How can I create a Delanay point in a cube?

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Chenglin Li 2022-7-30

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https://ww2.mathworks.cn/matlabcentral/answers/1770945-how-can-i-create-a-delanay-point-in-a-cube

评论： Chenglin Li 2022-8-3

I want to generate Mesh for a cube,but the points inside the cube can only be regularly distributed so far, and I want the surface and volume meshes to be regular triangles and regular tetrahedra.Matlab only. What do I need to do?

I would appreciate some help :)

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Bruno Luong 2022-7-30

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1770945-how-can-i-create-a-delanay-point-in-a-cube#answer_1018025

编辑：Bruno Luong 2022-7-30

在 MATLAB Online 中打开

A cube can be devided in 6 tetrahedra

nx=4;

ny=3;

nz=2;

grid = arrayfun(@(n)linspace(0,n,n+1),[nx,ny,nz], 'unif', 0);

[grid{:}] = ndgrid(grid{:});

grid = cat(4,grid{:});

grid = reshape(grid,[],3);

Tcube = [...

5, 1, 3, 2;

7, 5, 3, 2;

7, 6, 5, 2;

7, 4, 6, 2;

7, 3, 4, 2;

7, 8, 6, 4];

[Tx, Ty, Tz]=ind2sub([2 2 2],Tcube);

Tx = Tx-1;

Ty = Ty-1;

Tz = Tz-1;

C = zeros([nx,ny,nz,size(Tcube)]);

for k=1:nz

for j=1:ny

for i=1:nx

Cijk = sub2ind([nx,ny,nz]+1,i+Tx,j+Ty,k+Tz);

C(i,j,k,:,:) = reshape(Cijk,[1,1,1,size(Tcube)]);

end

C = reshape(C, [], 4);

TR = triangulation(C,grid);

% Graphical plot

patch('Faces', TR.ConnectivityList, 'Vertices', TR.Points,'FaceColor', 'g', 'FaceAlpha', 0.5);

view(3);

axis equal

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Bruno Luong 2022-8-3

编辑：Bruno Luong 2022-8-3

You always speak about "triangles" as if you want to mesh the surface and not the volume.

In 2D this FileExchange gives very doof result.

Chenglin Li 2022-8-3

I have seen this 2D program and it works very well，but I still want to generate regular tetrahedral volume mesh in 3D, but the grid points in the volume are not clear how to generate.

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