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mpm_liquid_with_floating_boat.py
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import taichi as ti
ti.init(arch=ti.gpu)
n_particles = 8192
n_grid = 128
dx = 1 / n_grid
dt = 2e-4
p_rho = 1
p_vol = (dx * 0.5)**2
p_mass = p_vol * p_rho
gravity = 9.8
bound = 3
E = 400
x = ti.Vector.field(2, float, n_particles)
v = ti.Vector.field(2, float, n_particles)
C = ti.Matrix.field(2, 2, float, n_particles)
J = ti.field(float, n_particles)
grid_v = ti.Vector.field(2, float, (n_grid, n_grid))
grid_m = ti.field(float, (n_grid, n_grid))
n2_particles = 1024
x2_ = ti.Vector.field(2, float, n2_particles)
x2 = ti.Vector.field(2, float, n2_particles)
x2c = ti.Vector.field(2, float, ())
v2 = ti.Vector.field(2, float, ())
rot = ti.field(float, ())
wrot = ti.field(float, ())
@ti.kernel
def substep():
for i, j in grid_m:
grid_v[i, j] = [0, 0]
grid_m[i, j] = 0
for p in x:
Xp = x[p] / dx
base = int(Xp - 0.5)
fx = Xp - base
w = [0.5 * (1.5 - fx)**2, 0.75 - (fx - 1)**2, 0.5 * (fx - 0.5)**2]
stress = -dt * 4 * E * p_vol * (J[p] - 1) / dx**2
affine = ti.Matrix([[stress, 0], [0, stress]]) + p_mass * C[p]
for i, j in ti.static(ti.ndrange(3, 3)):
offset = ti.Vector([i, j])
dpos = (offset - fx) * dx
weight = w[i].x * w[j].y
grid_v[base + offset] += weight * (p_mass * v[p] + affine @ dpos)
grid_m[base + offset] += weight * p_mass
for i, j in grid_m:
if grid_m[i, j] > 0:
grid_v[i, j] /= grid_m[i, j]
grid_v[i, j].y -= dt * gravity
dist = attractor_pos[None] - dx * ti.Vector([i, j])
grid_v[i, j] += dist / (
0.01 + dist.norm()) * attractor_strength[None] * dt * 10
if i < bound and grid_v[i, j].x < 0:
grid_v[i, j].x = 0
if i > n_grid - bound and grid_v[i, j].x > 0:
grid_v[i, j].x = 0
if j < bound and grid_v[i, j].y < 0:
grid_v[i, j].y = 0
if j > n_grid - bound and grid_v[i, j].y > 0:
grid_v[i, j].y = 0
dis_mass = 0.0
v2_fld = ti.Vector.zero(float, 2)
J2 = 0.0
for p in x2:
Xp = x2[p] / dx
base = int(Xp - 0.5)
fx = Xp - base
w = [0.5 * (1.5 - fx)**2, 0.75 - (fx - 1)**2, 0.5 * (fx - 0.5)**2]
new_v = ti.Vector.zero(float, 2)
new_m = 0.0
for i, j in ti.static(ti.ndrange(3, 3)):
offset = ti.Vector([i, j])
dpos = (offset - fx) * dx
weight = w[i].x * w[j].y
g_v = grid_v[base + offset]
g_m = grid_m[base + offset]
new_v += weight * g_v
new_m += weight * g_m
v2_fld += new_v
J2 += (x2[p]-x2c[None]).cross(new_v)*new_m + (x2[p]-x2c[None]).cross(ti.Vector([0, -gravity * dt]))
dis_mass += new_m
v2_fld /= n2_particles
v2_self = v2[None]
v2_self.y -= dt * gravity
inertia = n2_particles*0.8
ratio_free = dis_mass/p_mass/inertia
ratio = min(ratio_free, 1)
v2[None] = v2_self*(1-ratio) + v2_fld*ratio
floating = 20
v2[None].y += ratio * ratio_free * dt * floating
if (x2c[None].x-w2/2)*n_grid < bound and v2[None].x < 0:
v2[None].x *= -1
if (x2c[None].x+w2/2)*n_grid > n_grid - bound and v2[None].x > 0:
v2[None].x *= -1
if (x2c[None].y-h2/2)*n_grid < bound and v2[None].y < 0:
v2[None].y *= -1
if (x2c[None].y+h2/2)*n_grid > n_grid - bound and v2[None].y > 0:
v2[None].y *= -1
wrot[None] *= (1-ratio*wrot[None]**2*5e-4)
wrot[None] += J2*0.4
rot[None] += wrot[None]*dt
c, s = ti.cos(rot[None]), ti.sin(rot[None])
x2c[None] += dt * v2[None]
for p in x2:
x2[p].x = x2c[None].x + c*x2_[p].x + s*x2_[p].y
x2[p].y = x2c[None].y + -s*x2_[p].x + c*x2_[p].y
for p in x:
Xp = x[p] / dx
base = int(Xp - 0.5)
fx = Xp - base
w = [0.5 * (1.5 - fx)**2, 0.75 - (fx - 1)**2, 0.5 * (fx - 0.5)**2]
new_v = ti.Vector.zero(float, 2)
new_C = ti.Matrix.zero(float, 2, 2)
for i, j in ti.static(ti.ndrange(3, 3)):
offset = ti.Vector([i, j])
dpos = (offset - fx) * dx
weight = w[i].x * w[j].y
g_v = grid_v[base + offset]
new_v += weight * g_v
new_C += 4 * weight * (g_v.outer_product(dpos) / dx**2)
v[p] = new_v
x[p] += dt * v[p]
J[p] *= 1 + dt * new_C.trace()
C[p] = new_C
w2, h2 = 0.2, 0.05
@ti.kernel
def init():
for i in range(n_particles):
x[i] = [ti.random() * 0.7 + 0.2, ti.random() * 0.7 + 0.2]
v[i] = [0, -1]
J[i] = 1
x2c[None] = [0.4, 0.9]
for i in range(n2_particles):
x2_[i] = [ti.random()-0.5, ti.random()-0.5]
x2_[i][0] += (x2_[i][1]+1) * x2_[i][0]
x2_[i][0] = x2_[i][0]/2 *w2
x2_[i][1] = x2_[i][1] *h2
x2_[i]+= [0, 0.1*h2] #bias center
x2[i] = x2_[i] + x2c[None]
v2[None] = [0.0, 0.0]
rot[None] = 20.0
wrot[None] = 10.0
attractor_strength = ti.field(dtype=float, shape=())
attractor_pos = ti.Vector.field(2, dtype=float, shape=())
init()
gui = ti.GUI('floating boat')
# tick=0
while gui.running:
if gui.get_event(ti.GUI.PRESS):
if gui.event.key == 'r': init()
elif gui.event.key in [ti.GUI.ESCAPE, ti.GUI.EXIT]: break
mouse = gui.get_cursor_pos()
gui.circle((mouse[0], mouse[1]), color=0x336699, radius=15)
attractor_pos[None] = [mouse[0], mouse[1]]
attractor_strength[None] = 0
if gui.is_pressed(ti.GUI.LMB):
attractor_strength[None] = 1
if gui.is_pressed(ti.GUI.RMB):
attractor_strength[None] = -1
for s in range(50):
substep()
gui.clear(0x112F41)
gui.circles(x.to_numpy(), radius=1.5, color=0x068587)
gui.circles(x2.to_numpy(), radius=2.0, color=0xED553B)
gui.show()
# tick+=1
# gui.show(f'img/{tick:0>3d}.png')