Important: Please read the installation page for details about how to install the toolboxes. $\newcommand{\dotp}[2]{\langle #1, #2 \rangle}$ $\newcommand{\enscond}[2]{\lbrace #1, #2 \rbrace}$ $\newcommand{\pd}[2]{ \frac{ \partial #1}{\partial #2} }$ $\newcommand{\umin}[1]{\underset{#1}{\min}\;}$ $\newcommand{\umax}[1]{\underset{#1}{\max}\;}$ $\newcommand{\umin}[1]{\underset{#1}{\min}\;}$ $\newcommand{\uargmin}[1]{\underset{#1}{argmin}\;}$ $\newcommand{\norm}[1]{\|#1\|}$ $\newcommand{\abs}[1]{\left|#1\right|}$ $\newcommand{\choice}[1]{ \left\{ \begin{array}{l} #1 \end{array} \right. }$ $\newcommand{\pa}[1]{\left(#1\right)}$ $\newcommand{\diag}[1]{{diag}\left( #1 \right)}$ $\newcommand{\qandq}{\quad\text{and}\quad}$ $\newcommand{\qwhereq}{\quad\text{where}\quad}$ $\newcommand{\qifq}{ \quad \text{if} \quad }$ $\newcommand{\qarrq}{ \quad \Longrightarrow \quad }$ $\newcommand{\ZZ}{\mathbb{Z}}$ $\newcommand{\CC}{\mathbb{C}}$ $\newcommand{\RR}{\mathbb{R}}$ $\newcommand{\EE}{\mathbb{E}}$ $\newcommand{\Zz}{\mathcal{Z}}$ $\newcommand{\Ww}{\mathcal{W}}$ $\newcommand{\Vv}{\mathcal{V}}$ $\newcommand{\Nn}{\mathcal{N}}$ $\newcommand{\NN}{\mathcal{N}}$ $\newcommand{\Hh}{\mathcal{H}}$ $\newcommand{\Bb}{\mathcal{B}}$ $\newcommand{\Ee}{\mathcal{E}}$ $\newcommand{\Cc}{\mathcal{C}}$ $\newcommand{\Gg}{\mathcal{G}}$ $\newcommand{\Ss}{\mathcal{S}}$ $\newcommand{\Pp}{\mathcal{P}}$ $\newcommand{\Ff}{\mathcal{F}}$ $\newcommand{\Xx}{\mathcal{X}}$ $\newcommand{\Mm}{\mathcal{M}}$ $\newcommand{\Ii}{\mathcal{I}}$ $\newcommand{\Dd}{\mathcal{D}}$ $\newcommand{\Ll}{\mathcal{L}}$ $\newcommand{\Tt}{\mathcal{T}}$ $\newcommand{\si}{\sigma}$ $\newcommand{\al}{\alpha}$ $\newcommand{\la}{\lambda}$ $\newcommand{\ga}{\gamma}$ $\newcommand{\Ga}{\Gamma}$ $\newcommand{\La}{\Lambda}$ $\newcommand{\si}{\sigma}$ $\newcommand{\Si}{\Sigma}$ $\newcommand{\be}{\beta}$ $\newcommand{\de}{\delta}$ $\newcommand{\De}{\Delta}$ $\newcommand{\phi}{\varphi}$ $\newcommand{\th}{\theta}$ $\newcommand{\om}{\omega}$ $\newcommand{\Om}{\Omega}$
This tour explores the processing of volumetric tetrahedral meshes.
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
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
Load a volumetric mesh.
[vertex, faces] = read_tet('hand.tet')
Display it.
clear options
options.plot_points = 1
clf; plot_mesh(vertex, faces, options)
Display it.
options.cutting_plane = [0 0 1]
options.plot_points = 0
clf; plot_mesh(vertex, faces, options)
Another view.
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)
One can compute averaging operator inside the mesh.
Exercise 1
Compute the combinatorial adjacency matrix |W|. ompute edge list. ompute the adjacency matrix.
solutions.exo1()
## Insert your code here.
Compute the combinatorial Laplacian, stored as a sparse matrix.
n = size(W, 1)
D = spdiags(sum(W)', 0, n, n)
L = D-W
Compute a set of random sources.
i = round(rand(20, 1)*n) + 1
b = zeros(n, 1)
b(i) = (-1).^(1: length(i))
Compute the diffusion with fixed boundary conditions.
L1 = L
L1(i, : ) = 0; L1(i + (i-1)*n) = 1
v = L1\b
Display.
options.face_vertex_color = v
clf; plot_mesh(vertex, faces, options)
view(-20, 45); zoom(.8)
shading interp
colormap jet(256)