Disabled external gits
This commit is contained in:
5316 files changed
+4563444
-6
No files matched your search
@@ -0,0 +1,454 @@
|
||||
{
|
||||
"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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 truncated
|
||||
"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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 truncated
|
||||
"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
|
||||
}
|
||||
@@ -0,0 +1,210 @@
|
||||
{
|
||||
"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": [],
|
||||
"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": 3,
|
||||
"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",
|
||||
"# ee = NeoHookeanElasticEnergy(young, poisson)\n",
|
||||
"solid = ElasticSolid(v, t, 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": 4,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"fd_validation_elastic(solid)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Validate External Energy Gradient (External Forces) using Finite Differences on External Energy"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"fd_validation_ext(solid)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
},
|
||||
{
|
||||
"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
|
||||
}
|
||||
@@ -0,0 +1,454 @@
|
||||
{
|
||||
"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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 truncated
|
||||
"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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 truncated
|
||||
"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
|
||||
}
|
||||
@@ -0,0 +1,223 @@
|
||||
{
|
||||
"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": [],
|
||||
"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": 6,
|
||||
"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": 8,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": "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 truncated
|
||||
"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": 9,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"image/png": "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 truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"image/png": "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 truncated
|
||||
"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": "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
|
||||
}
|
||||
Reference in new issue
Block a user