Creating hollow sphere mesh with tetrahedral elements

Question

Divyaprakash 2024-3-20

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https://ww2.mathworks.cn/matlabcentral/answers/2096801-creating-hollow-sphere-mesh-with-tetrahedral-elements

回答： SOUMNATH PAUL 2024-4-8，5:44

With the help of this file in file exchange I am creating points on the inner and outer surface of a hollow sphere.

clear; clc; close all;
% Description: Attempt at generating a meshed spherical shell with 
% tetrahedral elements
scale = 1.2;
generation = 3;
[P1,~] = generateSphereMesh(generation,'tet');
P2 = P1*scale;
X1 = P1(1,:); Y1 = P1(2,:); Z1 = P1(3,:);
X2 = P2(1,:); Y2 = P2(2,:); Z2 = P2(3,:);
X = [X1(:);X2(:)];
Y = [Y1(:);Y2(:)];
Z = [Z1(:);Z2(:)];
DT = delaunay(X,Y,Z);
figure;
XX = [X(:) Y(:) Z(:)];
tetramesh(DT,XX,'FaceAlpha',0.1)

Currently I get tetrahedrals in the entire sphere.

I need only the shell to be filled with tetrahedrals when I use delaunay Triangulation. Is it possible?

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Answer 1

SOUMNATH PAUL 2024-4-8，5:44

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https://ww2.mathworks.cn/matlabcentral/answers/2096801-creating-hollow-sphere-mesh-with-tetrahedral-elements#answer_1437911

Hi,

It looks like you trying to generate a mesh that only fills the shell of a hollow sphere rather than the entire volume. The current method used is generating points on the inner and outer surfaces but then uses “Delaunay triangulation” on all these points which fills the entire volume between these surfaces with tetrahedral.

Kindly use “Constrained Delaunay triangulation” which will allow you to define the outer and inner surfaces as constraints ensuring the tetrahedra's are only generated between these boundaries.

Here is how you can do that, refer to the following link: https://in.mathworks.com/help/matlab/math/delaunay-triangulation.html#bspqi8a-12%22 (check the section "constrained delaunay triangulation")

Hope it helps!

Regards,

Soumnath