python/todo/meshproc_6_volumetric.ipynb

{"worksheets": [{"cells": [{"cell_type": "markdown", "metadata": {}, "source": ["Volumetric Meshes", "=================", "", "*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_python/) for details about how to install the toolboxes.", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$", "$\\newcommand{\\enscond}[2]{\\lbrace #1, #2 \\rbrace}$", "$\\newcommand{\\pd}[2]{ \\frac{ \\partial #1}{\\partial #2} }$", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$", "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$", "$\\newcommand{\\uargmin}[1]{\\underset{#1}{argmin}\\;}$", "$\\newcommand{\\norm}[1]{\\|#1\\|}$", "$\\newcommand{\\abs}[1]{\\left|#1\\right|}$", "$\\newcommand{\\choice}[1]{ \\left\\{  \\begin{array}{l} #1 \\end{array} \\right. }$", "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$", "$\\newcommand{\\diag}[1]{{diag}\\left( #1 \\right)}$", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$", "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$", "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$", "$\\newcommand{\\CC}{\\mathbb{C}}$", "$\\newcommand{\\RR}{\\mathbb{R}}$", "$\\newcommand{\\EE}{\\mathbb{E}}$", "$\\newcommand{\\Zz}{\\mathcal{Z}}$", "$\\newcommand{\\Ww}{\\mathcal{W}}$", "$\\newcommand{\\Vv}{\\mathcal{V}}$", "$\\newcommand{\\Nn}{\\mathcal{N}}$", "$\\newcommand{\\NN}{\\mathcal{N}}$", "$\\newcommand{\\Hh}{\\mathcal{H}}$", "$\\newcommand{\\Bb}{\\mathcal{B}}$", "$\\newcommand{\\Ee}{\\mathcal{E}}$", "$\\newcommand{\\Cc}{\\mathcal{C}}$", "$\\newcommand{\\Gg}{\\mathcal{G}}$", "$\\newcommand{\\Ss}{\\mathcal{S}}$", "$\\newcommand{\\Pp}{\\mathcal{P}}$", "$\\newcommand{\\Ff}{\\mathcal{F}}$", "$\\newcommand{\\Xx}{\\mathcal{X}}$", "$\\newcommand{\\Mm}{\\mathcal{M}}$", "$\\newcommand{\\Ii}{\\mathcal{I}}$", "$\\newcommand{\\Dd}{\\mathcal{D}}$", "$\\newcommand{\\Ll}{\\mathcal{L}}$", "$\\newcommand{\\Tt}{\\mathcal{T}}$", "$\\newcommand{\\si}{\\sigma}$", "$\\newcommand{\\al}{\\alpha}$", "$\\newcommand{\\la}{\\lambda}$", "$\\newcommand{\\ga}{\\gamma}$", "$\\newcommand{\\Ga}{\\Gamma}$", "$\\newcommand{\\La}{\\Lambda}$", "$\\newcommand{\\si}{\\sigma}$", "$\\newcommand{\\Si}{\\Sigma}$", "$\\newcommand{\\be}{\\beta}$", "$\\newcommand{\\de}{\\delta}$", "$\\newcommand{\\De}{\\Delta}$", "$\\newcommand{\\phi}{\\varphi}$", "$\\newcommand{\\th}{\\theta}$", "$\\newcommand{\\om}{\\omega}$", "$\\newcommand{\\Om}{\\Omega}$"]}, {"cell_type": "markdown", "metadata": {}, "source": ["This tour explores the processing of volumetric tetrahedral meshes."]}, {"cell_type": "code", "language": "python", "metadata": {}, "outputs": [], "collapsed": false, "input": ["from __future__ import division", "import nt_toolbox as nt", "from nt_solutions import meshproc_6_volumetric as solutions", "%matplotlib inline", "%load_ext autoreload", "%autoreload 2"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Tetrahedral Mesh Loading and Displaying", "---------------------------------------", "You can load and display volumetric tetrahedral meshes.", "Important: .tet files and *not* included in the toolbox distribution (too", "large files). You should download them from", "", "", "http://www.aimatshape.net/", "", "", "Load a volumetric mesh."]}, {"cell_type": "code", "language": "python", "metadata": {}, "outputs": [], "collapsed": false, "input": ["[vertex, faces] = read_tet('hand.tet')"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Display it."]}, {"cell_type": "code", "language": "python", "metadata": {}, "outputs": [], "collapsed": false, "input": ["clear options", "options.plot_points = 1", "clf; plot_mesh(vertex, faces, options)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Display it."]}, {"cell_type": "code", "language": "python", "metadata": {}, "outputs": [], "collapsed": false, "input": ["options.cutting_plane = [0 0 1]", "options.plot_points = 0", "clf; plot_mesh(vertex, faces, options)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Another view."]}, {"cell_type": "code", "language": "python", "metadata": {}, "outputs": [], "collapsed": false, "input": ["options.cutting_plane = [0 -1 0]", "options.plot_points = 0", "options.cutting_offs = -.2", "options.face_vertex_color = vertex(1, : )'", "clf; plot_mesh(vertex, faces, options)", "view(-20, 45); zoom(.8)", "colormap jet(256)"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Difusion Inside the Volume", "--------------------------", "One can compute averaging operator inside the mesh."]}, {"cell_type": "markdown", "metadata": {}, "source": ["__Exercise 1__", "", "Compute the combinatorial adjacency matrix |W|.", "ompute edge list.", "ompute the adjacency matrix."]}, {"cell_type": "code", "language": "python", "metadata": {}, "outputs": [], "collapsed": false, "input": ["solutions.exo1()"]}, {"cell_type": "code", "language": "python", "metadata": {}, "outputs": [], "collapsed": false, "input": ["## Insert your code here."]}, {"cell_type": "markdown", "metadata": {}, "source": ["Compute the combinatorial Laplacian, stored as a sparse matrix."]}, {"cell_type": "code", "language": "python", "metadata": {}, "outputs": [], "collapsed": false, "input": ["n = size(W, 1)", "D = spdiags(sum(W)', 0, n, n)", "L = D-W"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Compute a set of random sources."]}, {"cell_type": "code", "language": "python", "metadata": {}, "outputs": [], "collapsed": false, "input": ["i = round(rand(20, 1)*n) + 1", "b = zeros(n, 1)", "b(i) = (-1).^(1: length(i))"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Compute the diffusion with fixed boundary conditions."]}, {"cell_type": "code", "language": "python", "metadata": {}, "outputs": [], "collapsed": false, "input": ["L1 = L", "L1(i, : ) = 0; L1(i + (i-1)*n) = 1", "v = L1\\b"]}, {"cell_type": "markdown", "metadata": {}, "source": ["Display."]}, {"cell_type": "code", "language": "python", "metadata": {}, "outputs": [], "collapsed": false, "input": ["options.face_vertex_color = v", "clf; plot_mesh(vertex, faces, options)", "view(-20, 45); zoom(.8)", "shading interp", "colormap jet(256)"]}]}], "nbformat": 3, "metadata": {"name": ""}, "nbformat_minor": 0}