How do i obtain a cross section from a 3D volume? - matlab

Question

I want to obtain a 2D slice from the 3D volume in the example (slightly modified) How do I resolve this issue with 3D image visualization? as follows:
% create input image
imageSizeX = 10;
imageSizeY = 10;
imageSizeZ = 10
% generate 3D grid using voxel size = 0.5
[Xq, Yq, Zq] = ndgrid(1:0.5:imageSizeX-1, 1:0.5:imageSizeY-1, 1:0.5:imageSizeZ-1);
% obtain coordinates of all internal vertices, faces, and edges
allCoords = [Xq(:), Yq(:), Zq(:)]; % i need this bit for something very important but not shown in the question.
% Re-generate 3D grid using voxel size = 1
[columnsInImage, rowsInImage, pagesInImage] = ndgrid(1: imageSizeX-1, 1: imageSizeY-1, 1: imageSizeZ-1);
% create the sphere in the image.
centerY = imageSizeY/2;
centerX = imageSizeX/2;
centerZ = imageSizeZ/2;
diameter = 4;
radius = diameter/2;
sphereVoxels = flipud((rowsInImage - centerY).^2 ...
+ (columnsInImage - centerX).^2 + (pagesInImage - centerZ).^2 <= radius.^2);
% change image from logical to numeric labels.
Img = double(sphereVoxels);
for ii = 1:numel(Img)
if Img(ii) == 0
Img(ii) = 2; % intermediate phase voxels
end
end
% specify the desired angle
angle = 30;
% specify desired pixel height and width of solid
width = imageSizeX;
height = imageSizeY;
page = imageSizeZ;
% Find the row point at which theta will be created
y = centerY - ( radius*cos(angle * pi/180) )
% determine top of the solid bar
y0 = max(1, y-height);
% label everything from y0 to y to be = 3 (solid)
Img(1:width, y0:y, 1:page)=3;
%%%%%% Plot the surfaces
[X, Y, Z, C] = build_voxels(Img > 0);
hSurface = patch(X, Y, Z, Img(C),...
'AmbientStrength', 0.5, ...
'BackFaceLighting', 'unlit', ...
'EdgeColor', 'none', ...
'FaceLighting', 'flat');
colormap([1 0 0; 1 1 0]);
axis equal;
axis tight;
view(45, 45);
grid on;
xlabel('x-axis (voxels)');
ylabel('y-axis (voxels)');
zlabel('z-axis (voxels)');
light('Position', get(gca, 'CameraPosition'), 'Style', 'local');
zoom on;
hold on;
Vq = griddata(columnsInImage, rowsInImage, pagesInImage, Img, Xq, Yq, Zq);
figure
h1 = slice(permute(Xq, [2 1 3]),permute(Yq, [2 1 3]),permute(Zq, [2 1 3]), Vq, 5,2,5);
When i run the code, i get an Error message:
"The number of data point locations should equal the number of data point values.
Error in griddata>useScatteredInterp (line 188)
F = scatteredInterpolant(inargs{1}(:),inargs{2}(:),inargs{3}(:), ..."
I want to believe this is so because the size of columnsInImage and size of pagesInImage are not equal to size(P,1) and size(P,3), respectively.
Nonetheless, I also tried to use a vector as follows:
figure
h1 = slice(Img(:,1), Img(:,2), Img(:,3), Img, 5,2,5);
I however still end up with the error message:
"Error using griddedInterpolant
The grid was created from grid vectors that were not strictly monotonic increasing.
Error in interp3 (line 142)
F = griddedInterpolant(X, Y, Z, V, method,extrap);"
Please, guys i need suggestions/ideas on how i could remedy these. Many thanks in advance!..