455 lines
66 KiB
Plaintext
455 lines
66 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": 1,
|
||
|
|
"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": 2,
|
||
|
|
"metadata": {
|
||
|
|
"scrolled": false
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"application/vnd.jupyter.widget-view+json": {
|
||
|
|
"model_id": "fb09ceba0f474ff6a670b5386fe53817",
|
||
|
|
"version_major": 2,
|
||
|
|
"version_minor": 0
|
||
|
|
},
|
||
|
|
"text/plain": [
|
||
|
|
"Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(-1.987469…"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
" v, _, _, t, _, _ = igl.read_obj(\"../data/dinosaur.obj\")\n",
|
||
|
|
"#v, _, _, t, _, _ = igl.read_obj(\"../data/beam.obj\")\n",
|
||
|
|
"\n",
|
||
|
|
"# t = np.array([\n",
|
||
|
|
"# [0, 1, 2, 3],\n",
|
||
|
|
"# [1, 2, 3, 4]\n",
|
||
|
|
"# ])\n",
|
||
|
|
"# v = np.array([\n",
|
||
|
|
"# [0., 0., 0.],\n",
|
||
|
|
"# [1., 0., 0.],\n",
|
||
|
|
"# [0., 1., 0.],\n",
|
||
|
|
"# [0., 0., 1.],\n",
|
||
|
|
"# [2/3, 2/3, 2/3]\n",
|
||
|
|
"# ])\n",
|
||
|
|
"\n",
|
||
|
|
"be = igl.edges(igl.boundary_facets(t))\n",
|
||
|
|
"e = igl.edges(t)\n",
|
||
|
|
"\n",
|
||
|
|
"aabb = np.max(v, axis=0) - np.min(v, axis=0)\n",
|
||
|
|
"length_scale = np.mean(aabb)\n",
|
||
|
|
"\n",
|
||
|
|
"p = mp.plot(v @ rot.T, t, shading=shadingOptions)"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"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": 10,
|
||
|
|
"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",
|
||
|
|
"lin_ee = LinearElasticEnergy(young, poisson)\n",
|
||
|
|
"neo_ee = NeoHookeanElasticEnergy(young, poisson)\n",
|
||
|
|
"\n",
|
||
|
|
"lin_solid = ElasticSolid(v, t, lin_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",
|
||
|
|
"\n",
|
||
|
|
"solid = neo_solid\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Deform the mesh\n",
|
||
|
|
"\n",
|
||
|
|
"This should now involve elastic forces computation."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 11,
|
||
|
|
"metadata": {
|
||
|
|
"scrolled": false
|
||
|
|
},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"name": "stderr",
|
||
|
|
"output_type": "stream",
|
||
|
|
"text": [
|
||
|
|
"/opt/notebooks/assignment_2_2/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_2/notebook/../src/elasticenergy.py:131: RuntimeWarning: invalid value encountered in log\n",
|
||
|
|
" j = np.log(np.linalg.det(jac))\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"application/vnd.jupyter.widget-view+json": {
|
||
|
|
"model_id": "327564baf8ad4d3fb73b223d8fd921f9",
|
||
|
|
"version_major": 2,
|
||
|
|
"version_minor": 0
|
||
|
|
},
|
||
|
|
"text/plain": [
|
||
|
|
"Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(-0.865849…"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"3"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 11,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"v_def = v.copy()\n",
|
||
|
|
"v_def[:, 0] *= 2.\n",
|
||
|
|
"solid.update_def_shape(v_def)\n",
|
||
|
|
"\n",
|
||
|
|
"p = mp.plot(solid.v_def @ rot.T, solid.t, shading=shadingOptions)\n",
|
||
|
|
"p.add_points(solid.v_def[solid.pin_idx, :] @ rot.T, shading={\"point_color\":\"black\", \"point_size\": 0.1 * length_scale})\n",
|
||
|
|
"forcesScale = 2 * np.max(np.linalg.norm(solid.f_ext, axis=1))\n",
|
||
|
|
"p.add_lines(solid.v_def @ rot.T, (solid.v_def + solid.f_ext / forcesScale) @ rot.T)\n",
|
||
|
|
"p.add_edges(v @ rot.T, be, shading={\"line_color\": \"blue\"})\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Find equilibrium\n",
|
||
|
|
"\n",
|
||
|
|
"We compare different methods: number of steps, computation time."
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 12,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [],
|
||
|
|
"source": [
|
||
|
|
"n_steps = 1000\n",
|
||
|
|
"thresh = 1.\n",
|
||
|
|
"v_init = v.copy()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Gradient descent"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 13,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"application/vnd.jupyter.widget-view+json": {
|
||
|
|
"model_id": "59861d218fad43e6b57b45bed934c9a3",
|
||
|
|
"version_major": 2,
|
||
|
|
"version_minor": 0
|
||
|
|
},
|
||
|
|
"text/plain": [
|
||
|
|
"Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(-1.987468…"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"3"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 13,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"report_GD = equilibrium_convergence_report_GD(solid, v_init, n_steps, 5e-5, thresh=thresh)\n",
|
||
|
|
"energies_el_GD = report_GD['energies_el']\n",
|
||
|
|
"energies_ext_GD = report_GD['energies_ext']\n",
|
||
|
|
"energy_GD = energies_el_GD + energies_ext_GD\n",
|
||
|
|
"residuals_GD = report_GD['residuals']\n",
|
||
|
|
"times_GD = report_GD['times']\n",
|
||
|
|
"idx_stop_GD = report_GD['idx_stop']\n",
|
||
|
|
"v_def_GD = solid.v_def.copy()\n",
|
||
|
|
"\n",
|
||
|
|
"# Lastly, plot the resulting shape\n",
|
||
|
|
"p = mp.plot(v_def_GD @ rot.T, solid.t, shading=shadingOptions)\n",
|
||
|
|
"forcesScale = 2 * np.max(np.linalg.norm(solid.f_ext, axis=1))\n",
|
||
|
|
"p.add_lines(v_def_GD @ rot.T, (solid.v_def + solid.f_ext / forcesScale) @ rot.T)\n",
|
||
|
|
"p.add_points(v_def_GD[pin_idx, :] @ rot.T, shading={\"point_color\":\"black\", \"point_size\": 0.1 * length_scale})\n",
|
||
|
|
"p.add_edges(v @ rot.T, be, shading={\"line_color\": \"blue\"})"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## BFGS\n"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 14,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"application/vnd.jupyter.widget-view+json": {
|
||
|
|
"model_id": "4fac36847fef413586d1026fc645eeae",
|
||
|
|
"version_major": 2,
|
||
|
|
"version_minor": 0
|
||
|
|
},
|
||
|
|
"text/plain": [
|
||
|
|
"Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(-3.283369…"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "display_data"
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"text/plain": [
|
||
|
|
"3"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"execution_count": 14,
|
||
|
|
"metadata": {},
|
||
|
|
"output_type": "execute_result"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"report_BFGS = equilibrium_convergence_report_BFGS(solid, v_init, n_steps, 1e-7, thresh=thresh)\n",
|
||
|
|
"energies_el_BFGS = report_BFGS['energies_el']\n",
|
||
|
|
"energies_ext_BFGS = report_BFGS['energies_ext']\n",
|
||
|
|
"energy_BFGS = energies_el_BFGS + energies_ext_BFGS\n",
|
||
|
|
"residuals_BFGS = report_BFGS['residuals']\n",
|
||
|
|
"times_BFGS = report_BFGS['times']\n",
|
||
|
|
"idx_stop_BFGS = report_BFGS['idx_stop']\n",
|
||
|
|
"v_def_BFGS = solid.v_def.copy()\n",
|
||
|
|
"\n",
|
||
|
|
"# Lastly, plot the resulting shape\n",
|
||
|
|
"p = mp.plot(v_def_BFGS @ rot.T, solid.t, shading=shadingOptions)\n",
|
||
|
|
"forcesScale = 2 * np.max(np.linalg.norm(solid.f_ext, axis=1))\n",
|
||
|
|
"p.add_lines(v_def_BFGS @ rot.T, (solid.v_def + solid.f_ext / forcesScale) @ rot.T)\n",
|
||
|
|
"p.add_points(v_def_BFGS[pin_idx, :] @ rot.T, shading={\"point_color\":\"black\", \"point_size\": 0.1 * length_scale})\n",
|
||
|
|
"p.add_edges(v @ rot.T, be, shading={\"line_color\": \"blue\"})"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "markdown",
|
||
|
|
"metadata": {},
|
||
|
|
"source": [
|
||
|
|
"## Compare the different algorithms"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 15,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 720x432 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"cmap = plt.get_cmap('viridis')\n",
|
||
|
|
"colors = cmap(np.linspace(0., 1., 4))\n",
|
||
|
|
"\n",
|
||
|
|
"gs = gridspec.GridSpec(nrows=1, ncols=1, width_ratios=[1], height_ratios=[1])\n",
|
||
|
|
"fig = plt.figure(figsize=(10, 6))\n",
|
||
|
|
"\n",
|
||
|
|
"axTmp = plt.subplot(gs[0, 0])\n",
|
||
|
|
"axTmp.plot(times_GD[:idx_stop_GD+1], residuals_GD[:idx_stop_GD+1], c=colors[0], \n",
|
||
|
|
" label=\"Gradient Descent ({:}its)\".format(idx_stop_GD))\n",
|
||
|
|
"axTmp.plot(times_BFGS[:idx_stop_BFGS+1], residuals_BFGS[:idx_stop_BFGS+1], c=colors[2], \n",
|
||
|
|
" label=\"BFGS ({:}its)\".format(idx_stop_BFGS))\n",
|
||
|
|
"y_lim = axTmp.get_ylim()\n",
|
||
|
|
"axTmp.set_title(\"Residuals as optimization goes\", fontsize=14)\n",
|
||
|
|
"axTmp.set_xlabel(\"Computation time [s]\", fontsize=12)\n",
|
||
|
|
"axTmp.set_ylabel(\"Force residuals [N]\", fontsize=12)\n",
|
||
|
|
"axTmp.set_ylim(y_lim)\n",
|
||
|
|
"plt.legend(fontsize=12)\n",
|
||
|
|
"plt.grid()\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"cell_type": "code",
|
||
|
|
"execution_count": 16,
|
||
|
|
"metadata": {},
|
||
|
|
"outputs": [
|
||
|
|
{
|
||
|
|
"data": {
|
||
|
|
"image/png": "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
|
||
|
|
"text/plain": [
|
||
|
|
"<Figure size 720x432 with 1 Axes>"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
"metadata": {
|
||
|
|
"needs_background": "light"
|
||
|
|
},
|
||
|
|
"output_type": "display_data"
|
||
|
|
}
|
||
|
|
],
|
||
|
|
"source": [
|
||
|
|
"gs = gridspec.GridSpec(nrows=1, ncols=1, width_ratios=[1], height_ratios=[1])\n",
|
||
|
|
"fig = plt.figure(figsize=(10, 6))\n",
|
||
|
|
"\n",
|
||
|
|
"axTmp = plt.subplot(gs[0, 0])\n",
|
||
|
|
"axTmp.plot(times_GD[:idx_stop_GD+1], energy_GD[:idx_stop_GD+1], c=colors[0], \n",
|
||
|
|
" label=\"Gradient Descent ({:}its)\".format(idx_stop_GD))\n",
|
||
|
|
"axTmp.plot(times_BFGS[:idx_stop_BFGS+1], energy_BFGS[:idx_stop_BFGS+1], c=colors[2], \n",
|
||
|
|
" label=\"BFGS ({:}its)\".format(idx_stop_BFGS))\n",
|
||
|
|
"y_lim = axTmp.get_ylim()\n",
|
||
|
|
"axTmp.set_title(\"Total energy as optimization goes\", fontsize=14)\n",
|
||
|
|
"axTmp.set_xlabel(\"Computation time [s]\", fontsize=12)\n",
|
||
|
|
"axTmp.set_ylabel(\"Energy [J]\", fontsize=12)\n",
|
||
|
|
"axTmp.set_ylim(y_lim)\n",
|
||
|
|
"plt.legend(fontsize=12)\n",
|
||
|
|
"plt.grid()\n",
|
||
|
|
"plt.show()"
|
||
|
|
]
|
||
|
|
},
|
||
|
|
{
|
||
|
|
"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
|
||
|
|
}
|