometryBasics -using PProf -using Profile - -fn_sphere(v) = sqrt(sum(v.^2)) -1 -algo = DistMeshSetup(distribution=:packed) - -distmesh(fn_sphere,HUniform(),0.15,algo,origin = GeometryBasics.Point{3,Float64}(-1),widths = GeometryBasics.Point{3,Float64}(2),stats=false) - -Profile.clear() -@pprof distmesh(fn_sphere,HUniform(),0.15,algo,origin = GeometryBasics.Point{3,Float64}(-1),widths = GeometryBasics.Point{3,Float64}(2),stats=false) diff --git a/bench/util.jl b/bench/util.jl deleted file mode 100644 index b4388a0..0000000 --- a/bench/util.jl +++ /dev/null @@ -1,31 +0,0 @@ - -function plotout(statsdata, qualities, folder, name) - - qual_hist = Plots.histogram(qualities, title = "Quality", bins=30, legend=false) - # avg_plt = Plots.plot(statsdata.average_qual, title = "Average Tri Quality", legend=false, ylabel="Quality") - # vline!(statsdata.retriangulations, line=(0.2, :dot, [:red])) - - # med_plt = Plots.plot(statsdata.median_qual, title = "Median Tri Quality", legend=false, ylabel="Quality") - # vline!(statsdata.retriangulations, line=(0.2, :dot, [:red])) - - # min_plt = Plots.plot(statsdata.minimum_qual, title = "Minimum Tri Quality", legend=false, ylabel="Quality") - # vline!(statsdata.retriangulations, line=(0.2, :dot, [:red])) - - # max_plt = Plots.plot(statsdata.maximum_qual, title = "Maximum Tri Quality", legend=false, ylabel="Quality") - # vline!(statsdata.retriangulations, line=(0.2, :dot, [:red])) - data = hcat(statsdata.average_volume_edge_ratio, statsdata.min_volume_edge_ratio, statsdata.max_volume_edge_ratio) - - tq_plt = Plots.plot(data, title = "Tet Quality", legend=true, label=["Avg","Min","Max"], ylabel="Vol/Edge Ratio") - vline!(statsdata.retriangulations, line=(0.2, :dot, [:red])) - - maxdp_plt = Plots.plot(statsdata.maxdp, title = "Max Displacement", legend=false, ylabel="Edge Displacement") - vline!(statsdata.retriangulations, line=(0.2, :dot, [:red])) - - maxmove_plt = Plots.plot(statsdata.maxmove, title = "Max Move", legend=false, ylabel="Point Displacement") - vline!(statsdata.retriangulations, line=(0.2, :dot, [:red])) - - plt = Plots.plot(tq_plt,maxdp_plt,maxmove_plt,layout=(3,1), xlabel="Iteration") - - savefig(plt, "$folder/result_stat$name.svg") - savefig(qual_hist, "$folder/result_qual$name.svg") -end diff --git a/docs/make.jl b/docs/make.jl index 0042863..7ce5b6c 100644 --- a/docs/make.jl +++ b/docs/make.jl @@ -61,12 +61,11 @@ end makedocs( sitename = "DistMesh.jl", modules = [DistMesh], - authors = "Steve Kelly and Per-Olof Persson ", + authors = "Per-Olof Persson ", pages = [ "Home" => "index.md", "Examples" => "examples.md", - "API Reference" => "api.md", - "Legacy (N-D & Theory)" => "distmeshnd.md", + "API Reference" => "api.md" ], warnonly = [:missing_docs], format = Documenter.HTML( diff --git a/docs/src/api.md b/docs/src/api.md index 03981df..eec30b0 100644 --- a/docs/src/api.md +++ b/docs/src/api.md @@ -6,7 +6,6 @@ The primary interface for generating meshes and handling the resulting data stru ```@docs distmesh2d -distmesh DMesh as_arrays diff --git a/docs/src/distmeshnd.md b/docs/src/distmeshnd.md deleted file mode 100644 index 8c51d17..0000000 --- a/docs/src/distmeshnd.md +++ /dev/null @@ -1,55 +0,0 @@ -# Legacy & Theory - -The `DistMeshND` module preserves the original N-dimensional algorithm structure, closely mirroring the original MATLAB implementation. - -## Background & Theory - -DistMesh.jl implements **simplex refinement** on signed distance functions. The algorithm was first presented in 2004 by Per-Olof Persson and assumes the geometry is defined by any function that returns a signed distance (negative inside, positive outside). - -### What is Simplex Refinement? - -In layman's terms, a **simplex** is a triangle in 2D or a tetrahedron in 3D. When simulating physics, you often want a mesh of simplices that offers: - -* **Accurate approximation** of boundaries and features. -* **Adaptive mesh sizes** to improve accuracy where needed. -* **High Element Quality** (Near-regular simplices). - -DistMesh is designed to address these needs using a physical analogy: it treats the mesh nodes as particles connected by springs (edges). The nodes "relax" into a configuration that balances the internal spring forces with the geometric constraints of the Signed Distance Function. - -### Algorithm Overview - -1. **Initial Distribution:** Nodes are distributed stochastically or on a grid inside the bounding box. -2. **Delaunay Triangulation:** Nodes are connected to form a mesh topology. -3. **Force Equilibrium:** Edges act as springs. Nodes move to minimize energy. -4. **Boundary Projection:** Nodes that move outside the geometry are projected back onto the zero-level set (the boundary) using the SDF gradient. -5. **Refinement:** Triangles that are too large (according to your size function) are split; edges that are too short are collapsed. - -### Comparison to Other Methods - -DistMesh generally has a very low memory footprint and avoids complex boundary patching logic found in advancing front methods. Since the global state of simplex qualities is optimized in each iteration, this often leads to very high-quality meshes for smooth geometries. - -Unlike surface-based meshing tools (which require Piecewise Linear Complexes/STLs as input), DistMesh works directly on mathematical functions or volumetric data, making it ideal for topology optimization, level-set methods, and image-based meshing. - -### Differences from MATLAB - -Given the same parameters, the Julia implementation of DistMesh will generally perform significantly faster than the original MATLAB implementation. - -* **Memory:** Reduced allocation overhead. -* **Triangulation:** While MATLAB uses QHull, Julia's ecosystem (and this package's legacy N-D modules) often leverages `VoronoiDelaunay.jl` or `MiniQhull` for efficiency. - -### Working with Signed Distance Functions - -You can define SDFs manually (as shown in the examples), or generate them from data. Useful libraries for turning gridded/level-set data into SDFs include: - -* [Interpolations.jl](https://github.com/JuliaMath/Interpolations.jl) -* AdaptiveDistanceFields.jl - ---- - -## Legacy API - -These functions belong to the internal `DistMeshND` module. - -```@autodocs -Modules = [DistMesh.DistMeshND] -``` diff --git a/src/DistMesh.jl b/src/DistMesh.jl index 00c8a67..4bb38af 100644 --- a/src/DistMesh.jl +++ b/src/DistMesh.jl @@ -4,21 +4,16 @@ using StaticArrays using LinearAlgebra using Delaunator -# --- 1. Load Types --- +# --- Load Types --- include("dmesh.jl") -# --- 2. Load Utilities and 2D Implementation --- +# --- Load Utilities and 2D Implementation --- include("distfuncs.jl") include("meshutils.jl") include("distmesh2d.jl") -# --- 3. Load Legacy 3D Module --- -include("distmeshnd/DistMeshND.jl") -using .DistMeshND +# --- Exports --- -# --- 4. Exports --- - -# New API export DMesh, as_arrays export distmesh2d @@ -30,21 +25,4 @@ export naca_coeffs, dnaca export element_qualities, element_volumes, cleanup_mesh -# Legacy API (Re-exports) -export distmeshnd, DistMeshSetup, DistMeshStatistics, HUniform - -# --- 5. Deprecations --- - -""" - distmesh(args...) - -[DEPRECATED] Please use `distmeshnd` for 3D meshes or `distmesh2d` for 2D meshes. -""" -function distmesh(args...; kwargs...) - Base.depwarn("distmesh() is deprecated. Please use `distmeshnd()` or `distmesh2d()`.", :distmesh) - return distmeshnd(args...; kwargs...) -end - -export distmesh - end # module diff --git a/src/distmeshnd/DistMeshND.jl b/src/distmeshnd/DistMeshND.jl deleted file mode 100644 index 57df97b..0000000 --- a/src/distmeshnd/DistMeshND.jl +++ /dev/null @@ -1,125 +0,0 @@ -module DistMeshND - -using LinearAlgebra, - TetGen -using GeometryBasics -using GeometryBasics: Triangle, Tetrahedron, Mesh, Polytope, Point - -const tetpairs = ((1,2),(1,3),(1,4),(2,3),(2,4),(3,4)) -const tettriangles = ((1,2,3),(1,2,4),(2,3,4),(1,3,4)) - -abstract type AbstractDistMeshAlgorithm end - -""" - DistMeshSetup - -Takes Keyword arguments as follows: - - iso (default: 0): Value of which to extract the isosurface, inside surface is negative - deltat (default: 0.1): the fraction of edge displacement to apply each iteration - sort (default:false): If true and no fixed points, sort points using a hilbert sort. - sort_interval (default:20) Use hilbert sort after the specified retriangulations - distribution (default: :regular) Initial point distribution, either :regular or :packed. -""" -struct DistMeshSetup{T} <: AbstractDistMeshAlgorithm - iso::T - deltat::T - ttol::T - ptol::T - sort::Bool # use hilbert sort to cache-localize points - sort_interval::Int # retriangulations before resorting - nonlinear::Bool # uses nonlinear edge force - distribution::Symbol # intial point distribution -end - -function DistMeshSetup(;iso=0, - ptol=.001, - deltat=0.05, - ttol=0.02, - sort=false, - sort_interval=20, - nonlinear=false, - distribution=:regular) - T = promote_type(typeof(iso),typeof(ptol),typeof(deltat), typeof(ttol)) - DistMeshSetup{T}(iso, - deltat, - ttol, - ptol, - sort, - sort_interval, - nonlinear, - distribution) -end - -""" - DistMeshQuality - -Use Tetrahedral quality analysis to control the meshing process - - iso (default: 0): Value of which to extract the iso surface, inside negative - deltat (default: 0.1): the fraction of edge displacement to apply each iteration -""" -struct DistMeshQuality{T} <: AbstractDistMeshAlgorithm - iso::T - deltat::T - filter_less_than::T # Remove tets less than the given quality - #allow_n_regressions::Int # Might want this - termination_quality::T # Once achieved, terminate - sort::Bool # use hilbert sort to cache-localize points - sort_interval::Int # retriangulations before resorting - nonlinear::Bool # uses nonlinear edge force - distribution::Symbol # intial point distribution -end - -function DistMeshQuality(;iso=0, - deltat=0.05, - filter_less_than=0.02, - termination_quality=0.3, - sort=false, - sort_interval=20, - nonlinear=true, - distribution=:regular) - DistMeshQuality(iso, - deltat, - filter_less_than, - termination_quality, - sort, - sort_interval, - nonlinear, - distribution) -end - -""" - DistMeshStatistics - - Statistics about the convergence between iterations -""" -struct DistMeshStatistics{T} - maxmove::Vector{T} # max point move in an iteration - maxdp::Vector{T} # max displacmeent induced by an edge - min_volume_edge_ratio::Vector{T} - max_volume_edge_ratio::Vector{T} - average_volume_edge_ratio::Vector{T} - retriangulations::Vector{Int} # Iteration num where retriangulation occured -end - -DistMeshStatistics() = DistMeshStatistics{Float64}([],[],[],[],[],[]) - -""" -Uniform edge length function. -""" -struct HUniform end - - -include("diff.jl") -include("pointdistribution.jl") -include("core.jl") -include("tetgen.jl") -include("quality.jl") -include("decompositions.jl") -include("hilbertsort.jl") - -#export distmeshsurface -export distmeshnd, DistMeshSetup, DistMeshStatistics, HUniform - -end # module diff --git a/src/distmeshnd/core.jl b/src/distmeshnd/core.jl deleted file mode 100644 index ca0a55b..0000000 --- a/src/distmeshnd/core.jl +++ /dev/null @@ -1,266 +0,0 @@ -""" - distmeshnd - 3D Mesh Generator using Signed Distance Functions. - Arguments: - fdist: Distance function - fh: Edge length function - h: Smallest edge length - - Returns: - p: Node positions - t: Triangle indices - - - Example: Unit ball - d(p) = sqrt(sum(p.^2))-1 - p,t = distmeshnd(d,huniform,0.2) -""" -function distmeshnd(fdist::Function, - fh::Union{Function,HUniform}, - h::Number, - setup::AbstractDistMeshAlgorithm=DistMeshSetup(); - origin=GeometryBasics.Point{3,Float64}(-1,-1,-1), - widths=GeometryBasics.Point{3,Float64}(2,2,2), - fix=nothing, - stats=false) - # TODO: tetgen only handles Float64 - VT = GeometryBasics.Point{3,Float64} - if isa(fix, Nothing) - fp = nothing - else - fp = convert(Vector{VT}, fix) - end - o = VT(origin...) - w = VT(widths...) - distmeshnd(fdist, fh, h, setup, o, w, fp, Val(stats), VT) -end - -""" - DistMeshResult - -A struct returned from the `distmeshnd` function that includes point, simplex, -and interation statistics. -""" -struct DistMeshResult{PT, TT, STATS} - points::Vector{PT} - tetrahedra::Vector{TT} - stats::STATS -end - -function distmeshnd(fdist::Function, - fh, - h::Number, - setup::DistMeshSetup, - origin, - widths, - fix, - ::Val{stats}, - ::Type{VertType}) where {VertType, stats} - - geps=1e-1*h+setup.iso # parameter for filtering tets outside bounds and considering for max displacment of a node - - # static parameter info - non_uniform = isa(fh, Function) # so we can elide fh calls - have_fixed = !isa(fix, Nothing) - - #ptol=.001; ttol=.1; L0mult=1+.4/2^(dim-1); deltat=.2; geps=1e-1*h; - - # initialize Vertex Arrays - # the first N points in the array correspond to'fix' points that do not move - if have_fixed - p = copy(fix) - else - p = VertType[] - end - - pt_dists = eltype(VertType)[] - - # setup the initial point distribution specified in setup - point_distribution!(fdist,p,pt_dists,h, setup, origin, widths, VertType) - - # Result struct for holding points, simplices, and iteration statistics - result = DistMeshResult(p, - GeometryBasics.SimplexFace{4,Int32}[], - stats ? DistMeshStatistics() : nothing) - - # initialize arrays - pair_set = Set{Tuple{Int32,Int32}}() # set used for ensure we have a unique set of edges - pair = Tuple{Int32,Int32}[] # edge indices (Int32 since we use Tetgen) - dp = zeros(VertType, length(p)) # displacement at each node - bars = VertType[] # the vector of each edge - L = eltype(VertType)[] # vector length of each edge - L0 = non_uniform ? eltype(VertType)[] : nothing # desired edge length computed by dh (edge length function) - maxmove = typemax(eltype(VertType)) # stores an iteration max movement for retriangulation - - # information on each iteration - lcount = 0 # iteration counter - triangulationcount = 0 # triangulation counter - num_pairs = 0 - - @inbounds while true - # if large move, retriangulation - if maxmove>setup.ttol*h - - # compute a new delaunay triangulation - retriangulate!(fdist, result, geps, setup, triangulationcount, pt_dists) - - num_pairs = tet_to_edges!(pair, pair_set, result.tetrahedra) # Describe each edge by a unique pair of nodes - - # resize arrays for new pair count - if length(L) < num_pairs - resize!(bars, num_pairs) - resize!(L, num_pairs) - non_uniform && resize!(L0, num_pairs) - end - - triangulationcount += 1 - stats && push!(result.stats.retriangulations, lcount) - end - - compute_displacements!(fh, dp, pair, num_pairs, L, L0, bars, result.points, setup, VertType) - - # Zero out forces on fix points - if have_fixed - for i in eachindex(fix) - dp[i] = zero(VertType) - end - end - - # apply point forces and - # bring outside points back to the boundary - maxdp = typemin(eltype(VertType)) - maxmove = typemin(eltype(VertType)) - for i in eachindex(p) - - p0 = p[i] # store original point location - p[i] = p[i].+setup.deltat.*dp[i] # apply displacements to points - - # Check if we are verifiably within the bounds and use this value - # to avoid recomputing fdist. This increases performance greatly on - # complex distance functions and large node counts - move = sqrt(sum((p[i]-p0).^2)) # compute movement from the displacement - d_est = pt_dists[i] + move # apply the movement to our cache point - d = d_est < -geps ? d_est : fdist(result.points[i]) # determine if we need correct or approximate distance - - if d < -geps - maxdp = max(maxdp, setup.deltat*sqrt(sum(dp[i].^2))) - end - - if d <= setup.iso - pt_dists[i] = d # store distance - maxmove = max(move,maxmove) - else - # bring points back to boundary if outside using central difference - p[i] = p[i] .- centraldiff(fdist,p[i]).*(d+setup.iso) - maxmove = max(sqrt(sum((p[i]-p0).^2)), maxmove) - pt_dists[i] = setup.iso # ideally - end - end - - # increment iteration counter - lcount = lcount + 1 - - # save iteration stats - if stats - push!(result.stats.maxmove,maxmove) - push!(result.stats.maxdp,maxdp) - min_v_edge, avg_v_edge, max_v_edge = volume_edge_stats(result.points,result.tetrahedra) - push!(result.stats.min_volume_edge_ratio, min_v_edge) - push!(result.stats.average_volume_edge_ratio, avg_v_edge) - push!(result.stats.max_volume_edge_ratio, max_v_edge) - end - - # Termination criterion - if maxdp p2 ? (p2,p1) : (p1,p2) - if !in(elt, pair_set) - push!(pair_set, elt) - num_pair += 1 - pair[num_pair] = elt - end - end - end - - # sort the edge pairs for better point lookup - sort!(view(pair, 1:num_pair)) - - return num_pair # return the number of pairs -end - -function bitpack(xi,yi) - (unsafe_trunc(UInt64, xi) << 32) | unsafe_trunc(UInt64, yi) -end diff --git a/src/distmeshnd/diff.jl b/src/distmeshnd/diff.jl deleted file mode 100644 index c0e11ea..0000000 --- a/src/distmeshnd/diff.jl +++ /dev/null @@ -1,7 +0,0 @@ -function centraldiff(f::Function,p::VT) where VT - deps = sqrt(eps(eltype(VT))) - dx = (f(p.+VT(deps,0,0)) - f(p.-VT(deps,0,0))) - dy = (f(p.+VT(0,deps,0)) - f(p.-VT(0,deps,0))) - dz = (f(p.+VT(0,0,deps)) - f(p.-VT(0,0,deps))) - grad = VT(dx,dy,dz)./(2deps) #normalize? -end diff --git a/src/distmeshnd/hilbertsort.jl b/src/distmeshnd/hilbertsort.jl deleted file mode 100644 index 7cced41..0000000 --- a/src/distmeshnd/hilbertsort.jl +++ /dev/null @@ -1,145 +0,0 @@ -# This file is licensed under the MIT "Expat" License. - -# implementing scale-free Hilbert ordering. Real all about it here: -# http://doc.cgal.org/latest/Spatial_sorting/index.html - -# original implementation in: -# https://github.com/JuliaGeometry/GeometricalPredicates.jl -# The GeometricalPredicates.jl package is licensed under the MIT "Expat" License: -# Copyright (c) 2014: Ariel Keselman. - -# modifications for StaticArrays: sjkelly (Under terms of MIT License) - -const coordinatex = 1 -const coordinatey = 2 -const coordinatez = 3 -next2d(c) = c % 2 + 1 -next3d(c) = c % 3 + 1 -nextnext3d(c) = (c + 1) % 3 + 1 - -const forward = true -const backward = false - -function select!(direction, coord, v::Array{T,1}, k::Integer, lo::Integer, hi::Integer, carry::CT) where {T<:AbstractVector, CT} - #lo <= k <= hi || error("select index $k is out of range $lo:$hi") - if direction == forward - @inbounds while lo < hi - if isone(hi-lo) - if v[hi][coord] < v[lo][coord] - v[lo], v[hi] = v[hi], v[lo] - if CT !== Nothing; carry[lo], carry[hi] = carry[hi], carry[lo]; end - end - return #v[k] - end - pivot = v[(lo+hi)>>>1] - i, j = lo, hi - while true - pivot_elt = pivot[coord] - while v[i][coord] < pivot_elt; i += 1; end - while pivot_elt < v[j][coord]; j -= 1; end - i <= j || break - v[i], v[j] = v[j], v[i] - if CT !== Nothing; carry[i], carry[j] = carry[j], carry[i]; end - i += 1; j -= 1 - end - if k <= j - hi = j - elseif i <= k - lo = i - else - return #pivot - end - end - else - @inbounds while lo < hi - if isone(hi-lo) - if v[hi][coord] > v[lo][coord] - v[lo], v[hi] = v[hi], v[lo] - if CT !== Nothing; carry[lo], carry[hi] = carry[hi], carry[lo]; end - end - return #v[k] - end - pivot = v[(lo+hi)>>>1] - i, j = lo, hi - while true - pivot_elt = pivot[coord] - while v[i][coord] > pivot_elt; i += 1; end - while pivot_elt > v[j][coord]; j -= 1; end - i <= j || break - v[i], v[j] = v[j], v[i] - if CT !== Nothing; carry[i], carry[j] = carry[j], carry[i]; end - i += 1; j -= 1 - end - if k <= j - hi = j - elseif i <= k - lo = i - else - return #pivot - end - end - end - #return v[lo] - nothing -end - - -# 2D version -# function hilbertsort!(directionx::AbstractDirection, directiony::AbstractDirection, coordinate::AbstractCoordinate, a::Array{T,1}, lo::Int64, hi::Int64, lim::Int64=4) where T<:AbstractPoint2D -# hi-lo <= lim && return a - -# i2 = (lo+hi)>>>1 -# i1 = (lo+i2)>>>1 -# i3 = (i2+hi)>>>1 - -# select!(directionx, coordinate, a, i2, lo, hi) -# select!(directiony, next2d(coordinate), a, i1, lo, i2) -# select!(!directiony, next2d(coordinate), a, i3, i2, hi) - -# hilbertsort!(directiony, directionx, next2d(coordinate), a, lo, i1, lim) -# hilbertsort!(directionx, directiony, coordinate, a, i1, i2, lim) -# hilbertsort!(directionx, directiony, coordinate, a, i2, i3, lim) -# hilbertsort!(!directiony, !directionx, next2d(coordinate), a, i3, hi, lim) - -# return a -# end - -function hilbertsort!(directionx, directiony, directionz, coordinate, a::Vector, lo::Integer, hi::Integer, lim::Integer, carry) - hi-lo <= lim && return a - - i4 = (lo+hi)>>>1 - i2 = (lo+i4)>>>1 - i1 = (lo+i2)>>>1 - i3 = (i2+i4)>>>1 - i6 = (i4+hi)>>>1 - i5 = (i4+i6)>>>1 - i7 = (i6+hi)>>>1 - - select!(directionx, coordinate, a, i4, lo, hi, carry) - select!(directiony, next3d(coordinate), a, i2, lo, i4, carry) - select!(directionz, nextnext3d(coordinate), a, i1, lo, i2, carry) - select!(!directionz, nextnext3d(coordinate), a, i3, i2, i4, carry) - select!(!directiony, next3d(coordinate), a, i6, i4, hi, carry) - select!(directionz, nextnext3d(coordinate), a, i5, i4, i6, carry) - select!(!directionz, nextnext3d(coordinate), a, i7, i6, hi, carry) - - hilbertsort!( directionz, directionx, directiony, nextnext3d(coordinate), a, lo, i1, lim, carry) - hilbertsort!( directiony, directionz, directionx, next3d(coordinate), a, i1, i2, lim, carry) - hilbertsort!( directiony, directionz, directionx, next3d(coordinate), a, i2, i3, lim, carry) - hilbertsort!( directionx, !directiony, !directionz, coordinate, a, i3, i4, lim, carry) - hilbertsort!( directionx, !directiony, !directionz, coordinate, a, i4, i5, lim, carry) - hilbertsort!(!directiony, directionz, !directionx, next3d(coordinate), a, i5, i6, lim, carry) - hilbertsort!(!directiony, directionz, !directionx, next3d(coordinate), a, i6, i7, lim, carry) - hilbertsort!(!directionz, !directionx, directiony, nextnext3d(coordinate), a, i7, hi, lim, carry) - - return a -end - -#hilbertsort!(a::Array{T,1}) where {T<:AbstractPoint2D} = hilbertsort!(backward, backward, coordinatey, a, 1, length(a)) -#hilbertsort!(a::Array{T,1}, lo::Int64, hi::Int64, lim::Int64) where {T<:AbstractPoint2D} = hilbertsort!(backward, backward, coordinatey, a, lo, hi, lim) -""" -Hilbert Sorting. If `carry` is specified, this array will be permuted in line with the -specified array. -""" -hilbertsort!(a::Vector, carry=nothing) = hilbertsort!(backward, backward, backward, coordinatez, a, 1, length(a), 8, carry) -hilbertsort!(a::Vector, lo::Int64, hi::Int64, lim::Int64) = hilbertsort!(backward, backward, backward, coordinatey, a, lo, hi, lim) diff --git a/src/distmeshnd/pointdistribution.jl b/src/distmeshnd/pointdistribution.jl deleted file mode 100644 index 5b74d8b..0000000 --- a/src/distmeshnd/pointdistribution.jl +++ /dev/null @@ -1,37 +0,0 @@ - -function simplecubic!(fdist, points, dists, h, iso, origin, widths, ::Type{VertType}) where VertType - @inbounds for xi = origin[1]:h:(origin[1]+widths[1]), yi = origin[2]:h:(origin[2]+widths[2]), zi = origin[3]:h:(origin[3]+widths[3]) - point = VertType(xi,yi,zi) - d = fdist(point) - if d < iso - push!(points,point) - push!(dists, d) - end - end -end - -function facecenteredcubic!(fdist, points, dists, h, iso, origin, widths, ::Type{VertType}) where VertType - # face-centered cubic point distribution - r = h/2 - counts = round.(widths./h).+2 - @inbounds for xi = -1:Int(counts[1]), yi = -1:Int(counts[2]), zi = -1:Int(counts[3]) - point = VertType(2xi+((yi+zi)%2), sqrt(3)*(yi+(zi%2)/3),2*sqrt(6)*zi/3).*r + origin - d = fdist(point) - if d < iso - push!(points,point) - push!(dists, d) - end - end -end - -function point_distribution!(fdist, p, pt_dists, h, setup, origin, widths, ::Type{VertType}) where VertType - map!(fdist, pt_dists, p) # cache to store point locations so we can minimize fdist calls - - # add points to p based on the initial distribution - if setup.distribution === :regular - simplecubic!(fdist, p, pt_dists, h, setup.iso, origin, widths, VertType) - elseif setup.distribution === :packed - # face-centered cubic point distribution - facecenteredcubic!(fdist, p, pt_dists, h, setup.iso, origin, widths, VertType) - end -end diff --git a/src/distmeshnd/quality.jl b/src/distmeshnd/quality.jl deleted file mode 100644 index 3ca45e6..0000000 --- a/src/distmeshnd/quality.jl +++ /dev/null @@ -1,137 +0,0 @@ -""" -Determine the quality of a triangle given 3 points. - -Points must be 3D. -""" -function triqual(p1, p2, p3) - d12 = p2 - p1 - d13 = p3 - p1 - d23 = p3 - p2 - n = cross(d12,d13) - vol = sqrt(sum(n.^2)) - den = dot(d12,d12) + dot(d13,d13) + dot(d23,d23) - return sqrt(3)*2*vol/den -end - -function triangle_qualities(p,tets) - tris = NTuple{3,Int}[] - tets_to_tris!(tris, tets) - qualities = Vector{Float64}(undef,length(tris)) - triangle_qualities!(tris,qualities,p,tets) -end - -function triangle_qualities!(tris,triset,qualities,p,tets) - tets_to_tris!(tris,triset,tets) - resize!(qualities, length(tris)) - for i in eachindex(tris) - tp = tris[i] - qualities[i] = triqual(p[tp[1]], p[tp[2]], p[tp[3]]) - end - qualities -end - -function triangle_qualities!(tris::Vector,qualities::Vector,p,tets) - triangle_qualities!(tris,Set{eltype(tris)}(),qualities,p,tets) -end - -const ⋅ = dot -const × = cross - -function dihedral(p0,p1,p2,p3) - b1 = p1 - p0 - b2 = p2 - p1 - b3 = p3 - p2 - - abs(atan(((b1×b2)×(b2×b3))⋅normalize(b2), (b1×b2)⋅(b2×b3))) -end - -""" - Compute dihedral angles within a tetrahedra - radians -""" -function dihedral_angles(p,t) - AT = eltype(eltype(p)) - nangs = length(t)*6 - a = fill(zero(AT), nangs) - for i in 1:length(t) - t1, t2, t3, t4 = t[i] - a[i*6-5] = dihedral(p[t1],p[t2],p[t3],p[t4]) - a[i*6-4] = dihedral(p[t1],p[t2],p[t4],p[t3]) - a[i*6-3] = dihedral(p[t2],p[t1],p[t4],p[t3]) - a[i*6-2] = dihedral(p[t2],p[t3],p[t4],p[t1]) - a[i*6-1] = dihedral(p[t2],p[t1],p[t3],p[t4]) - a[i*6] = dihedral(p[t3],p[t1],p[t2],p[t4]) - end - a -end - -""" - Compute the minimum dihedral angle within a tetrahedra - radians -""" -function min_dihedral_angles(p,t) - AT = eltype(eltype(p)) - nangs = length(t) - a = fill(zero(AT), nangs) - for i in 1:length(t) - t1, t2, t3, t4 = t[i] - d = (dihedral(p[t1],p[t2],p[t3],p[t4]), - dihedral(p[t1],p[t2],p[t4],p[t3]), - dihedral(p[t2],p[t1],p[t4],p[t3]), - dihedral(p[t2],p[t3],p[t4],p[t1]), - dihedral(p[t2],p[t1],p[t3],p[t4]), - dihedral(p[t3],p[t1],p[t2],p[t4])) - a[i] = minimum(d) - end - a -end - -""" - Computes the volume and edge-length ratio from four given points -""" -function volume_edge_ratio(a,b,c,d) - t = a .- d - u = b .- d - v = c .- d - volume = t[1]*(u[2]*v[3]-v[2]*u[3])-u[1]*(t[2]*v[3]-v[2]*t[3])+v[1]*(t[2]*u[3]-u[2]*t[3]) - edges = (t,u,v,a.-b,b.-c,a.-c) - lengths = dot.(edges,edges) - l_rms = sqrt(sum(lengths)/6) - return sqrt(2)*abs(volume)/(l_rms^3) -end - -""" - -returns the extrema elements (min, max) of the sampled qualities -""" -function volume_edge_extrema(points::Vector{T},tets) where {T} - n = length(tets) - min_q = typemax(eltype(T)) - max_q = typemin(eltype(T)) - @inbounds for i = 1:n - tet = tets[i] - q = volume_edge_ratio(points[tet[1]],points[tet[2]],points[tet[3]],points[tet[4]]) - min_q = min(q,min_q) - max_q = max(q,max_q) - end - min_q, max_q -end - -""" - -returns the (min, avg, max) of the sampled qualities -""" -function volume_edge_stats(points::Vector{T},tets) where {T} - n = length(tets) - min_q = typemax(eltype(T)) - max_q = typemin(eltype(T)) - sum_q = zero(eltype(T)) - @inbounds for i = 1:n - tet = tets[i] - q = volume_edge_ratio(points[tet[1]],points[tet[2]],points[tet[3]],points[tet[4]]) - min_q = min(q,min_q) - max_q = max(q,max_q) - sum_q += q - end - min_q, sum_q/n, max_q -end diff --git a/src/distmeshnd/tetgen.jl b/src/distmeshnd/tetgen.jl deleted file mode 100644 index cdc750f..0000000 --- a/src/distmeshnd/tetgen.jl +++ /dev/null @@ -1,22 +0,0 @@ -function delaunayn(points) - # M - no merge of close facets - # J - no jettison of points - # B - No boundary info - # N - No node output - # F - No face and edge info - # I - No mesh iteration numbers - # Q - Quiet - tetio = tetrahedralize(TetGen.JLTetGenIO(points), "JBNFIQ") - tetio -end - -function delaunayn_nosort(points) - tetio = tetrahedralize(TetGen.JLTetGenIO(points), "Qb/1") # Q- Quiet - tetio -end - -# needs some tweaks, gives garbage results, might need to twek the julia wrapper? -function reconstruct!(points, tets) - tetio = tetrahedralize(TetGen.JLTetGenIO(points,tetrahedrons=tets), "Qr") # Q- Quiet, r- retriangulate - tetio -end diff --git a/test/runtests.jl b/test/runtests.jl index c588cb9..7ca9a56 100644 --- a/test/runtests.jl +++ b/test/runtests.jl @@ -1,6 +1,5 @@ using DistMesh using Test -using GeometryBasics using CairoMakie # ------------------------------------------------------------------------------ @@ -84,117 +83,3 @@ const EXAMPLES_DIR = joinpath(@__DIR__, "..", "examples") end end end - -# ------------------------------------------------------------------------------ -# DistMesh ND Tests -# ------------------------------------------------------------------------------ - -include("vals.jl") - -const DistMeshND = DistMesh.DistMeshND - -@testset "point distributions" begin - vlen(a,b) = sqrt(sum((a-b).^2)) - @testset "simple cubic" begin - pts = [] - dists = [] - f(x) = -1 - DistMeshND.simplecubic!(f, pts, dists, 0.5, 0, Point{3,Float64}(0),Point{3,Float64}(1),Point{3,Float64}) - @test length(pts) == 27 - @test length(dists) == 27 - @test isapprox(vlen(pts[1],pts[2]),0.5) - @test length(pts) == length(unique(pts)) - end - - @testset "face centered cubic" begin - pts = [] - dists = [] - f(x) = -1 - DistMeshND.facecenteredcubic!(f, pts, dists, 0.5, 0, Point{3,Float64}(0),Point{3,Float64}(1),Point{3,Float64}) - @test length(pts) == 216 - @test length(dists) == 216 - @test isapprox(vlen(pts[1],pts[2]),0.5) - @test length(pts) == length(unique(pts)) - end - -end - -@testset "quality analysis" begin - @testset "triangles" begin - @test DistMeshND.triqual([0,0,0],[1,0,0],[0,1,0]) == DistMeshND.triqual([0,0,0],[2,0,0],[0,2,0]) - @test DistMeshND.triqual([0,0,0],[1,0,1],[0,1,1]) == DistMeshND.triqual([0,0,0],[2,0,2],[0,2,2]) - @test DistMeshND.triqual([0,0,0],[2,0,0],[1,sqrt(3),0]) ≈ 1 - @test DistMeshND.triqual([0,0,0],[1,sqrt(3),0],[2,0,0]) ≈ 1 - end - @testset "volume-length" begin - pts = ([1,0,-1/sqrt(2)], [-1,0,-1/sqrt(2)], [0,1,1/sqrt(2)], [0,-1,1/sqrt(2)]) - pts2 = ([1,1,1], [1,-1,-1], [-1,1,-1], [-1,-1,1]) - pts_degenerate = ([1,1,1], [1,1,1], [-1,1,-1], [-1,-1,1]) - @test DistMeshND.volume_edge_ratio(pts...) ≈ 1 - @test DistMeshND.volume_edge_ratio((pts.*2)...) ≈ 1 - @test DistMeshND.volume_edge_ratio((pts.*1e-6)...) ≈ 1 - @test isnan(DistMeshND.volume_edge_ratio((pts.*0)...)) - @test DistMeshND.volume_edge_ratio(pts2...) ≈ 1 - @test DistMeshND.volume_edge_ratio((pts2.*2)...) ≈ 1 - @test DistMeshND.volume_edge_ratio(pts_degenerate...) == 0 - - end -end - -@testset "decompositions" begin - @testset "tets to triangles" begin - simps = [[4,3,2,1],[5,4,3,2],[1,2,3,4]] - tris = Tuple{Int,Int,Int}[] - DistMeshND.tets_to_tris!(tris,simps) - @test tris == [(1, 2, 3), (1, 2, 4), (1, 3, 4), (2, 3, 4), (2, 3, 5), (2, 4, 5), (3, 4, 5)] - end -end - -@testset "hilbert sort" begin - rng = 0:0.3:1 - a = Vector{Vector{Float64}}(undef,length(rng)^3) - i = 1 - for xi in rng, yi in rng, zi in rng - a[i] = [xi,yi,zi] - i += 1 - end - DistMeshND.hilbertsort!(a) - @test a == hilbert_a -end - -@testset "distmesh 3D" begin - d(p) = sqrt(sum(p.^2))-1 - result = distmeshnd(d,HUniform(),0.2) - @test length(result.points) == 485 - @test length(result.tetrahedra) == 2207 - - result = distmeshnd(d,HUniform(),0.2, DistMeshSetup(distribution=:packed)) - @test length(result.points) == 742 - @test length(result.tetrahedra) == 3472 - - # test stats is not messing - result = distmeshnd(d,HUniform(),0.2, stats=true) - @test length(result.points) == 485 - @test length(result.tetrahedra) == 2207 - - result = distmeshnd(d,HUniform(),0.4, stats=true) - @test length(result.points) == 56 - @test length(result.tetrahedra) == 186 - #for fn in fieldnames(typeof(result.stats)) - # @test isapprox(getproperty(result.stats,fn), getproperty(stat_04,fn)) - #end -end - -@testset "dihedral metrics" begin - d(p) = sqrt(sum(p.^2))-1 - result = distmeshnd(d,HUniform(),0.2) - p = result.points - t = result.tetrahedra - all_angs = DistMeshND.dihedral_angles(p,t) - min_angs = DistMeshND.min_dihedral_angles(p,t) - ax = extrema(all_angs) - mx = extrema(min_angs) - @test ax[1] == mx[1] - @test all(ax .≈ (0.023502688273828173, 3.104396619996953)) - @test all(mx .≈ (0.023502688273828173, 1.2044902180168893)) -end diff --git a/test/vals.jl b/test/vals.jl deleted file mode 100644 index 193aa30..0000000 --- a/test/vals.jl +++ /dev/null @@ -1,4 +0,0 @@ -#stat_04 = DistMeshStatistics{Float64}([0.015861808197171447, 0.04333997993833317, 0.030539364290593892, 0.03136281119397018, 0.02563981053478331, 0.013146443917954281, 0.01175223918624788, 0.010072460884465097, 0.010095555217344735, 0.01013796999511984, 0.010140632643274205, 0.010304587497854923, 0.010462582532303984, 0.010716139899621396, 0.011021054862975449, 0.011240323884294448, 0.01142232855445764, 0.011612249108897528, 0.011811272270023909, 0.012034107769143534, 0.012056898531952622, 0.012293750640801487, 0.01253910968482863, 0.013004095618999076, 0.013252841175879744, 0.013917719093503656, 0.013396847948485273, 0.003189020157222165, 0.001562109707501573, 0.0009931741145458414, 0.0006511321515956363, 0.0004797453102939885, 0.00037832020260625596], [0.01586180819717149, 0.043339979938333134, 0.030539364290593937, 0.025048818294013803, 0.025639810534783355, 0.013146443917954269, 0.011752239186247897, 0.010072460884465097, 0.010095555217344726, 0.0101379699951199, 0.010140632643274243, 0.010304587497854942, 0.01046258253230403, 0.010716139899621346, 0.011021054862975494, 0.011240323884294462, 0.011422328554457682, 0.01161224910889749, 0.011811272270023897, 0.012034107769143534, 0.012056898531952602, 0.012293750640801451, 0.012539109684828593, 0.012245282734261766, 0.0023300852630041935, 0.002447933509399279, 0.0025695121186121712, 0.002338682036472209, 0.0015621097075015642, 0.0009931741145458226, 0.0006511321515956257, 0.00044189161676361335, 0.00031167049211313627], [0.8513479333014904, 0.7999266605934156, 0.8237832569578655, 0.817521012694373, 0.8296223294441304, 0.8782925269541574, 0.8923366367078434, 0.8927651653134971, 0.8945352521480744, 0.8976771953430919, 0.9006192563827091, 0.9015511578835772, 0.9023325838482263, 0.9021231128462143, 0.9013980826173323, 0.9013870765654909, 0.9016622807520963, 0.9018313595924459, 0.9018918673592288, 0.9018399155548923, 0.9017386119698663, 0.9014401063090378, 0.9010116089076747, 0.8993122456162714, 0.8985981708401958, 0.8955172651439618, 0.8942894809739554, 0.8907754718921969, 0.8909268818143122, 0.8910108579548632, 0.8910571422908532, 0.8910820499895338, 0.8910946964871009], [0.8652080743786591, 0.8543837234573923, 0.8623250243903223, 0.8600554459902974, 0.8623728487909205, 0.8675526892316004, 0.86813448792801, 0.867886604152207, 0.8683165255416818, 0.8741409899736776, 0.8874376497339312, 0.8871929206150294, 0.8868023977155903, 0.8862767476859909, 0.8855800788413576, 0.8847996249062478, 0.883963567834448, 0.8830513999087894, 0.8820448631022926, 0.8809192341868274, 0.8797024210613953, 0.8783238518802771, 0.8767724740675475, 0.8749410864744815, 0.872938454517967, 0.8706218244939238, 0.8702910360100947, 0.8684338642874472, 0.8683585516484286, 0.8682860253670031, 0.8682092206857535, 0.8681310653003876, 0.8680532945221214], [0.8042665470208608, 0.030882544034837138, 0.031205915063413674, 0.039027484580454345, 0.043185620349155414, 0.7801798146155217, 0.7757327592563474, 0.7895610286647429, 0.7982628961615663, 0.8019173511962595, 0.8080797261120612, 0.8113232071425015, 0.8141475611173873, 0.8164017608524986, 0.8162646723007843, 0.8161431245874965, 0.8160398512387739, 0.8159572530416423, 0.8158854172957702, 0.8158108155078492, 0.8157818549664978, 0.8157456416732362, 0.8157018839829728, 0.8155656386618806, 0.8154254644984282, 0.8152833339192274, 0.8151391827922918, 0.7527856381383334, 0.7513436255829244, 0.7502417424228109, 0.749393575220651, 0.7487360804668232, 0.7482227724278689], [1.0000000000000002, 1.0, 0.9999999999288185, 0.9999999997538248, 0.9999999998746554, 0.9999999996769505, 0.9999999998056341, 0.9999999998989167, 0.9999999999633605, 0.9999999999958346, 0.9999999999853654, 0.9999999999148561, 0.9999999997622445, 0.9999999995007761, 0.9999999991000814, 0.999999999251637, 0.9999999989511745, 0.9999999983301885, 0.9999999974434121, 0.9999999963425825, 0.9999999951246715, 0.9999999937977475, 0.9999999924659485, 0.9999999911705475, 0.9999999900045999, 0.9999999889813795, 0.9999999881198527, 0.999999983355277, 0.9999999885253779, 0.9999999920525013, 0.9999999944812701, 0.999999996164262, 0.9999999973343159], [0.567656495859004, 0.001208133246415821, 5.807412554687958e-5, 0.0007585537896351211, 0.005144029841366791, 1.8622515759872645e-5, 0.0010187380481615181, 0.00472431489407814, 0.0044099961715646846, 0.004097353626958525, 0.0037928020570145785, 0.0035002143173518386, 0.0032400946364245587, 0.0010802784097499337, 0.0009467684016039907, 0.0008722065889398544, 0.0015103488748075698, 0.0016375144330289203, 0.0012347159490814106, 0.0008279310464794467, 0.004262842381860203, 0.004971613172964763, 0.005683081137010508, 0.0023835115478611003, 0.002942999395935075, 0.0018751049144915893, 0.001311668048234658, 0.0003334346940654691, 0.000338146509556331, 0.0003375729016325274, 0.00033346089771292493, 0.0003270922983339331, 0.0003193882554204471] -#,[0.9993197499803357, 0.996275531043326, 0.9935584654924047, 0.9886977699392009, 0.9901266852334549, 0.9905268840250959, 0.9925334319042799, 0.9942877035837783, 0.9952835828669422, 0.9958803224524336, 0.9962760032478873, 0.9966123241717426, 0.9969339673790191, 0.9972731371313256, 0.9976289891233671, 0.9979765868142796, 0.9983021513556015, 0.998608051528163, 0.9988921395426992, 0.9991511627731727, 0.9994013273534111, 0.9996092165494008, 0.9997746356452248, 0.9998898901508024, 0.9999685361050338, 0.9999993773318173, 0.9999883870491219, 0.9999811777994916, 0.9999449029670939, 0.9999048076517231, 0.9998698615833159, 0.9998419637859888, 0.9998207131917966] -#, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27]) -hilbert_a = Array{Float64,1}[[0.9, 0.9, 0.9], [0.6, 0.6, 0.9], [0.6, 0.9, 0.9], [0.6, 0.6, 0.6], [0.9, 0.9, 0.6], [0.9, 0.6, 0.6], [0.6, 0.9, 0.6], [0.9, 0.6, 0.9], [0.6, 0.3, 0.9], [0.9, 0.3, 0.9], [0.6, 0.3, 0.6], [0.9, 0.0, 0.9], [0.9, 0.0, 0.6], [0.9, 0.3, 0.6], [0.6, 0.0, 0.9], [0.6, 0.0, 0.6], [0.3, 0.0, 0.6], [0.0, 0.0, 0.6], [0.0, 0.0, 0.9], [0.0, 0.3, 0.6], [0.0, 0.3, 0.9], [0.3, 0.3, 0.9], [0.3, 0.0, 0.9], [0.3, 0.3, 0.6], [0.0, 0.6, 0.6], [0.0, 0.6, 0.9], [0.3, 0.6, 0.6], [0.3, 0.9, 0.9], [0.3, 0.6, 0.9], [0.0, 0.9, 0.6], [0.3, 0.9, 0.6], [0.3, 0.9, 0.3], [0.3, 0.9, 0.0], [0.0, 0.9, 0.9], [0.0, 0.9, 0.3], [0.3, 0.6, 0.3], [0.0, 0.9, 0.0], [0.3, 0.6, 0.0], [0.0, 0.6, 0.3], [0.0, 0.6, 0.0], [0.3, 0.3, 0.0], [0.0, 0.3, 0.3], [0.3, 0.0, 0.0], [0.3, 0.3, 0.3], [0.0, 0.0, 0.0], [0.0, 0.0, 0.3], [0.0, 0.3, 0.0], [0.3, 0.0, 0.3], [0.9, 0.0, 0.3], [0.6, 0.0, 0.3], [0.9, 0.3, 0.3], [0.6, 0.0, 0.0], [0.6, 0.3, 0.3], [0.9, 0.0, 0.0], [0.6, 0.3, 0.0], [0.9, 0.3, 0.0], [0.6, 0.6, 0.3], [0.6, 0.6, 0.0], [0.9, 0.6, 0.0], [0.9, 0.6, 0.3], [0.6, 0.9, 0.3], [0.9, 0.9, 0.0], [0.9, 0.9, 0.3], [0.6, 0.9, 0.0]] From 1c0feb2baf0a94b7a5b2a9b5010aa16e6a245d7b Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Thu, 22 Jan 2026 10:29:11 -0800 Subject: [PATCH 33/42] Adding back weak dependency on GeometryBasics (for the GLMakie extension). --- Project.toml | 5 +++-- 1 file changed, 3 insertions(+), 2 deletions(-) diff --git a/Project.toml b/Project.toml index d3fa1a8..f615dc0 100644 --- a/Project.toml +++ b/Project.toml @@ -1,8 +1,8 @@ name = "DistMesh" uuid = "f7ee28b6-bfbf-11e9-3e31-8961b86f052c" +license = "MIT" version = "0.2.0" authors = ["Per-Olof Persson "] -license = "MIT" [deps] Delaunator = "466f8f70-d5e3-4806-ac0b-a54b75a91218" @@ -10,6 +10,7 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" [weakdeps] +GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" GLMakie = "e9467ef8-e4e7-5192-8a1a-b1aee30e663a" Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" @@ -29,8 +30,8 @@ StaticArrays = "1.9" julia = "1.10" [extras] -Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0" +Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" [targets] test = ["Test", "CairoMakie"] From dad2ad03e4013fdec2b1945829faf9f6a0aab2dd Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Fri, 23 Jan 2026 13:03:39 -0800 Subject: [PATCH 34/42] Adding missing GeometryBasics dependency in main Project.toml. --- Project.toml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/Project.toml b/Project.toml index f615dc0..d7a9bbf 100644 --- a/Project.toml +++ b/Project.toml @@ -17,7 +17,7 @@ Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" [extensions] DistMeshCairoMakieExt = "CairoMakie" -DistMeshGLMakieExt = "GLMakie" +DistMeshGLMakieExt = ["GLMakie", "GeometryBasics"] DistMeshPlotsExt = "Plots" [compat] From f87eb49355aea4c41fa0d1318d8b48628ac4ba7d Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Fri, 23 Jan 2026 13:04:22 -0800 Subject: [PATCH 35/42] Add examples environment with frozen dependencies --- examples/Manifest.toml | 1643 ++++++++++++++++++++++++++++++++++++++++ examples/Project.toml | 5 + 2 files changed, 1648 insertions(+) create mode 100644 examples/Manifest.toml create mode 100644 examples/Project.toml diff --git a/examples/Manifest.toml b/examples/Manifest.toml new file mode 100644 index 0000000..340abaf --- /dev/null +++ b/examples/Manifest.toml @@ -0,0 +1,1643 @@ +# This file is machine-generated - editing it directly is not advised + +julia_version = "1.12.4" +manifest_format = "2.0" +project_hash = "f945ad02627f75bbc9cad0b57cd87af37c76158a" + +[[deps.AbstractFFTs]] +deps = ["LinearAlgebra"] +git-tree-sha1 = "d92ad398961a3ed262d8bf04a1a2b8340f915fef" +uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c" +version = "1.5.0" + + [deps.AbstractFFTs.extensions] + AbstractFFTsChainRulesCoreExt = "ChainRulesCore" + AbstractFFTsTestExt = "Test" + + [deps.AbstractFFTs.weakdeps] + ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4" + Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40" + +[[deps.AbstractTrees]] +git-tree-sha1 = "2d9c9a55f9c93e8887ad391fbae72f8ef55e1177" +uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c" +version = "0.4.5" + +[[deps.Adapt]] +deps = ["LinearAlgebra", "Requires"] +git-tree-sha1 = "7e35fca2bdfba44d797c53dfe63a51fabf39bfc0" +uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e" +version = "4.4.0" +weakdeps = ["SparseArrays", "StaticArrays"] + + [deps.Adapt.extensions] + AdaptSparseArraysExt = "SparseArrays" + AdaptStaticArraysExt = "StaticArrays" + +[[deps.AdaptivePredicates]] +git-tree-sha1 = "7e651ea8d262d2d74ce75fdf47c4d63c07dba7a6" +uuid = "35492f91-a3bd-45ad-95db-fcad7dcfedb7" +version = "1.2.0" + +[[deps.AliasTables]] +deps = ["PtrArrays", "Random"] +git-tree-sha1 = "9876e1e164b144ca45e9e3198d0b689cadfed9ff" +uuid = "66dad0bd-aa9a-41b7-9441-69ab47430ed8" +version = "1.1.3" + +[[deps.Animations]] +deps = ["Colors"] +git-tree-sha1 = "e092fa223bf66a3c41f9c022bd074d916dc303e7" +uuid = "27a7e980-b3e6-11e9-2bcd-0b925532e340" +version = "0.4.2" + +[[deps.ArgTools]] +uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f" +version = "1.1.2" + +[[deps.Artifacts]] +uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33" +version = "1.11.0" + +[[deps.Automa]] +deps = ["PrecompileTools", "SIMD", "TranscodingStreams"] +git-tree-sha1 = "a8f503e8e1a5f583fbef15a8440c8c7e32185df2" +uuid = "67c07d97-cdcb-5c2c-af73-a7f9c32a568b" +version = "1.1.0" + +[[deps.AxisAlgorithms]] +deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"] +git-tree-sha1 = 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a/examples/Project.toml b/examples/Project.toml new file mode 100644 index 0000000..006f1dc --- /dev/null +++ b/examples/Project.toml @@ -0,0 +1,5 @@ +[deps] +DistMesh = "f7ee28b6-bfbf-11e9-3e31-8961b86f052c" +GLMakie = "e9467ef8-e4e7-5192-8a1a-b1aee30e663a" +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" +StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" From 61885283c43b4dbd4c8a15d97da30f20e529627a Mon Sep 17 00:00:00 2001 From: "Viral B. Shah" Date: Sat, 24 Jan 2026 07:25:03 -0500 Subject: [PATCH 36/42] Use v1 of Documenter always. --- docs/Project.toml | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/Project.toml b/docs/Project.toml index d94c96e..7c86727 100644 --- a/docs/Project.toml +++ b/docs/Project.toml @@ -8,3 +8,4 @@ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182" [compat] CairoMakie = "0.15" +Documenter = "1" From 7d81f5a0f04547df258e44d38305f950fa494928 Mon Sep 17 00:00:00 2001 From: "Viral B. Shah" Date: Sat, 24 Jan 2026 07:39:06 -0500 Subject: [PATCH 37/42] Update examples/002-naca_airfoil.jl Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com> --- examples/002-naca_airfoil.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/002-naca_airfoil.jl b/examples/002-naca_airfoil.jl index 786657a..cc9f38b 100644 --- a/examples/002-naca_airfoil.jl +++ b/examples/002-naca_airfoil.jl @@ -13,7 +13,7 @@ const Point2d = SVector{2, Float64} # First, we define the size function for the NACA airfoil. It consists of the minimum of several point sources and constants: # * A point source at the tip of the airfoil, with size `hlead` -# * A point source at the traling edge of the airfoil, with size `htrail` +# * A point source at the trailing edge of the airfoil, with size `htrail` # * A maximum element size in the entire domain `hmax` function hnaca(p; hlead=0.01, htrail=0.04, hmax=2.0) From 24a1c47c64b62498094291fa57822381aa9d320b Mon Sep 17 00:00:00 2001 From: "Viral B. Shah" Date: Sat, 24 Jan 2026 07:39:20 -0500 Subject: [PATCH 38/42] Update examples/002-naca_airfoil.jl Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com> --- examples/002-naca_airfoil.jl | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/002-naca_airfoil.jl b/examples/002-naca_airfoil.jl index cc9f38b..38a9969 100644 --- a/examples/002-naca_airfoil.jl +++ b/examples/002-naca_airfoil.jl @@ -40,7 +40,7 @@ function dm_naca(; hlead=0.01, htrail=0.04, hmax=2.0, circx=2.0, circr=4.0) ## Size function: Given by `hnaca` above hfcn(p) = hnaca(p; hlead=hlead, htrail=htrail, hmax=hmax) - ## Fix points: Add symmetry points for the circle plus the once from `fixnaca` + ## Fix points: Add symmetry points for the circle plus the ones from `fixnaca` fix = Point2d[(1,0),(0,1),(-1,0),(0,-1)] .* circr .+ Point2d[(circx,0)] fix = vcat(fix, fixnaca(htrail=htrail)) From 95a7f00a679587eddf9fcbf8e75c16c57a80d409 Mon Sep 17 00:00:00 2001 From: "Viral B. Shah" Date: Sat, 24 Jan 2026 07:39:50 -0500 Subject: [PATCH 39/42] Update .github/workflows/ci.yml Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com> --- .github/workflows/ci.yml | 1 - 1 file changed, 1 deletion(-) diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml index e843461..6a97620 100644 --- a/.github/workflows/ci.yml +++ b/.github/workflows/ci.yml @@ -5,7 +5,6 @@ on: push: branches: - master - - 'v0.2-revamp' tags: '*' jobs: test: From eb5a8940e7526afa7b32a8fe70de3fbe933c3bc7 Mon Sep 17 00:00:00 2001 From: "Viral B. Shah" Date: Sat, 24 Jan 2026 08:00:22 -0500 Subject: [PATCH 40/42] Revert "Update .github/workflows/ci.yml" This reverts commit 95a7f00a679587eddf9fcbf8e75c16c57a80d409. --- .github/workflows/ci.yml | 1 + 1 file changed, 1 insertion(+) diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml index 6a97620..e843461 100644 --- a/.github/workflows/ci.yml +++ b/.github/workflows/ci.yml @@ -5,6 +5,7 @@ on: push: branches: - master + - 'v0.2-revamp' tags: '*' jobs: test: From 43382c453cecc0f8a17726e678b871d1c6e77bd0 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Mon, 26 Jan 2026 19:40:27 -0800 Subject: [PATCH 41/42] Address Copilot feedback: fix unreachable code and edge cases --- src/distmesh2d.jl | 2 +- src/meshutils.jl | 16 ++++++++++------ 2 files changed, 11 insertions(+), 7 deletions(-) diff --git a/src/distmesh2d.jl b/src/distmesh2d.jl index 7004da8..39e8c0d 100644 --- a/src/distmesh2d.jl +++ b/src/distmesh2d.jl @@ -215,7 +215,7 @@ function distmesh2d(dfcn, hfcn, h0, bbox, pfix=Point2d[]; d = project_nodes!(p, dfcn, deps) # Terminate if small (interior) node movements - converged = maximum(norm.(dp[d.<-geps])) < dptol + converged = maximum(norm.(dp[d.<-geps]); init=0.0) < dptol converged && break end diff --git a/src/meshutils.jl b/src/meshutils.jl index 3a86209..ee767f8 100644 --- a/src/meshutils.jl +++ b/src/meshutils.jl @@ -47,16 +47,19 @@ Compute the generalized volume (area in 2D, volume in 3D) of a single element. function element_volume(el) # Generic simplex handling could go here later. # For now, explicit checks for standard shapes: + + N = length(el) + D = N > 0 ? length(el[1]) : 0 - if length(el) == 3 # Triangle (2D) + if D == 2 && N == 3 # Triangle (2D) p12 = el[2] - el[1] p13 = el[3] - el[1] return (p12[1] * p13[2] - p12[2] * p13[1]) / 2 - elseif length(el) == 4 # Tetrahedron (3D) + elseif D == 3 && N == 4 # Tetrahedron (3D) error("3D Tetrahedra not yet implemented") - elseif length(el) == 4 && length(el[1]) == 2 # Example: Quad (2D) logic check + elseif D == 2 && N == 4 # Example: Quad (2D) logic check # Quad logic error("2D Quadrilaterals not yet implemented") @@ -87,14 +90,12 @@ function element_quality(el) # R = a*b*c / (4*area) # Quality = 2*r/R - # Simplified equivalent formula: denom = (a * b * c) if denom ≈ 0 return 0.0 end - numerator = (b + c - a) * (c + a - b) * (a + b - c) - return 8 * (s - a) * (s - b) * (s - c) / (a * b * c) + return 8 * (s - a) * (s - b) * (s - c) / denom else error("Dimension not implemented") end @@ -155,6 +156,9 @@ function cleanup_mesh(msh::DMesh) # 1. Snap nodes to a grid to identify duplicates (relative tolerance) scaling = maximum(norm.(p)) + if scaling == 0.0 + scaling = 1.0 + end pp = [snap.(p1, scaling) for p1 in p] # 2. Find unique nodes From bbc6cef9b3c156d77ff7627768942ad1a7b1d709 Mon Sep 17 00:00:00 2001 From: Per-Olof Persson Date: Mon, 26 Jan 2026 19:41:41 -0800 Subject: [PATCH 42/42] Remove examples manifest and move readme image to docs assets --- README.md | 2 +- .../src/assets/circle_mesh.png | Bin examples/Manifest.toml | 1643 ----------------- 3 files changed, 1 insertion(+), 1644 deletions(-) rename circle_mesh.png => docs/src/assets/circle_mesh.png (100%) delete mode 100644 examples/Manifest.toml diff --git a/README.md b/README.md index ca12ffc..fd96ff3 100644 --- a/README.md +++ b/README.md @@ -46,7 +46,7 @@ using GLMakie # or Plots, or CairoMakie plot(msh) ``` -![Triangular mesh of the unit circle](circle_mesh.png) +![Triangular mesh of the unit circle](docs/src/assets/circle_mesh.png) For more details and extensive examples, please see the [DistMesh documentation](https://distmesh.juliageometry.org). diff --git a/circle_mesh.png b/docs/src/assets/circle_mesh.png similarity index 100% rename from circle_mesh.png rename to docs/src/assets/circle_mesh.png diff --git a/examples/Manifest.toml b/examples/Manifest.toml deleted file mode 100644 index 340abaf..0000000 --- a/examples/Manifest.toml +++ /dev/null @@ -1,1643 +0,0 @@ -# This file is machine-generated - 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