290 lines
128 KiB
Plaintext
290 lines
128 KiB
Plaintext
|
{
|
||
|
|
"cells": [
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"# Description\n",
|
||
|
|
"\n",
|
||
|
|
"This notebook intends to gather all the functionalities you'll have to implement for assignment 2.2.\n",
|
||
|
|
"\n",
|
||
|
|
"# Load libraries"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 13,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"import numpy as np\n",
|
||
|
|
"import igl\n",
|
||
|
|
"import meshplot as mp\n",
|
||
|
|
"import time\n",
|
||
|
|
"\n",
|
||
|
|
"import sys as _sys\n",
|
||
|
|
"_sys.path.append(\"../src\")\n",
|
||
|
|
"from elasticsolid import *\n",
|
||
|
|
"from elasticenergy import *\n",
|
||
|
|
"from matplotlib import gridspec\n",
|
||
|
|
"import matplotlib.pyplot as plt\n",
|
||
|
|
"\n",
|
||
|
|
"shadingOptions = {\n",
|
||
|
|
" \"flat\":True,\n",
|
||
|
|
" \"wireframe\":False, \n",
|
||
|
|
"}\n",
|
||
|
|
"\n",
|
||
|
|
"rot = np.array(\n",
|
||
|
|
" [[1, 0, 0 ],\n",
|
||
|
|
" [0, 0, 1],\n",
|
||
|
|
" [0, -1, 0 ]]\n",
|
||
|
|
")"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"# Load mesh\n",
|
||
|
|
"\n",
|
||
|
|
"Several meshes are available for you to play with under `data/`: `ball.obj`, `dinosaur.obj`, and `beam.obj`. You can also uncomment the few commented lines below to manipulate a simple mesh made out of 2 tetrahedra."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 14,
|
||
|
|
"metadata": {
|
||
|
|
"scrolled": false
|
||
|
|
},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"v, _, _, t, _, _ = igl.read_obj(\"../data/beam.obj\")\n",
|
||
|
|
"aabb = np.max(v, axis=0) - np.min(v, axis=0)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"# Linear/Non-Linear Elastic Solid\n",
|
||
|
|
"\n",
|
||
|
|
"## Instantiation\n",
|
||
|
|
"\n",
|
||
|
|
"We first specify the elasticity model to use for the elastic solid, as well as pinned vertices, and volumetric forces."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 15,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"rho = 131 # [kg.m-3]\n",
|
||
|
|
"young = 10e6 # [Pa] \n",
|
||
|
|
"poisson = 0.2\n",
|
||
|
|
"force_mass = np.zeros(shape = (3,))\n",
|
||
|
|
"force_mass[2] = - rho * 9.81\n",
|
||
|
|
"\n",
|
||
|
|
"minX = np.min(v[:, 0])\n",
|
||
|
|
"pin_idx = np.arange(v.shape[0])[v[:, 0] < minX + 0.2*aabb[0]]\n",
|
||
|
|
"\n",
|
||
|
|
"ee = LinearElasticEnergy(young, poisson)\n",
|
||
|
|
"neo_ee = NeoHookeanElasticEnergy(young, poisson)\n",
|
||
|
|
"solid = ElasticSolid(v, t, ee, rho=rho, pin_idx=pin_idx, f_mass=force_mass)\n",
|
||
|
|
"neo_solid = ElasticSolid(v, t, neo_ee, rho=rho, pin_idx=pin_idx, f_mass=force_mass)\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"# Validate Elastic Energy Gradient (Elastic Forces) using Finite Differences on Elastic Energy"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 16,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"fd_validation_elastic(solid)\n",
|
||
|
|
"fd_validation_elastic(neo_solid)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"# Validate External Energy Gradient (External Forces) using Finite Differences on External Energy"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 17,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAD8CAYAAACRkhiPAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAABJUklEQVR4nO29eXybd5Xv/z6SLcn7viS2E2df2qRNk7bQKa3b0pUu7LQMMDMUCjMwzB0ucwe43Au/O7fTucAwM5TOQKFlKUNLKcu0tNDdXWhCliZtsy/OYjuJHe+WbVnb9/fHI8mSLTm2JMeSfd6vl1+NHj3P9/meWn4+Oud8z/mKMQZFURRlfmKb7QkoiqIos4eKgKIoyjxGRUBRFGUeoyKgKIoyj1ERUBRFmceoCCiKosxjcmZ7AtOhsrLSNDY2Jn390NAQBQUF6ZvQLDFX7AC1JROZK3aA2hJmx44dXcaYqnjvZZUINDY2sn379qSvb25upqmpKX0TmiXmih2gtmQic8UOUFvCiMjxRO9pOEhRFGUeM6uegIjYgH8AioHtxpgfz+Z8FEVR5htJewIi8qCIdIrI7nHHbxCRAyJyWES+eJZhbgPqAB/QluxcFEVRlORIxRP4EfAd4CfhAyJiB+4DrsV6qG8TkccBO3DPuOs/DqwCNhtjvicijwHPpzAfRVEUZZokLQLGmJdFpHHc4UuAw8aYFgAReQS4zRhzD3Dz+DFEpA3whl4Gkp2LoiiKkhySShfRkAj81hhzfuj1+4EbjDGfCL3+KHCpMeazCa7PB+4FhoH9xpj74pxzF3AXQE1NzcZHHnkk6fm63W4KCwuTvj5TmCt2gNqSicwVO0BtCXPVVVftMMZsivdeuhPDEudYQpUxxgwDd042oDHmfhE5BdxSVFS0MZklUv0jPrYe7cHv2TMnlovpsrfMZK7YMlfsALVlKqR7iWgb0BD1uh44meZ7TJv23hE++ZPtHO4LzvZUFEVRMop0i8A2YIWILBERB3A78HiqgxpjnjDG3FVSUpLU9cV5lsMz7NcNdBRFUaJJZYnow8BmYJWItInIncYYP/BZ4GlgH/CoMWZPqpMUkVtE5P7+/v6kri/OywVg2JfqTBRFUeYWqawOuiPB8aeAp5KeUfwxnwCe2LRp0yeTub7QkYOIegKKoijjyYq2Eal6AjabUOTMYdinIqAoihJNVohAqjkBgCJXLsP+NE5KURRlDpAVIpCqJwBWXkA9AUVRlFiyQgTS4QkUu3Li5gT+o/kIhzvdqUxPURQla8kKEUgH8TyB/mEf/+/3+/nSr94klcppRVGUbCUrRCAt4aA4OYHeYatt0bZjvTQfPJPKFBVFUbKSrBCBtISD8iauDgqLgE3gm08fIBhUb0BRlPlFVohAOih25eIJgD8w1jqiL1Q99pG3LWbPyQF+t/v0bE1PURRlVsgKEUjX6iAA9+hYTCjsCfzZZY2srCnkn589ECMS6cDrD9JyRhPPiqJkJlkhAulaHQQwMBItApYnUFHg4L9ft4qWM0P8Zld6+9397I/Hue5fXuZU/0hax1UURUkHWSEC6SDsCQx4xhoI9Q17sYkVKrpubQ21xS5eOTT1BPEL+zt4ZOuJSc/ZfXIAf9Dw3L7O5CauKIoyg8wfEXCFRGBkTAR6h72U5OViswkiwtqFxRw4PTil8YwxfO3xvdz91L5JE8qHOqzxnt3bkcLsFUVRZob5IwKhdtLRnkDvsI+yfEfk9eraIg53uvH6z54X2Nnax4meYQY9flq6huKeY4zhUKcbm8DmI10MerSNqaIomUVWiEC66gQABjxjOYG+YS+l+bmR16sXFOMPGo5MIZH7+K6TSGgftTda++Kec7Lfw7A3wC0XLMQXMLx8sCvp+SuKoswEWSEC6akTiBMOGor1BNbUFgGw//TApGP5A0F+++ZJrl9bS6Ezh10JRCAcCvrQxQ2U5efy3D4NCSmKkllkhQikgyJnDkI8T2BMBJZUFuCw29h/avK8wKuHu+hye3nPRXWsqyvhjba+uOcd6rA8ijW1xVy9uoYX9nfiS/MSVEVRlFSYNyJgswmunPGJYR9lUeGgHLuNFTWF7DtLcvi/dp2k2JVD06oqLlxUyr5TA3h8gQnnHeocpLLQQVmBg2vXVtM/4mPbsZ70GaUoipIi80YEAPJzJJIY9vgCjPgClBU4Ys5ZXVvM/lOx4aAdx3t55dAZjDGMeAM8vec0N61bgDPHzgX1pfgChr2nJoaQDnW6WV5dCMA7VlThyLHx3F5dKqooSuYwv0QgVyLFYv0hj6AkLzfmnDULiugcHKXbPQqALxDkkz/Zzkcf2Mq7vv0q//jUPoa9AW67sA6ADYtKAdh1oi9mHGMMhzvcrKyx8gwFzhwuX17Js/tOa8dSRVEyhlkVARF5h4h8V0R+ICKvzfT98nPGloiGW0ZEJ4bB8gSASL3Aq4e76Bny8tG3LcbjD/DQluMsKHFx6ZJyAGqKXdQWuybkBU4PeBgc9bMi5AkAXLW6mtaeEVp7tHpYUZTMIOmN5kXkQeBmoNMYc37U8RuAfwPswA+MMf+UaAxjzCvAKyLybmBbsnOZKpYnEBKBIeu/0TkBgNULrG/u+04PctnySp4Ixf+/cvMacmw2nt/XQWWRE5tNItdc2FA6YYVQOCm8vLoocmx5lSUIJ3qGWVSRn17jFEVRkiAVT+BHwA3RB0TEDtwH3AisBe4QkbUisk5Efjvupzrq0g8DD6cwlymRnyMMhlYH9YU8gdJxnkBloZPKQif7Q8nep/ec5sbzrfi/3SZcd14tFy0qi7nmwkWlHO8epnfIGzl2KLRb2cqaMU+gviwPgPa+4fQbpyiKkgRJewLGmJdFpHHc4UuAw8aYFgAReQS4zRhzD5bXMAERWQT0G2PiLs4XkbuAuwBqampobm5Odsrk4qPH7ae5uZk/tlqewP43t9N5MFYLa5w+th06yb2/PMOQN8BiOTPpfU23tTLooadeZn2V9b/05d2jFOXCW9s3R87zBw0CvLprPzVDLUnb4Xa7U/r/kEmoLZnHXLED1JapkLQIJKAOaI163QZcepZr7gR+mOhNY8z9InIKuKWoqGhjU1NT0pP79aFnGPH7eMcVV7LnpSOw5wA3XXMlrlx7zHmvuvfy0JbjHPSWUlXUx6feczX2qPDPeC4e9fON7U8TLFtEU9NKAO7d9xpr6oWmprfHnLtw6wvkFpfT1HRh0nY0NzeTyv+HTEJtyTzmih2gtkyFdCeG4z0pJ10KY4z5qjFm0qRwOiqGwcoJALg9fvqGvbhybRMEAKz2EaP+IM/u7eBd6xZMKgBgrfxZUV0UyQsYYzjUMRiTFA5TV5ZHW68mhhVFyQzSLQJtQEPU63og5Qb96egdBNbqILBWCI1vHhfN6tqxZO6tFy6c0tibGst47XA3/7WrnTODowx4/JHlodHUl+bR1qs5AUVRMoN0h4O2AStEZAnQDtyOlfTNCMKeQP+Ib0LLiGiWVxditwkLS11saCid0thfuG4Vhzrc/M0ju7hmtZXzjucJ1JflcXrAgy8QJNc+r8o0FEXJQJJ+ConIw8BmYJWItInIncYYP/BZ4GlgH/CoMWZPqpNMWzgoxxKBMU8gN+55rlw7t1/cwGevWo7I5KGgMGUFDh76xCV8YGM9z++3qoKX18QPBwUNnO73JGmFoihK+khlddAdCY4/BTyV9IziICK3ALcsX748pXHCz/yBET+9w17WhArD4nH3e9ZNe3xnjp2vv389qxcUs+/UAFWFzgnn1JdZ9QFtvSM0lGutgKIos0u6w0EzgjHmCeCJTZs2fTKVcaI9gb5hX8xeAulCRLjz8iUJ368rtWoFrLxARdrvryiKMh3mVVA6khMY9k3YUOZcsaDUhQi09+kKIUVRZp+sEIF0rQ7KyyHyAA6aiX2DzgXOHDvVRU5dJqooSkaQFSKQrsSwTYRCZw7Hu609gROtDppp6svyaVcRUBQlA8gKEUiXJwDWXsPHe6x1+olWB800daV5tKWxf1AgaAgEJ29Pfbx7iC0t3Wm7p6Ioc4OsEIF0eQJg7TXcFmrlPHueQB6n+jxnfXB
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"fd_validation_ext(solid)\n",
|
||
|
|
"fd_validation_ext(neo_solid)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"# Validate Elastic Energy Force Differentials (Elastic Forces) using Finite Differences on Elastic Forces"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 18,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"name": "stderr",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"/opt/notebooks/assignment_2_3/notebook/../src/elasticenergy.py:145: RuntimeWarning: invalid value encountered in log\n",
|
||
|
|
" self.logJ = np.log(np.linalg.det(jac))\n",
|
||
|
|
"/opt/notebooks/assignment_2_3/notebook/../src/elasticenergy.py:131: RuntimeWarning: invalid value encountered in log\n",
|
||
|
|
" j = np.log(np.linalg.det(jac))\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 432x288 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"%run ../src/Utils.py\n",
|
||
|
|
"\n",
|
||
|
|
"v_def = v.copy()\n",
|
||
|
|
"v_def[:, 0] *= 2.\n",
|
||
|
|
"solid.update_def_shape(v_def)\n",
|
||
|
|
"neo_solid.update_def_shape(v_def)\n",
|
||
|
|
"\n",
|
||
|
|
"fd_validation_elastic_differentials(solid)\n",
|
||
|
|
"fd_validation_elastic_differentials(neo_solid)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": null,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": []
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"metadata": {
|
||
|
|
"kernelspec": {
|
||
|
|
"display_name": "Python 3 (ipykernel)",
|
||
|
|
"language": "python",
|
||
|
|
"name": "python3"
|
||
|
|
},
|
||
|
|
"language_info": {
|
||
|
|
"codemirror_mode": {
|
||
|
|
"name": "ipython",
|
||
|
|
"version": 3
|
||
|
|
},
|
||
|
|
"file_extension": ".py",
|
||
|
|
"mimetype": "text/x-python",
|
||
|
|
"name": "python",
|
||
|
|
"nbconvert_exporter": "python",
|
||
|
|
"pygments_lexer": "ipython3",
|
||
|
|
"version": "3.9.7"
|
||
|
|
},
|
||
|
|
"toc": {
|
||
|
|
"base_numbering": 1,
|
||
|
|
"nav_menu": {},
|
||
|
|
"number_sections": true,
|
||
|
|
"sideBar": true,
|
||
|
|
"skip_h1_title": false,
|
||
|
|
"title_cell": "Table of Contents",
|
||
|
|
"title_sidebar": "Contents",
|
||
|
|
"toc_cell": false,
|
||
|
|
"toc_position": {},
|
||
|
|
"toc_section_display": true,
|
||
|
|
"toc_window_display": false
|
||
|
|
}
|
||
|
|
},
|
||
|
|
"nbformat": 4,
|
||
|
|
"nbformat_minor": 4
|
||
|
|
}
|