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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import numpy as np\n",
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"import torch\n",
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"import igl\n",
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"\n",
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"import meshplot as mp\n",
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"import sys as _sys\n",
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"_sys.path.append(\"../src\")\n",
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"from elasticenergy import *\n",
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"from elasticsolid import *\n",
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"from adjoint_sensitivity import *\n",
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"from vis_utils import *\n",
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"from objectives import *\n",
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"from harmonic_interpolator import *\n",
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"from shape_optimizer import *\n",
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"\n",
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"from utils import *\n",
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"\n",
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"shadingOptions = {\n",
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" \"flat\":True,\n",
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" \"wireframe\":False, \n",
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"}\n",
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"\n",
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"rot = np.array(\n",
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" [[1, 0, 0 ],\n",
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" [0, 0, 1],\n",
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" [0, -1, 0 ]]\n",
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")\n",
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"\n",
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"torch.set_default_dtype(torch.float64)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Create the deformed object\n",
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"\n",
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"## Load the mesh"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {
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"scrolled": false
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},
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"outputs": [
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{
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"data": {
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"application/vnd.jupyter.widget-view+json": {
|
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"model_id": "9ae930440a43419c88fd82d71d7a6fa4",
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"version_major": 2,
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"version_minor": 0
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},
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"text/plain": [
|
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"Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(-1.987469…"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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},
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{
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"data": {
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"text/plain": [
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"<meshplot.Viewer.Viewer at 0x7f86840382e0>"
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]
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},
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"execution_count": 2,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"vNP, _, _, tNP, _, _ = igl.read_obj(\"../data/dinosaur.obj\")\n",
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"# vNP, _, _, tNP, _, _ = igl.read_obj(\"../data/beam.obj\")\n",
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"\n",
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"aabb = np.max(vNP, axis=0) - np.min(vNP, axis=0)\n",
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"length_scale = np.mean(aabb)\n",
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"\n",
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"\n",
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"v, t = torch.tensor(vNP), torch.tensor(tNP)\n",
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"eNP = igl.edges(tNP)\n",
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"beNP = igl.edges(igl.boundary_facets(tNP))\n",
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"\n",
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"bvNP, ivNP = get_boundary_and_interior(v.shape[0], tNP)\n",
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"\n",
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"mp.plot(vNP @ rot.T, np.array(tNP), shading=shadingOptions)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Add some physical characteristics"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Pinned vertices: [ 46 47 50 59 60 62 64 65 88 89 91 98 99 102 103 104]\n"
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]
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}
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],
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"source": [
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"rho = 131 # [kg.m-3], if aabb[0] ~ 14m, and m_tot = 6000kg\n",
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"young = 3e8 # [Pa] \n",
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"poisson = 0.2\n",
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"\n",
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"# Find some of the lowest vertices and pin them\n",
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"minZ = torch.min(v[:, 2])\n",
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"pin_idx = torch.arange(v.shape[0])[v[:, 2] < minZ + 0.01*aabb[2]]\n",
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"vIdx = np.arange(v.shape[0])\n",
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"pin_idx = vIdx[np.in1d(vIdx, bvNP) & np.in1d(vIdx, pin_idx)]\n",
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"print(\"Pinned vertices: {}\".format(pin_idx))"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Initial guess\n",
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"\n",
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"The idea is that we start deforming the mesh by inverting gravity."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {
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"scrolled": false
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},
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"outputs": [
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{
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"data": {
|
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"application/vnd.jupyter.widget-view+json": {
|
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"model_id": "1ee888e94cd641f4bbbce4b051acccfb",
|
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"version_major": 2,
|
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"version_minor": 0
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},
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"text/plain": [
|
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"Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(-2.468079…"
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]
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},
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"metadata": {},
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"output_type": "display_data"
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}
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],
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"source": [
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"# Inverted gravity\n",
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"force_mass = torch.zeros(size=(3,))\n",
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"force_mass[2] = + rho * 9.81\n",
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"\n",
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"# Gravity going in the wrong direction\n",
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"\n",
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"ee = NeoHookeanElasticEnergy(young, poisson)\n",
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"\n",
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"v = HarmonicInterpolator(v, t, ivNP).interpolate(v[bvNP])\n",
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"solid_init = ElasticSolid(v, t, ee, rho=rho, pin_idx=pin_idx, f_mass=force_mass)\n",
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"\n",
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"solid_init.find_equilibrium()\n",
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"plot_torch_solid(solid_init, beNP, rot, length_scale)\n",
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"\n",
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"# Use these as initial guesses\n",
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"v_init_rest = solid_init.v_def.clone().detach()\n",
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"v_init_def = solid_init.v_rest.clone().detach()\n",
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"\n",
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"# v_init_rest = solid_init.v_rest.clone().detach()\n",
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"# v_init_def = solid_init.v_def.clone().detach()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Inverse design\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"metadata": {
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"scrolled": false
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},
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"outputs": [
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{
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"ename": "TypeError",
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"evalue": "unsupported format string passed to NoneType.__format__",
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"output_type": "error",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)",
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"\u001b[0;32m/tmp/ipykernel_46/1868162750.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m 14\u001b[0m \u001b[0msolid_\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mupdate_def_shape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv_init_def\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 15\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 16\u001b[0;31m \u001b[0moptimizer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mShapeOptimizer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msolid_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvt_surf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mweight_reg\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0.\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 17\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[0mv_eq_init\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moptimizer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolid\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mv_def\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclone\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdetach\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#bookkeeping\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;32m/opt/notebooks/assignment_2_4/notebook/../src/shape_optimizer.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, solid, vt_surf, weight_reg)\u001b[0m\n\u001b[1;32m 48\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msolid\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfind_equilibrium\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 49\u001b[0m \u001b[0mobj_init\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtgt_fit\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msolid\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mv_def\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclone\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdetach\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 50\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Initial objective: {:.4e}\\n\"\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mobj_init\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 51\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 52\u001b[0m \u001b[0;31m# Initialize grad\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
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"\u001b[0;31mTypeError\u001b[0m: unsupported format string passed to NoneType.__format__"
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]
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}
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],
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"source": [
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"force_mass = torch.zeros(size=(3,))\n",
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"force_mass[2] = - rho * 9.81\n",
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"use_linear = False\n",
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"\n",
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"# The target is the initial raw mesh\n",
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"vt_surf = torch.tensor(vNP[bvNP, :])\n",
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"\n",
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"# Create solid\n",
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"if use_linear:\n",
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" ee = LinearElasticEnergy(young, poisson)\n",
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"else:\n",
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" ee = NeoHookeanElasticEnergy(young, poisson)\n",
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"solid_ = ElasticSolid(v_init_rest, t, ee, rho=rho, pin_idx=pin_idx, f_mass=force_mass)\n",
|
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"solid_.update_def_shape(v_init_def)\n",
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"\n",
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"optimizer = ShapeOptimizer(solid_, vt_surf, weight_reg=0.)\n",
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"\n",
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||||
"v_eq_init = optimizer.solid.v_def.clone().detach() #bookkeeping"
|
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]
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||||
},
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||||
{
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||||
"cell_type": "code",
|
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"execution_count": null,
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"metadata": {},
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||||
"outputs": [],
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||||
"source": [
|
||||
"optimizer.optimize(step_size_init=1e-4, max_l_iter=10, n_optim_steps=40)"
|
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]
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},
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||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
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"metadata": {},
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||||
"outputs": [],
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"source": [
|
||||
"import matplotlib.pyplot as plt\n",
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"\n",
|
||||
"plt.figure(figsize=(10, 6))\n",
|
||||
"plt.plot(to_numpy(optimizer.objectives[optimizer.objectives > 0]))\n",
|
||||
"plt.title(\"Objective as optimization goes\", fontsize=14)\n",
|
||||
"plt.xlabel(\"Optimization steps\", fontsize=12)\n",
|
||||
"plt.ylabel(\"Objective\", fontsize=12)\n",
|
||||
"plt.grid()\n",
|
||||
"plt.show()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
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||||
"source": [
|
||||
"Green (Initial guess for rest state) deploys to Black\n",
|
||||
"\n",
|
||||
"Blue (Optimized rest state) deploys to Yellow\n",
|
||||
"\n",
|
||||
"Red is the Target Shape\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"p = mp.plot(np.array(optimizer.solid.v_def) @ rot.T, tNP, shading=shadingOptions)\n",
|
||||
"# p.add_points(np.array(optimizer.solid.v_def)[pin_idx, :] @ rot.T, shading={\"point_color\":\"black\", \"point_size\": 0.2})\n",
|
||||
"p.add_edges(np.array(v_init_rest) @ rot.T, beNP, shading={\"line_color\": \"green\"})\n",
|
||||
"p.add_edges(vNP @ rot.T, beNP, shading={\"line_color\": \"red\"})\n",
|
||||
"p.add_edges(np.array(v_eq_init) @ rot.T, beNP, shading={\"line_color\": \"black\"})\n",
|
||||
"p.add_edges(np.array(optimizer.solid.v_rest) @ rot.T, beNP, shading={\"line_color\": \"blue\"})\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"v_rest_optim_g = optimizer.solid.v_rest.clone().detach() #bookkeeping"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Add point load to the right most vertices\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"maxX = torch.min(v[:, 0])\n",
|
||||
"f_point_idx = torch.arange(v.shape[0])[v[:, 0] > maxX - 0.01*aabb[0]]\n",
|
||||
"\n",
|
||||
"f_point = torch.zeros(size=(f_point_idx.shape[0], 3))\n",
|
||||
"f_point[:, 2] = -5e3\n",
|
||||
"\n",
|
||||
"optimizer.solid.add_point_load(f_point_idx, f_point)\n",
|
||||
"optimizer.set_params(optimizer.params)\n",
|
||||
"v_def_optim_g_under_point = optimizer.solid.v_def.clone().detach() #bookkeeping"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"optimizer.reset_BFGS()\n",
|
||||
"optimizer.optimize(step_size_init=1e-4, max_l_iter=10, n_optim_steps=20)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Green (Optimum rest state under gravity) deploys to Black with the additional point load\n",
|
||||
"\n",
|
||||
"Blue (Optimized rest state) deploys to Yellow\n",
|
||||
"\n",
|
||||
"Red is the Target Shape\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"p = mp.plot(np.array(optimizer.solid.v_def) @ rot.T, tNP, shading=shadingOptions)\n",
|
||||
"# p.add_points(np.array(optimizer.solid.v_def)[pin_idx, :] @ rot.T, shading={\"point_color\":\"black\", \"point_size\": 0.2})\n",
|
||||
"p.add_edges(np.array(v_rest_optim_g) @ rot.T, beNP, shading={\"line_color\": \"green\"})\n",
|
||||
"p.add_edges(vNP @ rot.T, beNP, shading={\"line_color\": \"red\"})\n",
|
||||
"p.add_edges(np.array(v_def_optim_g_under_point) @ rot.T, beNP, shading={\"line_color\": \"black\"})\n",
|
||||
"p.add_edges(np.array(optimizer.solid.v_rest) @ rot.T, beNP, shading={\"line_color\": \"blue\"})\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"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 +1,237 @@
|
||||
{
|
||||
"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",
|
||||
"import torch\n",
|
||||
"\n",
|
||||
"import sys as _sys\n",
|
||||
"_sys.path.append(\"../src\")\n",
|
||||
"from elasticsolid import *\n",
|
||||
"from elasticenergy import *\n",
|
||||
"from vis_utils import *\n",
|
||||
"from matplotlib import gridspec\n",
|
||||
"import matplotlib.pyplot as plt\n",
|
||||
"\n",
|
||||
"torch.set_default_dtype(torch.float64)\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`."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"metadata": {
|
||||
"scrolled": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"vNP, _, _, tNP, _, _ = igl.read_obj(\"../data/beam.obj\")\n",
|
||||
"aabb = np.max(vNP, axis=0) - np.min(vNP, axis=0)\n",
|
||||
"v = torch.tensor(vNP)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"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 = torch.zeros(size = (3,))\n",
|
||||
"force_mass[2] = - rho * 9.81\n",
|
||||
"\n",
|
||||
"minX = torch.min(v[:, 0])\n",
|
||||
"pin_idx = torch.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, tNP, 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": [
|
||||
"solid.update_def_shape(v)\n",
|
||||
"\n",
|
||||
"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": [
|
||||
"maxX = torch.max(v[:, 0])\n",
|
||||
"f_point_idx = torch.arange(v.shape[0])[v[:, 0] > maxX - 0.01*aabb[0]]\n",
|
||||
"\n",
|
||||
"f_point = torch.zeros(size=(f_point_idx.shape[0], 3))\n",
|
||||
"f_point[:, 2] = -5e3\n",
|
||||
"\n",
|
||||
"solid.add_point_load(f_point_idx, f_point)\n",
|
||||
"\n",
|
||||
"solid.update_def_shape(v)\n",
|
||||
"\n",
|
||||
"fd_validation_ext(solid)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Validate Elastic Energy Force Differentials (Elastic Forces) using Finite Differences on Elastic Forces"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"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": [
|
||||
"solid.update_def_shape(v)\n",
|
||||
"\n",
|
||||
"fd_validation_elastic_differentials(solid)"
|
||||
]
|
||||
}
|
||||
],
|
||||
"metadata": {
|
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"title_sidebar": "Contents",
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@@ -0,0 +1,483 @@
|
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{
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"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import numpy as np\n",
|
||||
"import torch\n",
|
||||
"import igl\n",
|
||||
"import time\n",
|
||||
"\n",
|
||||
"import meshplot as mp\n",
|
||||
"import sys as _sys\n",
|
||||
"_sys.path.append(\"../src\")\n",
|
||||
"from elasticenergy import *\n",
|
||||
"from elasticsolid import *\n",
|
||||
"from adjoint_sensitivity import *\n",
|
||||
"from vis_utils import *\n",
|
||||
"from objectives import *\n",
|
||||
"from harmonic_interpolator import *\n",
|
||||
"from shape_optimizer import *\n",
|
||||
"\n",
|
||||
"from utils import *\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",
|
||||
")\n",
|
||||
"\n",
|
||||
"torch.set_default_dtype(torch.float64)\n",
|
||||
"\n",
|
||||
"def to_numpy(tensor):\n",
|
||||
" return tensor.detach().clone().numpy()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Create the deformed object\n",
|
||||
"\n",
|
||||
"## Load the mesh"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"metadata": {
|
||||
"scrolled": false
|
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},
|
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"outputs": [
|
||||
{
|
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"data": {
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"application/vnd.jupyter.widget-view+json": {
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"model_id": "732bc7276b654a1db0b501b750c8fd87",
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"version_major": 2,
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"version_minor": 0
|
||||
},
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"text/plain": [
|
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"Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(5.0, 1.0,…"
|
||||
]
|
||||
},
|
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"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"<meshplot.Viewer.Viewer at 0x7f4f18719760>"
|
||||
]
|
||||
},
|
||||
"execution_count": 2,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"vNP, _, _, tNP, _, _ = igl.read_obj(\"../data/beam.obj\")\n",
|
||||
"\n",
|
||||
"aabb = np.max(vNP, axis=0) - np.min(vNP, axis=0)\n",
|
||||
"length_scale = np.mean(aabb)\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"v, t = torch.tensor(vNP), torch.tensor(tNP)\n",
|
||||
"eNP = igl.edges(tNP)\n",
|
||||
"beNP = igl.edges(igl.boundary_facets(tNP))\n",
|
||||
"\n",
|
||||
"def get_boundary_and_interior(vlen, t):\n",
|
||||
" bv = np.unique(igl.boundary_facets(t))\n",
|
||||
" vIdx = np.arange(vlen)\n",
|
||||
" iv = vIdx[np.invert(np.in1d(vIdx, bv))]\n",
|
||||
" return bv, iv\n",
|
||||
"# Compute boundary vertices and interior vertex indices\n",
|
||||
"bvNP, ivNP = get_boundary_and_interior(v.shape[0], tNP)\n",
|
||||
"\n",
|
||||
"mp.plot(vNP @ rot.T, np.array(tNP), shading=shadingOptions)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Add some physical characteristics"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Pinned vertices: [ 0 1 11 12 22 23 33 34 44 54 55 75 76 86 87 88 89]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"rho = 131 # [kg.m-3]\n",
|
||||
"damping = 0.\n",
|
||||
"young = 5e7 # [Pa] \n",
|
||||
"poisson = 0.2\n",
|
||||
"\n",
|
||||
"# Find some of the lowest vertices and pin them\n",
|
||||
"minX = torch.min(v[:, 0])\n",
|
||||
"pin_idx = torch.arange(v.shape[0])[v[:, 0] < minX + 0.2*aabb[0]]\n",
|
||||
"vIdx = np.arange(v.shape[0])\n",
|
||||
"pin_idx = vIdx[np.in1d(vIdx, bvNP) & np.in1d(vIdx, pin_idx)]\n",
|
||||
"print(\"Pinned vertices: {}\".format(pin_idx))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Initial guess\n",
|
||||
"\n",
|
||||
"The idea is that we start deforming the mesh by inverting gravity."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"metadata": {
|
||||
"scrolled": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "f4fe02d4e90b47cea101747098c5b3bd",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(4.9017367…"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# Inverted gravity\n",
|
||||
"force_mass = torch.zeros(size=(3,))\n",
|
||||
"force_mass[2] = + rho * 9.81\n",
|
||||
"\n",
|
||||
"# Gravity going in the wrong direction\n",
|
||||
"\n",
|
||||
"ee = NeoHookeanElasticEnergy(young, poisson)\n",
|
||||
"\n",
|
||||
"v = HarmonicInterpolator(v, t, ivNP).interpolate(v[bvNP])\n",
|
||||
"solid_init = ElasticSolid(v, t, ee, rho=rho, pin_idx=pin_idx, f_mass=force_mass)\n",
|
||||
"\n",
|
||||
"solid_init.find_equilibrium()\n",
|
||||
"plot_torch_solid(solid_init, beNP, rot, length_scale)\n",
|
||||
"\n",
|
||||
"# Use these as initial guesses\n",
|
||||
"v_init_rest = solid_init.v_def.clone().detach()\n",
|
||||
"v_init_def = solid_init.v_rest.clone().detach()\n",
|
||||
"\n",
|
||||
"# v_init_rest = solid_init.v_rest.clone().detach()\n",
|
||||
"# v_init_def = solid_init.v_def.clone().detach()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Inverse design\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"metadata": {
|
||||
"scrolled": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Initial objective: 1.6230e+00\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"force_mass = torch.zeros(size=(3,))\n",
|
||||
"force_mass[2] = - rho * 9.81\n",
|
||||
"use_linear = False\n",
|
||||
"\n",
|
||||
"# The target is the initial raw mesh\n",
|
||||
"vt_surf = torch.tensor(vNP[bvNP, :])\n",
|
||||
"\n",
|
||||
"# Create solid\n",
|
||||
"if use_linear:\n",
|
||||
" ee = LinearElasticEnergy(young, poisson)\n",
|
||||
"else:\n",
|
||||
" ee = NeoHookeanElasticEnergy(young, poisson)\n",
|
||||
"solid_ = ElasticSolid(v_init_rest, t, ee, rho=rho, pin_idx=pin_idx, f_mass=force_mass)\n",
|
||||
"solid_.update_def_shape(v_init_def)\n",
|
||||
"\n",
|
||||
"optimizer = ShapeOptimizer(solid_, vt_surf, weight_reg=10.)\n",
|
||||
"\n",
|
||||
"v_eq_init = optimizer.solid.v_def.clone().detach() #bookkeeping"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Objective after 40 optimization step(s): 1.5788e+00\n",
|
||||
" Line search Iters: 9\n",
|
||||
"Elapsed time: 97.1s. \n",
|
||||
"Estimated remaining time: 0.0s\n",
|
||||
"\n"
|
||||
]
|
||||
},
|
||||
{
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"data": {
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"version_major": 2,
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"version_minor": 0
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},
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"text/plain": [
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]
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"metadata": {},
|
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"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"optimizer.optimize(step_size_init=1e-2, max_l_iter=10, n_optim_steps=40)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
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"metadata": {},
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{
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"data": {
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||||
"image/png": 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truncated
|
||||
"text/plain": [
|
||||
"<Figure size 720x432 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"import matplotlib.pyplot as plt\n",
|
||||
"\n",
|
||||
"plt.figure(figsize=(10, 6))\n",
|
||||
"plt.plot(to_numpy(optimizer.objectives[optimizer.objectives > 0]))\n",
|
||||
"plt.title(\"Objective as optimization goes\", fontsize=14)\n",
|
||||
"plt.xlabel(\"Optimization steps\", fontsize=12)\n",
|
||||
"plt.ylabel(\"Objective\", fontsize=12)\n",
|
||||
"plt.grid()\n",
|
||||
"plt.show()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Green (Initial guess for rest state) deploys to Black\n",
|
||||
"\n",
|
||||
"Blue (Optimized rest state) deploys to Yellow\n",
|
||||
"\n",
|
||||
"Red is the Target Shape\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "cc0e6ec0eb174783a516c85f67697225",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(5.0444669…"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"4"
|
||||
]
|
||||
},
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"p = mp.plot(np.array(optimizer.solid.v_def) @ rot.T, tNP, shading=shadingOptions)\n",
|
||||
"# p.add_points(np.array(optimizer.solid.v_def)[pin_idx, :] @ rot.T, shading={\"point_color\":\"black\", \"point_size\": 0.2})\n",
|
||||
"p.add_edges(np.array(v_init_rest) @ rot.T, beNP, shading={\"line_color\": \"green\"})\n",
|
||||
"p.add_edges(vNP @ rot.T, beNP, shading={\"line_color\": \"red\"})\n",
|
||||
"p.add_edges(np.array(v_eq_init) @ rot.T, beNP, shading={\"line_color\": \"black\"})\n",
|
||||
"p.add_edges(np.array(optimizer.solid.v_rest) @ rot.T, beNP, shading={\"line_color\": \"blue\"})\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 9,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"v_rest_optim_g = optimizer.solid.v_rest.clone().detach() #bookkeeping"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Add point load to the right most vertices\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 10,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"maxX = torch.min(v[:, 0])\n",
|
||||
"f_point_idx = torch.arange(v.shape[0])[v[:, 0] > maxX - 0.01*aabb[0]]\n",
|
||||
"\n",
|
||||
"f_point = torch.zeros(size=(f_point_idx.shape[0], 3))\n",
|
||||
"f_point[:, 2] = -5e4\n",
|
||||
"\n",
|
||||
"optimizer.solid.add_point_load(f_point_idx, f_point)\n",
|
||||
"optimizer.set_params(optimizer.params)\n",
|
||||
"v_def_optim_g_under_point = optimizer.solid.v_def.clone().detach() #bookkeeping"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Objective after 21 optimization step(s): 2.2335e+01\n",
|
||||
" Line search Iters: 9\n",
|
||||
"Elapsed time: 2215.2s. \n",
|
||||
"Estimated remaining time: 8333.3s\n",
|
||||
"\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "f0b258afc95d4bdf8e8bb0e3fb529d05",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(5.0945925…"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"optimizer.reset_BFGS()\n",
|
||||
"optimizer.optimize(step_size_init=1e-2, max_l_iter=10, n_optim_steps=100)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Green (Optimum rest state under gravity) deploys to Black with the additional point load\n",
|
||||
"\n",
|
||||
"Blue (Optimized rest state) deploys to Yellow\n",
|
||||
"\n",
|
||||
"Red is the Target Shape\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"p = mp.plot(np.array(optimizer.solid.v_def) @ rot.T, tNP, shading=shadingOptions)\n",
|
||||
"# p.add_points(np.array(optimizer.solid.v_def)[pin_idx, :] @ rot.T, shading={\"point_color\":\"black\", \"point_size\": 0.2})\n",
|
||||
"p.add_edges(np.array(v_rest_optim_g) @ rot.T, beNP, shading={\"line_color\": \"green\"})\n",
|
||||
"p.add_edges(vNP @ rot.T, beNP, shading={\"line_color\": \"red\"})\n",
|
||||
"p.add_edges(np.array(v_def_optim_g_under_point) @ rot.T, beNP, shading={\"line_color\": \"black\"})\n",
|
||||
"p.add_edges(np.array(optimizer.solid.v_rest) @ rot.T, beNP, shading={\"line_color\": \"blue\"})\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"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 +1,474 @@
|
||||
{
|
||||
"cells": [
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 1,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"import numpy as np\n",
|
||||
"import torch\n",
|
||||
"import igl\n",
|
||||
"\n",
|
||||
"import meshplot as mp\n",
|
||||
"import sys as _sys\n",
|
||||
"_sys.path.append(\"../src\")\n",
|
||||
"from elasticenergy import *\n",
|
||||
"from elasticsolid import *\n",
|
||||
"from adjoint_sensitivity import *\n",
|
||||
"from vis_utils import *\n",
|
||||
"from objectives import *\n",
|
||||
"from harmonic_interpolator import *\n",
|
||||
"from shape_optimizer import *\n",
|
||||
"\n",
|
||||
"from utils import *\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",
|
||||
")\n",
|
||||
"\n",
|
||||
"torch.set_default_dtype(torch.float64)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Create the deformed object\n",
|
||||
"\n",
|
||||
"## Load the mesh"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"metadata": {
|
||||
"scrolled": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "35cf42b4eded4cb99f3811a16dcb4d67",
|
||||
"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"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"<meshplot.Viewer.Viewer at 0x7fa5b879cc10>"
|
||||
]
|
||||
},
|
||||
"execution_count": 2,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"vNP, _, _, tNP, _, _ = igl.read_obj(\"../data/dinosaur.obj\")\n",
|
||||
"# vNP, _, _, tNP, _, _ = igl.read_obj(\"../data/beam.obj\")\n",
|
||||
"\n",
|
||||
"aabb = np.max(vNP, axis=0) - np.min(vNP, axis=0)\n",
|
||||
"length_scale = np.mean(aabb)\n",
|
||||
"\n",
|
||||
"\n",
|
||||
"v, t = torch.tensor(vNP), torch.tensor(tNP)\n",
|
||||
"eNP = igl.edges(tNP)\n",
|
||||
"beNP = igl.edges(igl.boundary_facets(tNP))\n",
|
||||
"\n",
|
||||
"bvNP, ivNP = get_boundary_and_interior(v.shape[0], tNP)\n",
|
||||
"\n",
|
||||
"mp.plot(vNP @ rot.T, np.array(tNP), shading=shadingOptions)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Add some physical characteristics"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Pinned vertices: [ 46 47 50 59 60 62 64 65 88 89 91 98 99 102 103 104]\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"rho = 131 # [kg.m-3], if aabb[0] ~ 14m, and m_tot = 6000kg\n",
|
||||
"young = 3e8 # [Pa] \n",
|
||||
"poisson = 0.2\n",
|
||||
"\n",
|
||||
"# Find some of the lowest vertices and pin them\n",
|
||||
"minZ = torch.min(v[:, 2])\n",
|
||||
"pin_idx = torch.arange(v.shape[0])[v[:, 2] < minZ + 0.01*aabb[2]]\n",
|
||||
"vIdx = np.arange(v.shape[0])\n",
|
||||
"pin_idx = vIdx[np.in1d(vIdx, bvNP) & np.in1d(vIdx, pin_idx)]\n",
|
||||
"print(\"Pinned vertices: {}\".format(pin_idx))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Initial guess\n",
|
||||
"\n",
|
||||
"The idea is that we start deforming the mesh by inverting gravity."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"metadata": {
|
||||
"scrolled": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "5d62f192ccc940388718972e4a447f2b",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(-2.468080…"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"# Inverted gravity\n",
|
||||
"force_mass = torch.zeros(size=(3,))\n",
|
||||
"force_mass[2] = + rho * 9.81\n",
|
||||
"\n",
|
||||
"# Gravity going in the wrong direction\n",
|
||||
"\n",
|
||||
"ee = NeoHookeanElasticEnergy(young, poisson)\n",
|
||||
"\n",
|
||||
"v = HarmonicInterpolator(v, t, ivNP).interpolate(v[bvNP])\n",
|
||||
"solid_init = ElasticSolid(v, t, ee, rho=rho, pin_idx=pin_idx, f_mass=force_mass)\n",
|
||||
"\n",
|
||||
"solid_init.find_equilibrium()\n",
|
||||
"plot_torch_solid(solid_init, beNP, rot, length_scale)\n",
|
||||
"\n",
|
||||
"# Use these as initial guesses\n",
|
||||
"v_init_rest = solid_init.v_def.clone().detach()\n",
|
||||
"v_init_def = solid_init.v_rest.clone().detach()\n",
|
||||
"\n",
|
||||
"# v_init_rest = solid_init.v_rest.clone().detach()\n",
|
||||
"# v_init_def = solid_init.v_def.clone().detach()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Inverse design\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"metadata": {
|
||||
"scrolled": false
|
||||
},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Initial objective: 6.6351e+02\n",
|
||||
"\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"force_mass = torch.zeros(size=(3,))\n",
|
||||
"force_mass[2] = - rho * 9.81\n",
|
||||
"use_linear = False\n",
|
||||
"\n",
|
||||
"# The target is the initial raw mesh\n",
|
||||
"vt_surf = torch.tensor(vNP[bvNP, :])\n",
|
||||
"\n",
|
||||
"# Create solid\n",
|
||||
"if use_linear:\n",
|
||||
" ee = LinearElasticEnergy(young, poisson)\n",
|
||||
"else:\n",
|
||||
" ee = NeoHookeanElasticEnergy(young, poisson)\n",
|
||||
"solid_ = ElasticSolid(v_init_rest, t, ee, rho=rho, pin_idx=pin_idx, f_mass=force_mass)\n",
|
||||
"solid_.update_def_shape(v_init_def)\n",
|
||||
"\n",
|
||||
"optimizer = ShapeOptimizer(solid_, vt_surf, weight_reg=0.)\n",
|
||||
"\n",
|
||||
"v_eq_init = optimizer.solid.v_def.clone().detach() #bookkeeping"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Objective after 19 optimization step(s): 5.8586e+02\n",
|
||||
" Line search Iters: 8\n",
|
||||
"Elapsed time: 683.7s. \n",
|
||||
"Estimated remaining time: 755.7s\n",
|
||||
"\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "fa1a13b5101d4629a3d07e84205409dd",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(-0.497634…"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"An exception occured: . \n",
|
||||
"Halving the step.\n",
|
||||
"An exception occured: . \n",
|
||||
"Halving the step.\n",
|
||||
"An exception occured: . \n",
|
||||
"Halving the step.\n",
|
||||
"An exception occured: . \n",
|
||||
"Halving the step.\n",
|
||||
"An exception occured: . \n",
|
||||
"Halving the step.\n",
|
||||
"An exception occured: . \n",
|
||||
"Halving the step.\n",
|
||||
"An exception occured: . \n",
|
||||
"Halving the step.\n",
|
||||
"An exception occured: . \n",
|
||||
"Halving the step.\n",
|
||||
"An exception occured: . \n",
|
||||
"Halving the step.\n",
|
||||
"An exception occured: . \n",
|
||||
"Halving the step.\n",
|
||||
"Line search can't find a step to take\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"optimizer.optimize(step_size_init=1e-4, max_l_iter=10, n_optim_steps=40)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"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": [
|
||||
"import matplotlib.pyplot as plt\n",
|
||||
"\n",
|
||||
"plt.figure(figsize=(10, 6))\n",
|
||||
"plt.plot(to_numpy(optimizer.objectives[optimizer.objectives > 0]))\n",
|
||||
"plt.title(\"Objective as optimization goes\", fontsize=14)\n",
|
||||
"plt.xlabel(\"Optimization steps\", fontsize=12)\n",
|
||||
"plt.ylabel(\"Objective\", fontsize=12)\n",
|
||||
"plt.grid()\n",
|
||||
"plt.show()"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Green (Initial guess for rest state) deploys to Black\n",
|
||||
"\n",
|
||||
"Blue (Optimized rest state) deploys to Yellow\n",
|
||||
"\n",
|
||||
"Red is the Target Shape\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"application/vnd.jupyter.widget-view+json": {
|
||||
"model_id": "70afc138cf264b47b4fddfd6b9ae8624",
|
||||
"version_major": 2,
|
||||
"version_minor": 0
|
||||
},
|
||||
"text/plain": [
|
||||
"Renderer(camera=PerspectiveCamera(children=(DirectionalLight(color='white', intensity=0.6, position=(-0.497634…"
|
||||
]
|
||||
},
|
||||
"metadata": {},
|
||||
"output_type": "display_data"
|
||||
},
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"4"
|
||||
]
|
||||
},
|
||||
"execution_count": 8,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"p = mp.plot(np.array(optimizer.solid.v_def) @ rot.T, tNP, shading=shadingOptions)\n",
|
||||
"# p.add_points(np.array(optimizer.solid.v_def)[pin_idx, :] @ rot.T, shading={\"point_color\":\"black\", \"point_size\": 0.2})\n",
|
||||
"p.add_edges(np.array(v_init_rest) @ rot.T, beNP, shading={\"line_color\": \"green\"})\n",
|
||||
"p.add_edges(vNP @ rot.T, beNP, shading={\"line_color\": \"red\"})\n",
|
||||
"p.add_edges(np.array(v_eq_init) @ rot.T, beNP, shading={\"line_color\": \"black\"})\n",
|
||||
"p.add_edges(np.array(optimizer.solid.v_rest) @ rot.T, beNP, shading={\"line_color\": \"blue\"})\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 9,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"v_rest_optim_g = optimizer.solid.v_rest.clone().detach() #bookkeeping"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Add point load to the right most vertices\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"maxX = torch.min(v[:, 0])\n",
|
||||
"f_point_idx = torch.arange(v.shape[0])[v[:, 0] > maxX - 0.01*aabb[0]]\n",
|
||||
"\n",
|
||||
"f_point = torch.zeros(size=(f_point_idx.shape[0], 3))\n",
|
||||
"f_point[:, 2] = -5e3\n",
|
||||
"\n",
|
||||
"optimizer.solid.add_point_load(f_point_idx, f_point)\n",
|
||||
"optimizer.set_params(optimizer.params)\n",
|
||||
"v_def_optim_g_under_point = optimizer.solid.v_def.clone().detach() #bookkeeping"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"optimizer.reset_BFGS()\n",
|
||||
"optimizer.optimize(step_size_init=1e-4, max_l_iter=10, n_optim_steps=20)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Green (Optimum rest state under gravity) deploys to Black with the additional point load\n",
|
||||
"\n",
|
||||
"Blue (Optimized rest state) deploys to Yellow\n",
|
||||
"\n",
|
||||
"Red is the Target Shape\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"p = mp.plot(np.array(optimizer.solid.v_def) @ rot.T, tNP, shading=shadingOptions)\n",
|
||||
"# p.add_points(np.array(optimizer.solid.v_def)[pin_idx, :] @ rot.T, shading={\"point_color\":\"black\", \"point_size\": 0.2})\n",
|
||||
"p.add_edges(np.array(v_rest_optim_g) @ rot.T, beNP, shading={\"line_color\": \"green\"})\n",
|
||||
"p.add_edges(vNP @ rot.T, beNP, shading={\"line_color\": \"red\"})\n",
|
||||
"p.add_edges(np.array(v_def_optim_g_under_point) @ rot.T, beNP, shading={\"line_color\": \"black\"})\n",
|
||||
"p.add_edges(np.array(optimizer.solid.v_rest) @ rot.T, beNP, shading={\"line_color\": \"blue\"})\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"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 +1,290 @@
|
||||
{
|
||||
"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",
|
||||
"import torch\n",
|
||||
"\n",
|
||||
"import sys as _sys\n",
|
||||
"_sys.path.append(\"../src\")\n",
|
||||
"from elasticsolid import *\n",
|
||||
"from elasticenergy import *\n",
|
||||
"from vis_utils import *\n",
|
||||
"from matplotlib import gridspec\n",
|
||||
"import matplotlib.pyplot as plt\n",
|
||||
"\n",
|
||||
"torch.set_default_dtype(torch.float64)\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`."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 2,
|
||||
"metadata": {
|
||||
"scrolled": false
|
||||
},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"vNP, _, _, tNP, _, _ = igl.read_obj(\"../data/beam.obj\")\n",
|
||||
"aabb = np.max(vNP, axis=0) - np.min(vNP, axis=0)\n",
|
||||
"v = torch.tensor(vNP)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"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 = torch.zeros(size = (3,))\n",
|
||||
"force_mass[2] = - rho * 9.81\n",
|
||||
"\n",
|
||||
"minX = torch.min(v[:, 0])\n",
|
||||
"pin_idx = torch.arange(v.shape[0])[v[:, 0] < minX + 0.2*aabb[0]]\n",
|
||||
"\n",
|
||||
"ee_lin = LinearElasticEnergy(young, poisson)\n",
|
||||
"ee_neo = NeoHookeanElasticEnergy(young, poisson)\n",
|
||||
"solid_lin = ElasticSolid(v, tNP, ee_lin, rho=rho, pin_idx=pin_idx, f_mass=force_mass)\n",
|
||||
"solid_neo = ElasticSolid(v, tNP, ee_neo, 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"
|
||||
},
|
||||
{
|
||||
"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": [
|
||||
"solid_lin.update_def_shape(v)\n",
|
||||
"solid_neo.update_def_shape(v)\n",
|
||||
"\n",
|
||||
"fd_validation_elastic(solid_lin)\n",
|
||||
"fd_validation_elastic(solid_neo)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"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"
|
||||
},
|
||||
{
|
||||
"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": [
|
||||
"maxX = torch.max(v[:, 0])\n",
|
||||
"f_point_idx = torch.arange(v.shape[0])[v[:, 0] > maxX - 0.01*aabb[0]]\n",
|
||||
"\n",
|
||||
"f_point = torch.zeros(size=(f_point_idx.shape[0], 3))\n",
|
||||
"f_point[:, 2] = -5e3\n",
|
||||
"\n",
|
||||
"solid_lin.add_point_load(f_point_idx, f_point)\n",
|
||||
"solid_neo.add_point_load(f_point_idx, f_point)\n",
|
||||
"\n",
|
||||
"solid_lin.update_def_shape(v)\n",
|
||||
"solid_neo.update_def_shape(v)\n",
|
||||
"\n",
|
||||
"fd_validation_ext(solid_lin)\n",
|
||||
"fd_validation_ext(solid_neo)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# 4.4.5 Point Force\n",
|
||||
"\n",
|
||||
"I tried adding a call to `make_external_energy` in the `add_point_load` function since a new force would also lead to a different energy. However inside `make_external_energy`, after many tries to add the energy corresponding to the point force, I gave up."
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"# Validate Elastic Energy Force Differentials (Elastic Forces) using Finite Differences on Elastic Forces"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"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": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD8CAYAAAB0IB+mAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8/fFQqAAAACXBIWXMAAAsTAAALEwEAmpwYAAAlkElEQVR4nO3dd3gVZd7/8fedhCQQEkqAAKEEpEhvIQFrWHVBxYIdEUGarm11d33U1V11Vxfbs78VZVeQXqToog9NcS2xAknoXTqJAUINSSAh5f79EcBshBA452RO+byui+tiJpOZ77lJPsyZM3N/jbUWERHxf0FOFyAiIlVDgS8iEiAU+CIiAUKBLyISIBT4IiIBQoEvIhIgQpwuoCL16tWzcXFxTpfhFnl5eURERDhdhtfS+FRM43N+GqOfrVix4qC1tn759V4d+HFxcaSlpTldhlskJyeTlJTkdBleS+NTMY3P+WmMfmaM2X229bqkIyISIBT4IiIBQoEvIhIgFPgiIgFCgS8iEiAU+CIiAUKBLyLiRQ7lFrBkwz6OHj/p9n0r8EVEvMjan7J5cPoKth/Ic/u+FfgiIl5k79F8ABrVCnf7vhX4IiJeZG/2CYIMNIgMc/u+FfgiIl4k82g+MVHhhAS7P54V+CIiXmRv9gmPXM4BBb6IiFfZm51Po1rVPbJvBb6IiJew1pJ5VGf4IiJ+7+jxQgqKSmhUW2f4IiJ+bWtWLgDN69bwyP4V+CIiXmLVniMAdG1W2yP7V+CLiHiJVXuO0qxuDerVdP89+KDAFxHxCtZaVu45QjcPnd2DAl9ExCts2Z9DVk4BCS3qeuwYCnwRES/w6fp9GAPXtY/x2DEU+CIiDrPW8sm6fcQ3r0ODSM/cgw8KfBERx61KP8qW/Tnc0jXWo8dR4IuIOGz60t1EhAZzazcFvoiI39pxIJf/W/0Td/dsRs2wEI8eS4EvIuKgt77YSlhIML9JusTjx6qywDfGtDTGTDTGfFhVxxQR8WZb9uUwf00mQy+Po74HGp6UV6nAN8ZMMsZkGWPWl1vfzxizxRizzRjzTEX7sNbusNYOd6VYERF/Ya3lpQUbqBkWwqgrW1bJMSt7wWgK8A4w7fQKY0wwMBa4DsgAUo0x84FgYHS57x9mrc1yuVoRET/x0aqf+GH7IV4Z0JE6EaFVcsxKBb619htjTFy51QnANmvtDgBjzGzgFmvtaKC/W6sUEfEjh/NO8vKiTXRvVpuBPZtV2XFd+Ug4Fkgvs5wBJJ5rY2NMNPAK0M0Y8+yp/xjOtt0oYBRATEwMycnJLpToPXJzc/3mtXiCxqdiGp/z85UxstYyZlUBx44XM6BrMN9883WVHduVwDdnWWfPtbG19hDw0Pl2aq0dD4wHiI+Pt0lJSRdbn1dJTk7GX16LJ2h8KqbxOT9fGaPpy3azKms9f+rfnsFXtKjSY7tyl04G0LTMchMg07VyRET819b9Oby8cCNXt6nPA5fFVfnxXQn8VKC1MaaFMSYUuAeY756yRET8S15BEY++v4rI8BDevLMLQUFnu0jiWZW9LXMWsBRoa4zJMMYMt9YWAY8CS4BNwFxr7QbPlSoi4pustTz14Rq2ZuXw/+7uWiX33J9NZe/SGXiO9YuBxW6tSETEz/zr6+0sXrePZ6+/lCtb13esDk2tICLiQclbsnhjyRZu6tKYUVdVzQNW56LAFxHxkJ0H83h81iraxkTy2u2dMKbqr9uXpcAXEfGAQ7kFDJ2cQkhwEO/dH0+NUM/OhFkZCnwRETfLLyxm5LQ09mXn89798TStW8PpkgDXHrwSEZFySkosT85Zzar0o/zz3u70aF7H6ZLO0Bm+iIgbvfrpZj5Zv4/nbmjH9Z0aOV3Of1Hgi4i4yfSluxj/zQ7u792c4VU8bUJlKPBFRNzg8437eWH+Bq65tAF/7t/e8TtyzkaBLyLiopSdh3nk/ZV0jK3FmIHdCAn2zmj1zqpERHzExsxjDJ+aSmyd6kwe2pMIDzcid4UCX0TkIu05dJwhk1OICA1h+vBEoms6M0dOZSnwRUQuQlZOPvdNXE5hcQnThycQW7u60yWdlwJfROQCZZ8oZMikVA7kFDBpaE9ax0Q6XVKlKPBFRC5AfmExI6emsS0rh3cH96B7M+95sOp8vPfTBRERL1NUXMKj768idfdh3rqnG1e3cW6q44uhM3wRkUqw1vLMvHV8vmk/L93cgZu7NHa6pAumwBcRqYTRn2zmwxUZ/Paa1tzfO87pci6KAl9E5DzGfrWN8d/sYHCv5jxxbWuny7loCnwRkQpM/n4nbyzZwq1dG/PSzR28csqEylLgi4icw9zUdF5asJG+HWJ4884uBAX5btiDAl9E5KwWrMnkmXlruapNfa+eH+dC+P4rEBFxs8837ufJOauJb16Xcff1ICwk2OmS3EKBLyJSxvfbDvLw+ytp3ziKiUPjqR7qH2EPCnwRkTNW7D7CyGlptIiOYOoDCUSGV3O6JLdS4IuIAOt/ymbo5BQaRIYxfUQCdSJCnS7J7RT4IhLwtmXlcP+kFKLCqzFzZC8aRIY7XZJHKPBFJKDtOXScQROWE2QMM0Yk+sQ0xxdLgS8iAWtv9gnunbCMgqISZo5IpEW9CKdL8qgqC3xjTDtjzLvGmA+NMb+pquOKiJzNwdwCBk1YztHjhUwblkDbhr4xp70rKhX4xphJxpgsY8z6cuv7GWO2GGO2GWOeqWgf1tpN1tqHgLuA+IsvWUTENdnHCxk8MYXMoyeYNLQnnZvUdrqkKlHZM/wpQL+yK4wxwcBY4HqgPTDQGNPeGNPJGLOw3J8Gp77nZuA74Au3vQIRkQuQW1DE0CkpbM/KZdzgeBJa1HW6pCpTqQYo1tpvjDFx5VYnANustTsAjDGzgVustaOB/ufYz3xgvjFmEfD+RVctInIR8guLGTE1lbUZ2Yy9t7vPNTBxlSsdr2KB9DLLGUDiuTY2xiQBtwFhwOIKthsFjAKIiYkhOTnZhRK9R25urt+8Fk/Q+FRM43N+5xujohLLmFUFrDtQzMjOYYQf3Exy8uaqK9ALuBL4Z5s2zp5rY2ttMpB8vp1aa8cD4wHi4+NtUlLSxVXnZZKTk/GX1+IJGp+KaXzOr6IxKiou4bezV7P2wF7+NqAT9yY2q9rivIQrd+lkAE3LLDcBMl0rR0TEvUpKSlsTLlq3l+duaBewYQ+uBX4q0NoY08IYEwrcA8x3T1kiIq6z1vLSgg1nWhOOvKql0yU5qrK3Zc4ClgJtjTEZxpjh1toi4FFgCbAJmGut3eC5UkVELswbS7YwdeluRl7ZwqdbE7pLZe/SGXiO9Yup4ANYERGnjP1qG/9M3s69ic344w3tfLo1obtoagUR8Ttl+9C+fEtHhf0pCnwR8Sun+9D+ur1/9KF1JwW+iPiNhWtL+9Be2boeb9/rH31o3cmV+/BFRLzG6qwi3vlsNT2a12H84Hi/6UPrTvrvT0R83vfbDvLO6oJTfWh7+lUfWndS4IuITzvdh7ZhDcPUBxKI8rM+tO6kSzoi4rPK9qF9orP1yz607qQzfBHxSaf70EaGhTBjRCK1wxRn56MREhGfU7YP7cyRvWhSp4bTJfkEBb6I+JSyfWhnjEjw+z607qTAFxGfUbYP7dQHEri0YZTTJfkUBb6I+ITyfWi7NK3tdEk+R4EvIl4vkPvQupNuyxQRr5ZfWMzIqWkB24fWnXSGLyJe62RRCQ/PXMmynYd4887O9OvY0OmSfJoCX0S8UlFxCU/OWc2Xm7N4+daODOjWxOmSfJ4CX0S8Tvk+tIMSmztdkl9Q4IuIV1EfWs9R4IuIVzndh3bEFepD624KfBHxGqf70A5MaMZzN6oPrbsp8EXEK5zuQ3tL18a8fKv60HqCAl9EHFe+D22w+tB6hAJfRBxVvg9tNfWh9RiNrIg45otN+3litvrQVhUFvog44odtB/nNzJW0a6Q+tFVFgS8iVW7F7iOMmJZGXHQNpg1TH9qqosAXkSpVtg/tjOGJ6kNbhRT4IlJlyvehbRAV7nRJAaXKAt8Yk2SM+dYY864xJqmqjisi3kF9aJ1XqcA3xkwyxmQZY9aXW9/PGLPFGLPNGPPMeXZjgVwgHMi4uHJFxBfty85n0ET1oXVaZRugTAHeAaadXmGMCQbGAtdRGuCpxpj5QDAwutz3DwO+tdZ+bYyJAf4ODHKtdBHxBaV9aJdxJK+QmSMS1YfWQcZaW7kNjYkDFlprO55a7g28aK3te2r5WQBrbfmwL7+fUOB9a+0d5/j6KGAUQExMTI/Zs2dX7pV4udzcXGrWrOl0GV5L41MxXx2fvELLqyn57M8r4ffx4bSt67lbL311jDyhT58+K6y18eXXu9LiMBZIL7OcASSea2NjzG1AX6A2pe8WzspaOx4YDxAfH2+TkpJcKNF7JCcn4y+vxRM0PhXzxfHJLShi8MTl7Dt+gglDEzzemtAXx6iquRL4Z5vs4pxvF6y184B5LhxPRHyE+tB6J1fu0skAmpZZbgJkulaOiPg69aH1Xq4EfirQ2hjT4tR1+XuA+e4pS0R8UXGJVR9aL1bZ2zJnAUuBtsaYDGPMcGttEfAosATYBMy11m7wXKki4s1KSixP/3sti9bt5Y83XKo+tF6oUtfwrbUDz7F+MbDYrRWJiM8p24f28WtaM+qqS5wuSc5CUyuIiMvK9qF9Un1ovZYCX0Rcoj60vkOBLyIXbYr60PoUBb6IXJS5qem8uGAj16kPrc9Q4IvIBSvbh/Yd9aH1GfpXEpELUrYP7bjBPdSH1oco8EWk0sr3oa0R6srsLFLVFPgiUinqQ+v7FPgicl7qQ+sfFPgiUiH1ofUfCnwROaeyfWhnjEhUH1ofp8AXkbM63Yc2v7C0D23L+uom5esU+CLyC2X70E4blqA+tH5CgS8i/yX7eCH3T0zhp6MnmDgkni5NaztdkriJAl9EzsgtKGLolBS2ZuUwbnA8iS2jnS5J3EhPTYgLine truncated
|
||||
"text/plain": [
|
||||
"<Figure size 432x288 with 1 Axes>"
|
||||
]
|
||||
},
|
||||
"metadata": {
|
||||
"needs_background": "light"
|
||||
},
|
||||
"output_type": "display_data"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"solid_lin.update_def_shape(v)\n",
|
||||
"solid_neo.update_def_shape(v)\n",
|
||||
"\n",
|
||||
"fd_validation_elastic_differentials(solid_lin)\n",
|
||||
"fd_validation_elastic_differentials(solid_neo)"
|
||||
]
|
||||
}
|
||||
],
|
||||
"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