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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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v 0 0 1
|
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|
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|
||||
File diff suppressed because it is too large.
Load diff
Binary file not shown.
@@ -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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|
||||
"text/plain": [
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||||
"<Figure size 432x288 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
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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
|
||||
}
|
||||
@@ -0,0 +1,431 @@
|
||||
import numpy as np
|
||||
import time
|
||||
import math
|
||||
|
||||
def conjugate_gradient(L_method, b):
|
||||
'''
|
||||
Finds an inexact Newton descent direction using Conjugate Gradient (CG)
|
||||
Solves partially L(x) = b where A is positive definite, using CG.
|
||||
The method should be take care of checking whether the added direction is
|
||||
an ascent direction or not, and whether the residuals are small enough.
|
||||
Details can be found in the handout.
|
||||
|
||||
Input:
|
||||
- L_method : a method that computes the Hessian vector product. It should
|
||||
take an array of shape (n,) and return an array of shape (n,)
|
||||
- b : right hand side of the linear system (n,)
|
||||
|
||||
Output:
|
||||
- p_star : np array of shape (n,) solving the linear system approximately
|
||||
'''
|
||||
N = b.shape[0]
|
||||
fshape = (3*N,N)
|
||||
z = np.zeros(fshape)
|
||||
r = np.zeros(fshape)
|
||||
d = np.zeros(fshape)
|
||||
alpha = np.zeros(3*N)
|
||||
beta = np.zeros(3*N)
|
||||
r[0] = -b
|
||||
d[0] = -r[0]
|
||||
ck = 0
|
||||
for k in range(0,3*N):
|
||||
|
||||
if (d[k].T @ L_method(d[k]) <= 0).all():
|
||||
if (k==0):
|
||||
return b
|
||||
else:
|
||||
return z[k]
|
||||
alpha[k] = (r[k].T @ r[k])/(d[k].T @ L_method(d[k]))
|
||||
z[k+1] = z[k] + alpha[k]*d[k]
|
||||
r[k+1] = r[k] + alpha[k]*L_method(d[k])
|
||||
if (np.linalg.norm(r[k+1]) < min(0.5,math.sqrt(np.linalg.norm(b)))*math.sqrt(np.linalg.norm(b) )):
|
||||
break
|
||||
|
||||
beta[k+1] = (r[k].T @ r[k+1])/(r[k].T @ r[k])
|
||||
d[k+1] = -r[k+1] + beta[k+1]*d[k]
|
||||
ck = k
|
||||
|
||||
return z[ck+1]
|
||||
|
||||
|
||||
def compute_inverse_approximate_hessian_matrix(sk, yk, invB_prev):
|
||||
'''
|
||||
Input:
|
||||
- sk : previous step x_{k+1} - x_k, shape (n, 1)
|
||||
- yk : grad(f)_{k+1} - grad(f)_{k}, shape (n, 1)
|
||||
- invB_prev : previous Hessian estimate Bk, shape (n, n)
|
||||
|
||||
Output:
|
||||
- invB_new : previous Hessian estimate Bk, shape (n, n)
|
||||
'''
|
||||
invB_new = invB_prev.copy()
|
||||
invB_new += (sk.T @ yk + yk.T @ invB_prev @ yk) / ((sk.T @ yk) ** 2) * (sk @ sk.T)
|
||||
prod = (invB_prev @ yk) @ sk.T
|
||||
invB_new -= (prod + prod.T) / (sk.T @ yk)
|
||||
return invB_new
|
||||
|
||||
def evaluate_armijo_rule(f_x, f_x1, p, grad, c, alpha):
|
||||
"""
|
||||
Check the armijo rule, return true if the armijo condition is satisfied
|
||||
|
||||
Input:
|
||||
- f_x : float
|
||||
The function value at x
|
||||
- f_x1 : float
|
||||
The function value at x_(k+1) = x_k + alpha * p_k
|
||||
- p: np.array(2 * #V, 1)
|
||||
The flatten search direction
|
||||
Here, we use the flatten the search direction.
|
||||
The flatten process asks the all x coordinates to be first
|
||||
then all y cooridnates to be the second.
|
||||
- grad: np.array(2 * #V, 1)
|
||||
The gradient of the function at x
|
||||
Here, we use the flatten the gradient
|
||||
The flatten process asks the all x coordinates to be first
|
||||
then all y cooridnates to be the second.
|
||||
- c: float
|
||||
The coefficient for armijo condition
|
||||
- alpha: float
|
||||
The current step size
|
||||
|
||||
Output:
|
||||
- condition: bool
|
||||
True if the armijio condition is satisfied
|
||||
"""
|
||||
return f_x1 <= f_x + c*alpha*np.dot(p,grad)
|
||||
|
||||
def equilibrium_convergence_report_GD(solid, v_init, n_steps, step_size, thresh=1e-3):
|
||||
'''
|
||||
Finds the equilibrium by minimizing the total energy using gradient descent.
|
||||
|
||||
Input:
|
||||
- solid : an elastic solid to optimize
|
||||
- v_init : the initial guess for the equilibrium position
|
||||
- n_step : number of optimization steps
|
||||
- step_size : scaling factor of the gradient when taking the step
|
||||
- thresh : threshold to stop the optimization process on the gradient's magnitude
|
||||
|
||||
Ouput:
|
||||
- report : a dictionary containing various quantities of interest
|
||||
'''
|
||||
|
||||
solid.update_def_shape(v_init)
|
||||
|
||||
energies_el = np.zeros(shape=(n_steps+1,))
|
||||
energies_ext = np.zeros(shape=(n_steps+1,))
|
||||
residuals = np.zeros(shape=(n_steps+1,))
|
||||
times = np.zeros(shape=(n_steps+1,))
|
||||
step_sizes = np.zeros(shape=(n_steps,))
|
||||
|
||||
energies_el[0] = solid.energy_el
|
||||
energies_ext[0] = solid.energy_ext
|
||||
residuals[0] = np.linalg.norm((solid.f + solid.f_ext)[solid.free_idx, :])
|
||||
idx_stop = n_steps
|
||||
|
||||
energy_tot_prev = energies_el[0] + energies_ext[0]
|
||||
|
||||
t_start = time.time()
|
||||
for i in range(n_steps):
|
||||
## TODO: Find the descent direction
|
||||
## descent_dir has shape (#v, 3)
|
||||
descent_dir = (solid.f + solid.f_ext)
|
||||
|
||||
|
||||
step_size_tmp = step_size
|
||||
max_l_iter = 20
|
||||
for l_iter in range(max_l_iter):
|
||||
step_size_tmp *= 0.5
|
||||
solid.displace(step_size_tmp * descent_dir)
|
||||
|
||||
## TODO: Check if the armijo rule is satisfied
|
||||
## energy_tot_tmp is the current total energy
|
||||
## armijo is a boolean that says whether the condition is satisfied
|
||||
energy_tot_tmp = solid.energy_ext + solid.energy_el
|
||||
grad_tmp = -descent_dir
|
||||
armijo = energy_tot_tmp < energy_tot_prev + thresh * step_size_tmp * ((descent_dir*grad_tmp).sum())
|
||||
|
||||
if armijo or l_iter == max_l_iter-1:
|
||||
break
|
||||
else:
|
||||
solid.displace(-step_size_tmp * descent_dir)
|
||||
step_sizes[i] = step_size_tmp
|
||||
|
||||
# Measure the force residuals
|
||||
energies_el[i+1] = solid.energy_el
|
||||
energies_ext[i+1] = solid.energy_ext
|
||||
residuals[i+1] = np.linalg.norm((solid.f + solid.f_ext)[solid.free_idx, :])
|
||||
energy_tot_prev = energy_tot_tmp
|
||||
|
||||
if residuals[i+1] < thresh:
|
||||
energies_el[i+1:] = energies_el[i+1]
|
||||
energies_ext[i+1:] = energies_ext[i+1]
|
||||
residuals[i+1:] = residuals[i+1]
|
||||
idx_stop = i
|
||||
break
|
||||
|
||||
times[i+1] = time.time() - t_start
|
||||
|
||||
report = {}
|
||||
report['energies_el'] = energies_el
|
||||
report['energies_ext'] = energies_ext
|
||||
report['residuals'] = residuals
|
||||
report['times'] = times
|
||||
report['idx_stop'] = idx_stop
|
||||
report['step_sizes'] = step_sizes
|
||||
|
||||
return report
|
||||
|
||||
|
||||
def equilibrium_convergence_report_BFGS(solid, v_init, n_steps, step_size, thresh=1e-3):
|
||||
'''
|
||||
Finds the equilibrium by minimizing the total energy using BFGS.
|
||||
|
||||
Input:
|
||||
- solid : an elastic solid to optimize
|
||||
- v_init : the initial guess for the equilibrium position
|
||||
- n_step : number of optimization steps
|
||||
- step_size : scaling factor of the direction when taking the step
|
||||
- thresh : threshold to stop the optimization process on the gradient's magnitude
|
||||
|
||||
Ouput:
|
||||
- report : a dictionary containing various quantities of interest
|
||||
'''
|
||||
|
||||
solid.update_def_shape(v_init)
|
||||
|
||||
energies_el = np.zeros(shape=(n_steps+1,))
|
||||
energies_ext = np.zeros(shape=(n_steps+1,))
|
||||
residuals = np.zeros(shape=(n_steps+1,))
|
||||
times = np.zeros(shape=(n_steps+1,))
|
||||
energies_el[0] = solid.energy_el
|
||||
energies_ext[0] = solid.energy_ext
|
||||
## TODO: Collect free vertex positions
|
||||
## grad_tmp is the current flattened gradient of the total energy
|
||||
## with respect to the free vertices
|
||||
grad_tmp = - (solid.f + solid.f_ext)[solid.free_idx,:].reshape(-1,1)
|
||||
residuals[0] = np.linalg.norm(grad_tmp)
|
||||
idx_stop = n_steps
|
||||
|
||||
energy_tot_prev = energies_el[0] + energies_ext[0]
|
||||
|
||||
|
||||
## TODO: Collect free vertex positions
|
||||
## v_tmp are the current flattened free vertices
|
||||
v_tmp = solid.v_def[solid.free_idx,:].reshape(-1,1)
|
||||
dir_zeros = np.zeros_like(solid.v_def)
|
||||
invB_prev = np.eye(v_tmp.shape[0])
|
||||
|
||||
t_start = time.time()
|
||||
for i in range(n_steps):
|
||||
|
||||
dir_tmp = - invB_prev @ grad_tmp
|
||||
dir_zeros[solid.free_idx, :] = dir_tmp.reshape(-1, 3)
|
||||
|
||||
step_size_tmp = step_size
|
||||
max_l_iter = 20
|
||||
for l_iter in range(max_l_iter):
|
||||
step_size_tmp *= 0.5
|
||||
solid.displace(step_size_tmp * dir_zeros)
|
||||
|
||||
## TODO: Check if the armijo rule is satisfied
|
||||
## energy_tot_tmp is the current total energy
|
||||
## armijo is a boolean that says whether the condition is satisfied
|
||||
energy_tot_tmp = solid.energy_el + solid.energy_ext
|
||||
armijo = energy_tot_tmp < energy_tot_prev + thresh * step_size_tmp*((dir_tmp*grad_tmp).sum())
|
||||
|
||||
if armijo or l_iter == max_l_iter-1:
|
||||
break
|
||||
else:
|
||||
solid.displace(-step_size_tmp * dir_zeros)
|
||||
|
||||
## TODO: Update all quantities
|
||||
## v_new are the new flattened free vertices
|
||||
## grad_new is the new flattened gradient of the total energy
|
||||
## with respect to the free vertices
|
||||
v_new = solid.v_def[solid.free_idx,:].reshape(-1,1)
|
||||
grad_new = - (solid.f+solid.f_ext)[solid.free_idx,:].reshape(-1,1)
|
||||
invB_prev = compute_inverse_approximate_hessian_matrix(v_new - v_tmp,
|
||||
grad_new - grad_tmp,
|
||||
invB_prev)
|
||||
v_tmp = v_new.copy()
|
||||
grad_tmp = grad_new.copy()
|
||||
|
||||
energies_el[i+1] = solid.energy_el
|
||||
energies_ext[i+1] = solid.energy_ext
|
||||
residuals[i+1] = np.linalg.norm(grad_tmp)
|
||||
|
||||
if residuals[i+1] < thresh:
|
||||
residuals[i+1:] = residuals[i+1]
|
||||
energies_el[i+1:] = energies_el[i+1]
|
||||
energies_ext[i+1:] = energies_ext[i+1]
|
||||
idx_stop = i
|
||||
break
|
||||
|
||||
times[i+1] = time.time() - t_start
|
||||
|
||||
report = {}
|
||||
report['energies_el'] = energies_el
|
||||
report['energies_ext'] = energies_ext
|
||||
report['residuals'] = residuals
|
||||
report['times'] = times
|
||||
report['idx_stop'] = idx_stop
|
||||
|
||||
return report
|
||||
|
||||
def equilibrium_convergence_report_NCG(solid, v_init, n_steps, thresh=1e-3):
|
||||
'''
|
||||
Finds the equilibrium by minimizing the total energy using Newton CG.
|
||||
|
||||
Input:
|
||||
- solid : an elastic solid to optimize
|
||||
- v_init : the initial guess for the equilibrium position
|
||||
- n_step : number of optimization steps
|
||||
- thresh : threshold to stop the optimization process on the gradient's magnitude
|
||||
|
||||
Ouput:
|
||||
- report : a dictionary containing various quantities of interest
|
||||
'''
|
||||
|
||||
solid.update_def_shape(v_init)
|
||||
|
||||
energies_el = np.zeros(shape=(n_steps+1,))
|
||||
energies_ext = np.zeros(shape=(n_steps+1,))
|
||||
residuals = np.zeros(shape=(n_steps+1,))
|
||||
times = np.zeros(shape=(n_steps+1,))
|
||||
energies_el[0] = solid.energy_el
|
||||
energies_ext[0] = solid.energy_ext
|
||||
residuals[0] = np.linalg.norm((solid.f + solid.f_ext)[solid.free_idx, :])
|
||||
idx_stop = n_steps
|
||||
|
||||
t_start = time.time()
|
||||
for i in range(n_steps):
|
||||
# Take a Newton step
|
||||
solid.equilibrium_step()
|
||||
|
||||
# Measure the force residuals
|
||||
energies_el[i+1] = solid.energy_el
|
||||
energies_ext[i+1] = solid.energy_ext
|
||||
residuals[i+1] = np.linalg.norm((solid.f + solid.f_ext)[solid.free_idx, :])
|
||||
|
||||
if residuals[i+1] < thresh:
|
||||
residuals[i+1:] = residuals[i+1]
|
||||
energies_el[i+1:] = energies_el[i+1]
|
||||
energies_ext[i+1:] = energies_ext[i+1]
|
||||
idx_stop = i
|
||||
break
|
||||
|
||||
times[i+1] = time.time() - t_start
|
||||
|
||||
report = {}
|
||||
report['energies_el'] = energies_el
|
||||
report['energies_ext'] = energies_ext
|
||||
report['residuals'] = residuals
|
||||
report['times'] = times
|
||||
report['idx_stop'] = idx_stop
|
||||
|
||||
return report
|
||||
|
||||
import matplotlib.pyplot as plt
|
||||
def fd_validation_ext(solid):
|
||||
epsilons = np.logspace(-9,-3,100)
|
||||
perturb_global = np.random.uniform(-1e-3, 1e-3, size=solid.v_def.shape)
|
||||
solid.displace(perturb_global)
|
||||
v_def = solid.v_def.copy()
|
||||
perturb = np.random.uniform(-1, 1, size=solid.v_def.shape)
|
||||
errors = []
|
||||
for eps in epsilons:
|
||||
# Back to original
|
||||
solid.update_def_shape(v_def)
|
||||
grad = np.zeros(solid.f_ext.shape)
|
||||
grad[solid.free_idx] = -solid.f_ext.copy()[solid.free_idx]
|
||||
an_delta_E = (grad*perturb).sum()
|
||||
|
||||
# One step forward
|
||||
solid.displace(perturb * eps)
|
||||
E1 = solid.energy_ext.copy()
|
||||
|
||||
# Two steps backward
|
||||
solid.displace(-2*perturb * eps)
|
||||
E2 = solid.energy_ext.copy()
|
||||
|
||||
# Compute error
|
||||
fd_delta_E = (E1 - E2)/(2*eps)
|
||||
errors.append(abs(fd_delta_E - an_delta_E)/abs(an_delta_E))
|
||||
plt.loglog(epsilons, errors)
|
||||
plt.grid()
|
||||
plt.show()
|
||||
|
||||
def fd_validation_elastic(solid):
|
||||
epsilons = np.logspace(-9,-3,100)
|
||||
perturb_global = np.random.uniform(-1e-3, 1e-3, size=solid.v_def.shape)
|
||||
solid.displace(perturb_global)
|
||||
|
||||
v_def = solid.v_def.copy()
|
||||
solid.make_elastic_forces()
|
||||
|
||||
perturb = np.random.uniform(-1, 1, size=solid.v_def.shape)
|
||||
errors = []
|
||||
for eps in epsilons:
|
||||
# Back to original
|
||||
solid.update_def_shape(v_def)
|
||||
solid.make_elastic_forces()
|
||||
grad = np.zeros(solid.f.shape)
|
||||
grad[solid.free_idx] = -solid.f.copy()[solid.free_idx]
|
||||
an_delta_E = (grad*perturb).sum()
|
||||
|
||||
# One step forward
|
||||
solid.displace(perturb * eps)
|
||||
E1 = solid.energy_el.copy()
|
||||
|
||||
# Two steps backward
|
||||
solid.displace(-2*perturb * eps)
|
||||
E2 = solid.energy_el.copy()
|
||||
|
||||
# Compute error
|
||||
fd_delta_E = (E1 - E2)/(2*eps)
|
||||
errors.append(abs(fd_delta_E - an_delta_E)/abs(an_delta_E))
|
||||
solid.displace(perturb * eps)
|
||||
|
||||
plt.loglog(epsilons, errors)
|
||||
plt.grid()
|
||||
plt.show()
|
||||
|
||||
def fd_validation_elastic_differentials(solid):
|
||||
epsilons = np.logspace(-9, 3,500)
|
||||
perturb_global = 1e-3*np.random.uniform(-1., 1., size=solid.v_def.shape)
|
||||
solid.displace(perturb_global)
|
||||
|
||||
v_def = solid.v_def.copy()
|
||||
|
||||
perturb = np.random.uniform(-1, 1, size=solid.v_def.shape)
|
||||
errors = []
|
||||
for eps in epsilons:
|
||||
# Back to original
|
||||
solid.update_def_shape(v_def)
|
||||
perturb_0s = np.zeros_like(perturb)
|
||||
perturb_0s[solid.free_idx] = perturb[solid.free_idx]
|
||||
an_df = solid.compute_force_differentials(perturb_0s)[solid.free_idx, :]
|
||||
an_df_full = np.zeros(solid.f.shape)
|
||||
an_df_full[solid.free_idx] = an_df.copy()
|
||||
|
||||
# One step forward
|
||||
solid.displace(perturb * eps)
|
||||
f1 = solid.f[solid.free_idx, :]
|
||||
f1_full = np.zeros(solid.f.shape)
|
||||
f1_full[solid.free_idx] = f1
|
||||
|
||||
# Two steps backward
|
||||
solid.displace(-2*perturb * eps)
|
||||
f2 = solid.f[solid.free_idx, :]
|
||||
f2_full = np.zeros(solid.f.shape)
|
||||
f2_full[solid.free_idx] = f2
|
||||
|
||||
# Compute error
|
||||
fd_delta_f = (f1_full - f2_full)/(2*eps)
|
||||
norm_an_df = np.linalg.norm(an_df_full)
|
||||
norm_error = np.linalg.norm(an_df_full - fd_delta_f)
|
||||
errors.append(norm_error/norm_an_df)
|
||||
|
||||
plt.loglog(epsilons, errors)
|
||||
plt.grid()
|
||||
plt.show()
|
||||
@@ -0,0 +1,163 @@
|
||||
import numpy as np
|
||||
from numpy.core.einsumfunc import einsum
|
||||
from numpy.core.fromnumeric import swapaxes
|
||||
|
||||
class ElasticEnergy:
|
||||
def __init__(self, young, poisson):
|
||||
'''
|
||||
Input:
|
||||
- young : Young's modulus [Pa]
|
||||
- poisson : Poisson ratio
|
||||
'''
|
||||
self.young = young
|
||||
self.poisson = poisson
|
||||
self.lbda = young * poisson / ((1 + poisson) * (1 - 2 * poisson))
|
||||
self.mu = young / (2 * (1 + poisson))
|
||||
|
||||
self.psi = None
|
||||
self.E = None
|
||||
self.P = None
|
||||
|
||||
self.dE = None
|
||||
self.dP = None
|
||||
|
||||
def make_energy_density(self, jac):
|
||||
'''
|
||||
This method computes the energy density at each tetrahedron (#t,),
|
||||
and stores the result in self.psi
|
||||
|
||||
Input:
|
||||
- jac : jacobian of the deformation (#t, 3, 3)
|
||||
|
||||
Updated attributes:
|
||||
- psi : energy density per tet (#t,)
|
||||
'''
|
||||
|
||||
print("Please specify the kind of elasticity model.")
|
||||
raise NotImplementedError
|
||||
|
||||
def make_strain_tensor(self, jac):
|
||||
'''
|
||||
This method computes the strain tensor (#t, 3, 3), and stores it in self.E
|
||||
|
||||
Input:
|
||||
- jac : jacobian of the deformation (#t, 3, 3)
|
||||
|
||||
Updated attributes:
|
||||
- E : strain induced by the deformation (#t, 3, 3)
|
||||
'''
|
||||
|
||||
print("Please specify the kind of elasticity model.")
|
||||
raise NotImplementedError
|
||||
|
||||
def make_piola_kirchhoff_stress_tensor(self, jac):
|
||||
'''
|
||||
This method computes the stress tensor (#t, 3, 3), and stores it in self.P
|
||||
|
||||
Input:
|
||||
- jac : jacobian of the deformation (#t, 3, 3)
|
||||
|
||||
Updated attributes:
|
||||
- P : stress tensor induced by the deformation (#t, 3, 3)
|
||||
'''
|
||||
|
||||
print("Please specify the kind of elasticity model.")
|
||||
raise NotImplementedError
|
||||
|
||||
def make_differential_strain_tensor(self, jac, dJac):
|
||||
'''
|
||||
This method computes the differential of strain tensor (#t, 3, 3),
|
||||
and stores it in self.dE
|
||||
|
||||
Input:
|
||||
- jac : jacobian of the deformation (#t, 3, 3)
|
||||
- dJac : differential of the jacobian of the deformation (#t, 3, 3)
|
||||
|
||||
Updated attributes:
|
||||
- dE : differential of the strain tensor (#t, 3, 3)
|
||||
'''
|
||||
|
||||
print("Please specify the kind of elasticity model.")
|
||||
raise NotImplementedError
|
||||
|
||||
def make_differential_piola_kirchhoff_stress_tensor(self, jac, dJac):
|
||||
'''
|
||||
This method computes the differential of the stress tensor (#t, 3, 3), and stores it in self.dP
|
||||
|
||||
Input:
|
||||
- jac : jacobian of the deformation (#t, 3, 3)
|
||||
- dJac : differential of the jacobian of the deformation (#t, 3, 3)
|
||||
|
||||
Updated attributes:
|
||||
- dP : differential of the stress tensor (#t, 3, 3)
|
||||
'''
|
||||
|
||||
print("Please specify the kind of elasticity model.")
|
||||
raise NotImplementedError
|
||||
|
||||
class LinearElasticEnergy(ElasticEnergy):
|
||||
def __init__(self, young, poisson):
|
||||
super().__init__(young, poisson)
|
||||
|
||||
def make_energy_density(self, jac):
|
||||
fa = self.mu * np.einsum("ijk,ijk->i",self.E, self.E)
|
||||
fb = self.lbda/2.0 * np.einsum('ijj->i' ,self.E)**2
|
||||
self.psi = fa + fb
|
||||
|
||||
def make_strain_tensor(self, jac):
|
||||
self.E = (jac+np.transpose(jac,axes=(0,2,1)))/2.0 - np.identity(3)
|
||||
|
||||
def make_piola_kirchhoff_stress_tensor(self, jac):
|
||||
fa = 2.0*self.mu*self.E
|
||||
fb = self.lbda* np.einsum('i,jk->ijk',np.einsum('ijj->i',self.E), np.identity(3))
|
||||
self.P = fa + fb
|
||||
|
||||
def make_differential_strain_tensor(self, jac, dJac):
|
||||
self.dE = (dJac+np.transpose(dJac,axes=(0,2,1)))/2.0
|
||||
|
||||
def make_differential_piola_kirchhoff_stress_tensor(self, jac, dJac):
|
||||
fa = 2.0*self.mu*self.dE
|
||||
fb = self.lbda* np.einsum("i,jk->ijk",np.trace(self.dE, axis1=1,axis2=2), np.identity(3))
|
||||
self.dP = fa + fb
|
||||
|
||||
class NeoHookeanElasticEnergy(ElasticEnergy):
|
||||
def __init__(self, young, poisson):
|
||||
super().__init__(young, poisson)
|
||||
self.logJ = None
|
||||
self.Finv = None
|
||||
|
||||
def make_energy_density(self, jac):
|
||||
i1 = np.einsum('ijk,ijk->i',jac,jac)
|
||||
j = np.log(np.linalg.det(jac))
|
||||
fa = self.mu/2.0 * (i1-3 - 2*j)
|
||||
fb = self.lbda/2.0 * j**2
|
||||
self.psi = fa + fb
|
||||
|
||||
def make_strain_tensor(self, jac):
|
||||
pass
|
||||
|
||||
def make_piola_kirchhoff_stress_tensor(self, jac):
|
||||
'''
|
||||
Additional updated attributes:
|
||||
- logJ ; log of the determinant of the jacobians (#t,)
|
||||
- Finv : inverse of the jacobians (#t, 3, 3)
|
||||
'''
|
||||
self.logJ = np.log(np.linalg.det(jac))
|
||||
self.Finv = np.linalg.inv(jac)
|
||||
FinvT = np.transpose(self.Finv,axes=(0,2,1))
|
||||
fa = self.mu * (jac - FinvT)
|
||||
fb = self.lbda * np.einsum("i,ijk->ijk",self.logJ, FinvT)
|
||||
self.P = fa +fb
|
||||
|
||||
def make_differential_strain_tensor(self, jac, dJac):
|
||||
pass
|
||||
|
||||
def make_differential_piola_kirchhoff_stress_tensor(self, jac, dJac):
|
||||
self.logJ = np.log(np.linalg.det(jac))
|
||||
self.Finv = np.linalg.inv(jac)
|
||||
FinvT = np.transpose(self.Finv,axes=(0,2,1))
|
||||
dFT = np.transpose(dJac,axes=(0,2,1))
|
||||
fa = self.mu * dJac
|
||||
fb = np.einsum("i,ijk->ijk",(self.mu - self.lbda * self.logJ),FinvT @ dFT @ FinvT)
|
||||
fc = self.lbda * np.einsum("i,ijk->ijk",np.trace(self.Finv @ dJac, axis1=1,axis2=2),FinvT)
|
||||
self.dP = fa + fb + fc
|
||||
@@ -0,0 +1,404 @@
|
||||
import numpy as np
|
||||
from numpy import linalg
|
||||
from scipy import sparse
|
||||
from Utils import *
|
||||
import igl
|
||||
|
||||
|
||||
# -----------------------------------------------------------------------------
|
||||
# -----------------------------------------------------------------------------
|
||||
# ELASTIC SOLID CLASS
|
||||
# -----------------------------------------------------------------------------
|
||||
# -----------------------------------------------------------------------------
|
||||
|
||||
|
||||
class ElasticSolid(object):
|
||||
|
||||
def __init__(self, v_rest, t, ee, rho=1, pin_idx=[], f_mass=None):
|
||||
'''
|
||||
Input:
|
||||
- v_rest : position of the vertices of the mesh (#v, 3)
|
||||
- t : indices of the element's vertices (#t, 4)
|
||||
- ee : elastic energy object that can be found in elasticenergy.py
|
||||
- rho : mass per unit volume [kg.m-3]
|
||||
- pin_idx : list or np array of vertex indices to pin
|
||||
- f_mass : external force per unit mass (3,) [N.kg-1]
|
||||
'''
|
||||
|
||||
self.v_rest = v_rest.copy()
|
||||
self.v_def = v_rest.copy()
|
||||
self.t = t
|
||||
self.ee = ee
|
||||
self.rho = rho
|
||||
self.pin_idx = np.array(pin_idx)
|
||||
self.f_mass = f_mass.copy()
|
||||
self.free_idx = None
|
||||
self.pin_mask = None
|
||||
|
||||
self.W0 = None
|
||||
self.Dm = None
|
||||
self.Bm = None
|
||||
self.rest_barycenters = None
|
||||
|
||||
self.W = None
|
||||
self.Ds = None
|
||||
self.F = None
|
||||
self.def_barycenters = None
|
||||
|
||||
self.energy_el = None
|
||||
self.energy_ext = None
|
||||
|
||||
self.f = None
|
||||
self.f_vol = None
|
||||
self.f_ext = None
|
||||
|
||||
self.make_free_indices_and_pin_mask()
|
||||
self.update_rest_shape(self.v_rest)
|
||||
self.update_def_shape(self.v_def)
|
||||
|
||||
## Utils ##
|
||||
|
||||
def vertex_tet_sum(self, data):
|
||||
'''
|
||||
Distributes data specified at each tetrahedron to the neighboring vertices.
|
||||
All neighboring vertices will receive the value indicated at the corresponding tet position in data.
|
||||
|
||||
Input:
|
||||
- data : np array of shape (#t,) or (4*#t,)
|
||||
|
||||
Output:
|
||||
- data_sum : np array of shape (#v,), containing the summed data
|
||||
'''
|
||||
i = self.t.flatten('F') # (4*#t,)
|
||||
j = np.arange(len(self.t)) # (#t,)
|
||||
j = np.tile(j, 4) # (4*#t,)
|
||||
|
||||
if len(data) == len(self.t):
|
||||
data = data[j]
|
||||
|
||||
# Has shape (#v, #t)
|
||||
m = sparse.coo_matrix((data, (i, j)), (len(self.v_rest), len(self.t)))
|
||||
return np.array(m.sum(axis=1)).flatten()
|
||||
|
||||
## Precomputation ##
|
||||
|
||||
def make_free_indices_and_pin_mask(self):
|
||||
'''
|
||||
Should list all the free indices and the pin mask.
|
||||
|
||||
Updated attributes:
|
||||
- free_index : np array of shape (#free_vertices,) containing the list of unpinned vertices
|
||||
- pin_mask : np array of shape (#v, 1) containing 1 at free vertex indices and 0 at pinned vertex indices
|
||||
'''
|
||||
self.pin_mask = np.ones((self.v_rest.shape[0],1))
|
||||
self.free_idx = np.arange(0,self.v_rest.shape[0])
|
||||
if(self.pin_idx.shape[0]<=0):
|
||||
return
|
||||
self.pin_mask[self.pin_idx] = 0
|
||||
self.free_idx = np.where(self.pin_mask==1)[0]
|
||||
|
||||
|
||||
|
||||
## Methods related to rest quantities ##
|
||||
|
||||
def make_rest_barycenters(self):
|
||||
'''
|
||||
Construct the barycenters of the undeformed configuration
|
||||
|
||||
Updated attributes:
|
||||
- rest_barycenters : np array of shape (#t, 3) containing the position of each tet's barycenter
|
||||
'''
|
||||
self.rest_barycenters = np.einsum("ijk->ik",self.v_rest[self.t])/4
|
||||
|
||||
def make_rest_shape_matrices(self):
|
||||
'''
|
||||
Construct Ds that has shape (#t, 3, 3), and its inverse Bm
|
||||
|
||||
Updated attributes:
|
||||
- Dm : np array of shape (#t, 3, 3) containing the shape matrix of each tet
|
||||
- Bm : np array of shape (#t, 3, 3) containing the inverse shape matrix of each tet
|
||||
'''
|
||||
tv = self.v_rest[self.t]
|
||||
|
||||
tva = tv[:,:3,:]
|
||||
tvb = tv[:,3,:].reshape((self.t.shape[0],1,3))
|
||||
tvb= np.repeat(tvb, 3, axis=1)
|
||||
|
||||
tvs = tva - tvb
|
||||
tvsf = np.transpose(tvs,(0,2,1))
|
||||
|
||||
self.Dm = tvsf
|
||||
self.Bm = np.linalg.inv(tvsf)
|
||||
|
||||
def update_rest_shape(self, v_rest):
|
||||
'''
|
||||
Updates the vertex position, the shape matrices Dm and Bm, the volumes W0,
|
||||
and the mass matrix at rest
|
||||
|
||||
Input:
|
||||
- v_rest : position of the vertices of the mesh at rest state (#v, 3)
|
||||
|
||||
Updated attributes:
|
||||
- v_rest : np array of shape (#v, 3) containing the position of each vertex at rest
|
||||
- W0 : np array of shape (#t,) containing the signed volume of each tet
|
||||
'''
|
||||
self.v_rest = v_rest
|
||||
self.make_rest_barycenters()
|
||||
self.make_rest_shape_matrices()
|
||||
self.W0 = -np.linalg.det(self.Dm)/6
|
||||
self.update_def_shape(self.v_def)
|
||||
self.make_volumetric_and_external_forces()
|
||||
|
||||
## Methods related to deformed quantities ##
|
||||
|
||||
def make_def_barycenters(self):
|
||||
'''
|
||||
Construct the barycenters of the deformed configuration
|
||||
|
||||
Updated attributes:
|
||||
- def_barycenters : np array of shape (#t, 3) containing the position of each tet's barycenter
|
||||
'''
|
||||
self.def_barycenters = np.einsum("ijk->ik",self.v_def[self.t])/4
|
||||
|
||||
def make_def_shape_matrices(self):
|
||||
'''
|
||||
Construct Ds that has shape (#t, 3, 3)
|
||||
|
||||
Updated attributes:
|
||||
- Ds : np array of shape (#t, 3, 3) containing the shape matrix of each tet
|
||||
'''
|
||||
tv = self.v_def[self.t]
|
||||
|
||||
tva = tv[:,:3,:]
|
||||
tvb = tv[:,3,:].reshape((self.t.shape[0],1,3))
|
||||
tvb= np.repeat(tvb, 3, axis=1)
|
||||
|
||||
tvs = tva - tvb
|
||||
tvsf = np.transpose(tvs,(0,2,1))
|
||||
|
||||
self.Ds = tvsf
|
||||
|
||||
def make_jacobians(self):
|
||||
'''
|
||||
Compute the current Jacobian of the deformation
|
||||
|
||||
Updated attributes:
|
||||
- F : np array of shape (#t, 3, 3) containing Jacobian of the deformation in each tet
|
||||
'''
|
||||
self.F = self.Ds @ self.Bm # <=> np.einsum("lij,ljk->lik",self.Ds,self.Bm)
|
||||
|
||||
def update_def_shape(self, v_def):
|
||||
'''
|
||||
Updates the vertex position, the Jacobian of the deformation, and the
|
||||
resulting elastic forces.
|
||||
|
||||
Input:
|
||||
- v_def : position of the vertices of the mesh (#v, 3)
|
||||
|
||||
Updated attributes:
|
||||
- v_def : np array of shape (#v, 3) containing the position of each vertex after deforming the solid
|
||||
- W : np array of shape (#t,) containing the signed volume of each tet
|
||||
'''
|
||||
self.v_def = self.v_rest
|
||||
self.v_def[self.free_idx] = v_def[self.free_idx]
|
||||
self.make_def_barycenters()
|
||||
self.make_def_shape_matrices()
|
||||
self.W = -np.linalg.det(self.Ds)/6
|
||||
self.make_jacobians()
|
||||
if(self.f_vol is None):
|
||||
self.make_volumetric_and_external_forces()
|
||||
self.make_elastic_forces()
|
||||
self.make_elastic_energy()
|
||||
self.make_external_energy()
|
||||
|
||||
def displace(self, v_disp):
|
||||
'''
|
||||
Displace the whole mesh so that v_def += v_disp
|
||||
|
||||
Input:
|
||||
- v_disp : displacement of the vertices of the mesh (#v, 3)
|
||||
'''
|
||||
self.update_def_shape(self.v_def + v_disp)
|
||||
|
||||
## Energies ##
|
||||
|
||||
def make_elastic_energy(self):
|
||||
'''
|
||||
This updates the elastic energy
|
||||
|
||||
Updated attributes:
|
||||
- energy_el : elastic energy of the system [J]
|
||||
'''
|
||||
self.ee.make_strain_tensor(self.F)
|
||||
self.ee.make_energy_density(self.F)
|
||||
self.energy_el = np.sum(self.W0 * self.ee.psi)
|
||||
|
||||
def make_external_energy(self):
|
||||
'''
|
||||
This computes the external energy potential
|
||||
|
||||
Updated attributes:
|
||||
- energy_ext : postential energy due to external forces [J]
|
||||
'''
|
||||
dx = self.def_barycenters - self.rest_barycenters
|
||||
ifv = np.einsum('i,ij -> ij', self.W0, self.f_vol)
|
||||
self.energy_ext = - np.einsum("i,ij,ij->",self.W0, self.f_vol, dx)
|
||||
|
||||
## Forces ##
|
||||
|
||||
def make_elastic_forces(self):
|
||||
'''
|
||||
This method updates the elastic forces stored in self.f (#v, 3)
|
||||
|
||||
Updated attributes:
|
||||
- f : elastic forces per vertex (#v, 3)
|
||||
- ee : elastic energy, some attributes should be updated
|
||||
'''
|
||||
self.ee.make_strain_tensor(self.F)
|
||||
self.ee.make_piola_kirchhoff_stress_tensor(self.F)
|
||||
tdm = np.transpose(self.Bm,(0,2,1))
|
||||
ptdm = self.ee.P @ tdm
|
||||
f123 = -np.einsum("i,ijk->ikj",self.W0,ptdm )
|
||||
f4 = -f123[:,0] - f123[:,1] - f123[:,2]
|
||||
H = np.hstack((f123,f4[:,None]))
|
||||
|
||||
x = self.vertex_tet_sum(H[:,:,0].flatten('F'))
|
||||
y = self.vertex_tet_sum(H[:,:,1].flatten('F'))
|
||||
z = self.vertex_tet_sum(H[:,:,2].flatten('F'))
|
||||
|
||||
self.f = np.hstack((x[:,None],y[:,None],z[:,None]))
|
||||
|
||||
def make_volumetric_and_external_forces(self):
|
||||
'''
|
||||
Convert force per unit mass to volumetric forces, then distribute
|
||||
the forces to the vertices of the mesh.
|
||||
|
||||
Updated attributes:
|
||||
- f_vol : np array of shape (#t, 3) external force per unit volume acting on the tets
|
||||
- f_ext : np array of shape (#v, 3) external force acting on the vertices
|
||||
'''
|
||||
mpv = self.f_mass*self.rho
|
||||
self.f_vol = np.ones((self.W0.shape[0],1)) * mpv
|
||||
|
||||
ifv = np.einsum('i,ij -> ij', self.W0, self.f_vol)
|
||||
|
||||
f_ext_x = self.vertex_tet_sum(ifv[:,0])
|
||||
f_ext_y = self.vertex_tet_sum(ifv[:,1])
|
||||
f_ext_z = self.vertex_tet_sum(ifv[:,2])
|
||||
|
||||
self.f_ext = np.stack((f_ext_x,f_ext_y,f_ext_z),axis=1) / 4.0
|
||||
|
||||
## Force Differentials
|
||||
|
||||
def compute_force_differentials(self, v_disp):
|
||||
'''
|
||||
This computes the differential of the force given a displacement dx,
|
||||
where df = df/dx|x . dx = - K(x).dx. Where K(x) is the stiffness matrix (or Hessian)
|
||||
of the solid. Note that the implementation doesn't need to construct the stiffness matrix explicitly.
|
||||
|
||||
Input:
|
||||
- v_disp : displacement of the vertices of the mesh (#v, 3)
|
||||
|
||||
Output:
|
||||
- df : force differentials at the vertices of the mesh (#v, 3)
|
||||
|
||||
Updated attributes:
|
||||
- ee : elastic energy, some attributes should be updated
|
||||
'''
|
||||
|
||||
# First compute the differential of the Jacobian
|
||||
tv = v_disp[self.t]
|
||||
tva = tv[:,:3,:]
|
||||
tvb = tv[:,3,:].reshape((-1,1,3))
|
||||
|
||||
tvb= np.repeat(tvb, 3, axis=1)
|
||||
|
||||
tvs = tva - tvb
|
||||
tvsf = np.transpose(tvs,(0,2,1))
|
||||
|
||||
dDs = tvsf
|
||||
dF = dDs @ self.Bm
|
||||
|
||||
# Then update differential quantities in self.ee
|
||||
self.ee.make_differential_strain_tensor(self.F,dF)
|
||||
self.ee.make_differential_piola_kirchhoff_stress_tensor(self.F,dF)
|
||||
|
||||
# Compute the differential of the forces
|
||||
tdm = np.transpose(self.Bm,(0,2,1))
|
||||
ptdm = self.ee.dP @ tdm
|
||||
f123 = -np.einsum("i,ijk->ikj",self.W0,ptdm )
|
||||
f4 = -f123[:,0] - f123[:,1] - f123[:,2]
|
||||
H = np.hstack((f123,f4[:,None]))
|
||||
|
||||
x = self.vertex_tet_sum(H[:,:,0].flatten('F'))
|
||||
y = self.vertex_tet_sum(H[:,:,1].flatten('F'))
|
||||
z = self.vertex_tet_sum(H[:,:,2].flatten('F'))
|
||||
|
||||
return np.hstack((x[:,None],y[:,None],z[:,None]))
|
||||
|
||||
def equilibrium_step(self, step_size_init = 2, max_l_iter = 20, c1 = 1e-4):
|
||||
'''
|
||||
This function displaces the whole solid to the next deformed configuration
|
||||
using a Newton-CG step.
|
||||
|
||||
Updated attributes:
|
||||
- LHS : The hessian vector product
|
||||
- RHS : Right hand side for the conjugate gradient linear solve
|
||||
Other than them, only attributes updated by displace(self, v_disp) should be changed
|
||||
'''
|
||||
|
||||
# Define LHS
|
||||
def LHS(dx):
|
||||
'''
|
||||
Should implement the Hessian-Vector Product L(dx), and take care of pinning constraints
|
||||
as described in the handout.
|
||||
'''
|
||||
if len(dx.shape)==1:
|
||||
dx = dx.reshape((-1,3))
|
||||
|
||||
if (dx.shape[0] < self.v_rest.shape[0]):
|
||||
dxf = np.zeros((self.v_rest.shape[0],3))
|
||||
dxf[self.free_idx] = dx
|
||||
dx = dxf
|
||||
|
||||
res = self.compute_force_differentials(dx)
|
||||
|
||||
return res[self.free_idx].flatten()
|
||||
|
||||
self.LHS = LHS # Save to class for testing
|
||||
|
||||
# Define RHS
|
||||
RHS = - (self.f + self.f_ext)[self.free_idx]
|
||||
|
||||
self.RHS = RHS # Save to class for testing
|
||||
|
||||
# Use conjugate gradient to find a descent direction
|
||||
# (see conjugate_gradient in Utils.py)
|
||||
dx_CG = conjugate_gradient(LHS,RHS.flatten()) # shape (#v, 3)
|
||||
|
||||
|
||||
# Run line search on the direction
|
||||
step_size = step_size_init
|
||||
ft = self.f + self.f_ext
|
||||
energy_tot_prev = self.energy_el + self.energy_ext
|
||||
for l_iter in range(max_l_iter):
|
||||
step_size *= 0.5 # DO NOT CHANGE
|
||||
dx_search = dx_CG * step_size
|
||||
self.displace(dx_search)
|
||||
|
||||
# Current force norm for unpinned vertices
|
||||
f_tmp = (self.f + self.f_ext)
|
||||
f_tmp[self.free_idx] = 0
|
||||
g = np.linalg.norm(f_tmp)
|
||||
|
||||
energy_tot_tmp = self.energy_el + self.energy_ext
|
||||
|
||||
#Make sure you only use the gradient of the unpinned vertices
|
||||
# USE parameter c1 = 1e-4 (from the function arguments) when you submit
|
||||
armijo = evaluate_armijo_rule(energy_tot_prev, energy_tot_tmp, dx_CG, -dx_CG, c1, step_size)
|
||||
|
||||
if armijo or l_iter == max_l_iter-1:
|
||||
print("Energy: " + str(energy_tot_tmp) + " Force norm: " + str(g) + " Line search Iters: " + str(l_iter))
|
||||
break
|
||||
else:
|
||||
self.displace(-dx_search)
|
||||
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@@ -0,0 +1,114 @@
|
||||
import time
|
||||
import pytest
|
||||
import json
|
||||
import sys
|
||||
import igl
|
||||
import numpy as np
|
||||
sys.path.append('../')
|
||||
sys.path.append('../src')
|
||||
from elasticsolid import *
|
||||
from elasticenergy import *
|
||||
eps = 1E-6
|
||||
|
||||
with open('test_data2.json', 'r') as infile:
|
||||
homework_datas = json.load(infile)
|
||||
|
||||
@pytest.mark.timeout(0.5)
|
||||
@pytest.mark.parametrize("data", homework_datas[0])
|
||||
def test_linear_psi(data):
|
||||
young, poisson, F, psi_gt = data
|
||||
ee = LinearElasticEnergy(young, poisson)
|
||||
print(np.array(F).shape)
|
||||
ee.make_strain_tensor(np.array(F))
|
||||
ee.make_energy_density(np.array(F))
|
||||
assert np.linalg.norm(ee.psi - np.array(psi_gt)) < eps
|
||||
|
||||
@pytest.mark.timeout(0.5)
|
||||
@pytest.mark.parametrize("data", homework_datas[1])
|
||||
def test_linear_strain(data):
|
||||
young, poisson, F, E_gt = data
|
||||
ee = LinearElasticEnergy(young, poisson)
|
||||
ee.make_strain_tensor(np.array(F))
|
||||
print(np.array(E_gt).shape, np.array(E_gt)[0])
|
||||
assert np.linalg.norm(ee.E - np.array(E_gt)) < eps
|
||||
|
||||
@pytest.mark.timeout(0.5)
|
||||
@pytest.mark.parametrize("data", homework_datas[2])
|
||||
def test_linear_stress(data):
|
||||
young, poisson, F, P_gt = data
|
||||
ee = LinearElasticEnergy(young, poisson)
|
||||
ee.make_strain_tensor(np.array(F))
|
||||
ee.make_piola_kirchhoff_stress_tensor(np.array(F))
|
||||
assert np.linalg.norm(ee.P - np.array(P_gt)) < eps
|
||||
|
||||
|
||||
@pytest.mark.timeout(0.5)
|
||||
@pytest.mark.parametrize("data", homework_datas[3])
|
||||
def test_neo_psi(data):
|
||||
young, poisson, F, psi_gt = data
|
||||
ee = NeoHookeanElasticEnergy(young, poisson)
|
||||
ee.make_energy_density(np.array(F))
|
||||
assert np.linalg.norm(ee.psi - np.array(psi_gt)) < eps
|
||||
|
||||
@pytest.mark.timeout(0.5)
|
||||
@pytest.mark.parametrize("data", homework_datas[4])
|
||||
def test_neo_stress(data):
|
||||
young, poisson, F, P_gt, logJ_gt, Finv_gt = data
|
||||
ee = NeoHookeanElasticEnergy(young, poisson)
|
||||
ee.make_piola_kirchhoff_stress_tensor(np.array(F))
|
||||
assert np.linalg.norm(ee.P - np.array(P_gt)) < eps
|
||||
assert np.linalg.norm(ee.logJ - np.array(logJ_gt)) < eps
|
||||
assert np.linalg.norm(ee.Finv - np.array(Finv_gt)) < eps
|
||||
|
||||
@pytest.mark.timeout(0.5)
|
||||
@pytest.mark.parametrize("data", homework_datas[5])
|
||||
def test_energy_el(data):
|
||||
etype, young, poisson, v, t, rho, pin_idx, force_mass, v_def, ee_gt = data
|
||||
if etype == "linear":
|
||||
ee = LinearElasticEnergy(young, poisson)
|
||||
else:
|
||||
ee = NeoHookeanElasticEnergy(young, poisson)
|
||||
|
||||
es = ElasticSolid(np.array(v), np.array(t), ee, rho=rho, pin_idx=np.array(pin_idx), f_mass=np.array(force_mass))
|
||||
es.update_def_shape(np.array(v_def))
|
||||
assert np.linalg.norm(es.energy_el - np.array(ee_gt)) < eps
|
||||
|
||||
@pytest.mark.timeout(0.5)
|
||||
@pytest.mark.parametrize("data", homework_datas[6])
|
||||
def test_forces_el(data):
|
||||
etype, young, poisson, v, t, rho, pin_idx, force_mass, v_def, ef_gt = data
|
||||
if etype == "linear":
|
||||
ee = LinearElasticEnergy(young, poisson)
|
||||
else:
|
||||
ee = NeoHookeanElasticEnergy(young, poisson)
|
||||
|
||||
es = ElasticSolid(np.array(v), np.array(t), ee, rho=rho, pin_idx=np.array(pin_idx), f_mass=np.array(force_mass))
|
||||
es.update_def_shape(np.array(v_def))
|
||||
assert np.linalg.norm(es.f - np.array(ef_gt)) < eps
|
||||
|
||||
@pytest.mark.timeout(0.5)
|
||||
@pytest.mark.parametrize("data", homework_datas[7])
|
||||
def test_energy_ext(data):
|
||||
etype, young, poisson, v, t, rho, pin_idx, force_mass, v_def, exte_gt = data
|
||||
if etype == "linear":
|
||||
ee = LinearElasticEnergy(young, poisson)
|
||||
else:
|
||||
ee = NeoHookeanElasticEnergy(young, poisson)
|
||||
|
||||
es = ElasticSolid(np.array(v), np.array(t), ee, rho=rho, pin_idx=np.array(pin_idx), f_mass=np.array(force_mass))
|
||||
es.update_def_shape(np.array(v_def))
|
||||
assert np.linalg.norm(es.energy_ext - np.array(exte_gt)) < eps
|
||||
|
||||
@pytest.mark.timeout(0.5)
|
||||
@pytest.mark.parametrize("data", homework_datas[8])
|
||||
def test_forces_ext(data):
|
||||
etype, young, poisson, v, t, rho, pin_idx, force_mass, v_def, fext_gt, fvol_gt = data
|
||||
if etype == "linear":
|
||||
ee = LinearElasticEnergy(young, poisson)
|
||||
else:
|
||||
ee = NeoHookeanElasticEnergy(young, poisson)
|
||||
|
||||
es = ElasticSolid(np.array(v), np.array(t), ee, rho=rho, pin_idx=np.array(pin_idx), f_mass=np.array(force_mass))
|
||||
es.update_def_shape(np.array(v_def))
|
||||
assert np.linalg.norm(es.f_ext - np.array(fext_gt)) < eps
|
||||
assert np.linalg.norm(es.f_vol - np.array(fvol_gt)) < eps
|
||||
@@ -0,0 +1 @@
|
||||
[[[10000000.0, 0.2, [[[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[3.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]], [[2.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0Line truncated
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Reference in new issue
Block a user