Code covered by the BSD License

# Polygon2Voxel

### Dirk-Jan Kroon (view profile)

12 May 2009 (Updated )

Convert a triangulated mesh into a voxel volume

Volume=polygon2voxel(FV,VolumeSize,mode,Yxz)
```function Volume=polygon2voxel(FV,VolumeSize,mode,Yxz)
% This function POLYGON2VOXEL will convert a Triangulated Mesh into a
% Voxel Volume which will contain the discretized mesh. Discretization of a
% polygon is done by splitting/refining the face, until the longest edge
% is smaller than 0.5 voxels. Followed by setting the voxel beneath the vertice
% coordinates of that small triangle to one.
%
% Volume=polygon2voxel(FV,VolumeSize,Mode,Yxz);
%
% Inputs,
%   FV : A struct containing FV.faces with a facelist Nx3 and FV.vertices
%        with a Nx3 vertice list. Such a structure is created by Matlab
%        Patch function
%   VolumeSize : The size of the output volume, example [100 100 100]
%   Mode : (optional) if set to:
%               'none', The vertices data is directly used as coordinates
%                       in the voxel volume.
%               'wrap', The vertices data is directly used as coordinates
%                       in the voxel volume, coordinates outside are
%                       circular wrapped to the inside.
%               'auto', The vertices data is translated and
%                       scaled with a scalar to fit inside the new volume.
%               'center', coordinate 0,0,0 is set as the center of the volume
%                       instead of the corner of the voxel volume.
%               'clamp', The vertices data is directly used as coordinates
%                       in the voxel volume, coordinates outside are
%                       clamped to the inside.
%   (Optional)
%   Yxz : If true (default) use Matlab convention 1th dimension Y,
%         2th dimension X, and last dimension Z. Otherwise 1th
%         dimension is X, 2th Y and last Z.
%
%
% Outputs,
%   Volume : The 3D logical volume, with all voxels part of the discretized
%           mesh one, and all other voxels zero.
%
% Example,
%   % Compile the c-coded function
%   mex polygon2voxel_double.c -v
%
%   % Load a triangulated mesh of a sphere
%
%   % Show the mesh
%   figure, patch(FV,'FaceColor',[1 0 0]); axis square;
%
%   % Convert the mesh to a voxelvolume
%   Volume=polygon2voxel(FV,[50 50 50],'auto');
%
%   % Show x,y,z slices
%   figure,
%   subplot(1,3,1), imshow(squeeze(Volume(25,:,:)));
%   subplot(1,3,2), imshow(squeeze(Volume(:,25,:)));
%   subplot(1,3,3), imshow(squeeze(Volume(:,:,25)));
%
%   %  Show iso surface of result
%   figure, patch(isosurface(Volume,0.1), 'Facecolor', [1 0 0]);
%
% Example2,
%   % Compile the c-coded function
%   mex polygon2voxel_double.c -v
%
%   % Make A Volume with a few blocks
%   I = false(120,120,120);
%   I(40:60,50:70,60:80)=1; I(60:90,45:75,60:90)=1;
%   I(20:60,40:80,20:60)=1; I(60:110,35:85,10:60)=1;
%
%   % Convert the volume to a triangulated mesh
%   FV = isosurface(I,0.8);
%
%   % Convert the triangulated mesh back to a surface in a volume
%   J = polygon2voxel(FV,[120, 120, 120],'none');
%   % Fill the volume
%   J=imfill(J,'holes');
%
%   % Differences between original and reconstructed
%   VD = abs(J-I);
%
%   % Show the original Mesh and Mesh of new volume
%   figure,
%   subplot(1,3,1),  title('original')
%     patch(FV,'facecolor',[1 0 0],'edgecolor','none'), camlight;view(3);
%   subplot(1,3,2), title('converted');
%     patch(isosurface(J,0.8),'facecolor',[0 0 1],'edgecolor','none'), camlight;view(3);
%   subplot(1,3,3), title('difference');
%     patch(isosurface(VD,0.8),'facecolor',[0 0 1],'edgecolor','none'), camlight;view(3);
%
% Function is written by D.Kroon University of Twente (May 2009)

if(nargin<4), Yxz=true; end

% Check VolumeSize size
if(length(VolumeSize)==1)
VolumeSize=[VolumeSize VolumeSize VolumeSize];
end
if(length(VolumeSize)~=3)
error('polygon2voxel:inputs','VolumeSize must be a array of 3 elements ')
end

% Volume Size must always be an integer value
VolumeSize=round(VolumeSize);

sizev=size(FV.vertices);
% Check size of vertice array
if((sizev(2)~=3)||(length(sizev)~=2))
error('polygon2voxel:inputs','The vertice list is not a m x 3 array')
end

sizef=size(FV.faces);
% Check size of vertice array
if((sizef(2)~=3)||(length(sizef)~=2))
error('polygon2voxel:inputs','The vertice list is not a m x 3 array')
end

% Check if vertice indices exist
if(max(FV.faces(:))>size(FV.vertices,1))
error('polygon2voxel:inputs','The face list contains an undefined vertex index')
end

% Check if vertice indices exist
if(min(FV.faces(:))<1)
error('polygon2voxel:inputs','The face list contains an vertex index smaller then 1')
end

% Matlab dimension convention YXZ
if(Yxz)
FV.vertices=FV.vertices(:,[2 1 3]);
end

switch(lower(mode(1:2)))
case {'au'} % auto
% Make all vertices-coordinates positive
FV.vertices=FV.vertices-min(FV.vertices(:));
scaling=min((VolumeSize-1)./(max(FV.vertices(:))));
% Make the vertices-coordinates to range from 0 to 100
FV.vertices=FV.vertices*scaling+1;
Wrap=0;
case {'ce'} % center
% Center the vertices
FV.vertices=FV.vertices+repmat((VolumeSize/2),size(FV.vertices,1),1);
Wrap=0;
case {'wr'} %wrap
Wrap=1;
case{'cl'} % clamp
Wrap=2;
otherwise
Wrap=0;
end

% Separate the columns;
FacesA=double(FV.faces(:,1));
FacesB=double(FV.faces(:,2));
FacesC=double(FV.faces(:,3));
VerticesX=double(FV.vertices(:,1));
VerticesY=double(FV.vertices(:,2));
VerticesZ=double(FV.vertices(:,3));

% Volume size to double
VolumeSize=double(VolumeSize);

% Call the mex function
Volume=polygon2voxel_double(FacesA,FacesB,FacesC,VerticesX,VerticesY,VerticesZ,VolumeSize,Wrap);
```