How to get corresponding coordinates of vertices in a 3D volume after voxelisation?

I use Mesh Voxelisation to voxelise a triangular-polygon mesh. The mesh contains faces and the coordinates of vertices. My question is after voxelisation, how to find the corresponding coordinates of the vertices in the volume?

For example, if the original coordinate of the vertex is (-0.4,-0.26,0.5), how can I get the corresponding coordinate (16,69,196) in the volume. I tried to locate the original coordinates in the output gridX, gridY and gridZ, but the corresponding values in the gridOUTPUT are not always equal to 1.

Answer 1

[Matt J]

Perhaps as follows,

fcn=(z,g)interp1(g,1:numel(g),z);

i=fcn(v(1),gridCOx); %v is vertex coordinate in the original space
j=fcn(v(2),gridCOy);
k=fcn(v(3),gridCOz);

[Huahua]

Thanks for your answer. However, the fact is that gridCO does not cover the range of vertex coordinates, its range is slightly smaller than the range of vertex coordinates. Even if I delete the vertices that are outside the range, the result is still incorrect. I also tried mapping the original space to grid space and then using your function and it still didn't work.

[Matt J]

I notice the Mesh Voxelisation contribution let's you input the gridX,gridY,gridZ that will be used to build the grid, so perhaps that will let you control the range over which the grid stretches

[Huahua]

Yes, you are right. Thank you for pointing this out. However, the count is still not equal to the number of vertices after changing the grid range. The code is as follows，

meshXmin = min(FV.vertices(:,1));
meshXmax = max(FV.vertices(:,1));
meshYmin = min(FV.vertices(:,2));
meshYmax = max(FV.vertices(:,2));
meshZmin = min(FV.vertices(:,3));
meshZmax = max(FV.vertices(:,3));
gridX = linspace(meshXmin, meshXmax, 100);
gridY = linspace(meshYmin, meshYmax, 100);
gridZ = linspace(meshZmin, meshZmax, 100);
[gridOUTPUT,gridCOx,gridCOy,gridCOz] = VOXELISE(gridX,gridY,gridZ,FV,'xyz');

store = zeros(1,length(FV.vertices));
for i = 1:length(FV.vertices)
    vertexCO = FV.vertices(i,:);
    idx = floor(interp1(gridCOx, 1:numel(gridCOx), vertexCO(1)));
    idy = floor(interp1(gridCOy, 1:numel(gridCOy), vertexCO(2)));
    idz = floor(interp1(gridCOz, 1:numel(gridCOz), vertexCO(3)));
    store(1,i) = gridOUTPUT(idx,idy,idz);
end
count = length(find(store == 1));

[Matt J]

You can't expect gridOUTPUT to be equal to 1 at the vertices. Firstly, the vertices are not strictly in the interior of the object. Secondly, the volume is discretized into voxels, so the boundaries of the object will not carry over precisely from continuous space.

[Huahua]

I got it. Thank you very much. One of my research scenarios is to describe local surface on a volume using descriptors with invariant properties. After rotating the object and regenerating the volume, I would have liked to experiment with the vertices before and after the rotation, but I cannot now guarantee that the value of the vertex in gridOUTPUT is always equal to 1, and probably not for the other surface points either. I wonder if you have a suggestion.

[Matt J]

I got it. Thank you very much.

You're welcome, but please Accept-click the answer if your question has been addressed.

After rotating the object and regenerating the volume, I would have liked to experiment with the vertices before and after the rotation

It's not clear to me why you need a voxelization for that. It should be clear what happens to the vertices after a rotation of the volume. The vertices should move to new locations that should be easily predictable with a 3x3 rotation matrix. It would probably be better to elaborate on what you are doing in a new post.