visualize_function.ipynb

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 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import igl\n",
    "import scipy as sp\n",
    "import numpy as np\n",
    "from meshplot import plot, subplot, interact\n",
    "import meshplot as mp\n",
    "\n",
    "import os\n",
    "root_folder = os.getcwd()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Load sphere mesh"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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       "Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(0.0, 0.0,…"
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      "text/plain": [
       "interactive(children=(Dropdown(description='mesh', options=(('sphere', 0),), value=0), Output()), _dom_classes…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<meshplot.Viewer.Viewer at 0x7f5ef5ecfdf0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## Load a mesh in OFF format\n",
    "v, f = igl.read_triangle_mesh(os.path.join(root_folder, \"data\", \"sphere_s3.off\"))\n",
    "\n",
    "p = mp.plot(v, f, return_plot=True)\n",
    "\n",
    "@mp.interact(mesh=[('sphere', 0)])\n",
    "def ff(mesh):\n",
    "    mp.plot(v, f, plot=p)\n",
    "p\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calculate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import exp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalize_g_weights(N: list[np.array], sigma: float):\n",
    "\tmat = np.zeros((len(N), len(N)))\n",
    "\tmat = np.array([[exp(sigma * N[i][:].dot(N[j][:])) for j in range(len(N))] for i in range(len(N))])\n",
    "\treturn sp.linalg.solve(mat, np.ones(len(N)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def g_value(x, N, w, sigma):\n",
    "\treturn sum([w[i] * exp(sigma * N[i][:].dot(x)) for i in range(len(N))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = [\n",
    "\t\tnp.array([1,0,0]), np.array([-1,0,0]),\n",
    "\t\tnp.array([0,1,0]), np.array([0,-1,0]),\n",
    "\t\tnp.array([0,0,1]), np.array([0,0,-1]),\n",
    "\t]\n",
    "sigma = 4\n",
    "w = normalize_g_weights(N, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "new_v = np.array([x * g_value(x, N, w, sigma) for x in v[:]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(0.0, 0.0,…"
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       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(Dropdown(description='mesh', options=(('displaced', 0), ('sphere', 1)), value=0), Output…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<meshplot.Viewer.Viewer at 0x7f5ef4e67190>"
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     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = mp.plot(new_v, f, return_plot=True)\n",
    "\n",
    "vertices = [new_v, v]\n",
    "\n",
    "@mp.interact(mesh=[('displaced', 0), ('sphere', 1)])\n",
    "def ff(mesh):\n",
    "    mp.plot(vertices[mesh], f, plot=p)\n",
    "p"
   ]
  }
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