Rasterize a triangle in 3-D space.

I would like to rasterize a triangle in 3-D space... This is, if I have X,Y,Z generated by a meshgrid, I would like to mark all voxel centered on XYZ through which a triangle (specified by 3-D vertices) passes through. Are there any Matlab native methods to do this? It seems pretty basic, but I can't figure out what functions would be a straightforward path.

[darova]

Do you have any attempts? Your data where is?

Answer 1

[Matt J]

One way is to use vert2lcon,

https://www.mathworks.com/matlabcentral/fileexchange/30892-analyze-n-dimensional-polyhedra-in-terms-of-vertices-or-in-equalities

as follows,

tolerance1=1;
tolerance2=1.5;

V=[x1,y1,z1;...    %triangle vertices
    x2,y2,z2;
    x3,y3,z3;]

[A,b,Aeq,beq]=vert2lcon(V);

C=[X(:).';Y(:).';Z(:).'];

intriangle = all( A*C<=b+tolerance1 & abs(Aeq*C-beq)<=tolerance2 ,1);

result=reshape(intriangle, size(X));

[Kenneth]

Thanks, it makes sense - I'm gettting the chance to look into it. I think this should work for my purposes. I'm just a little concerned it will be sensitive to the tolerance settings either leading to holes or too thick areas.