MATLAB: Help to vectorize this matrix operation

Question

Hello, I am trying to translate a shape's convex hull to a bunch of different locations to analyze all the translated convex hulls.

Here is the code I have so far:

TCH=[];
for t=1:3:length(tmat)/3
   TCH=[TCH;(CH*tmat(i:i+2,:))'];
end

tmat is a matrix that holds all of the different affine matrices for each different translation so it looks something like this:

tmat =

     1     0     0
     0     1     0
   -94   -64     1
     1     0     0
     0     1     0
   -93   -63     1
     1     0     0
     0     1     0
   -92   -62     1
     1     0     0
     0     1     0
   -91   -61     1
     1     0     0
     0     1     0
   -90   -60     1......

CH is the x y coordinates of the original convex hull with an additional column of 1's so it can be multiplied by the affine matrices. CH looks like this:

CH =

155.0000  124.5000    1.0000
151.0000  124.5000    1.0000
149.5000  126.0000    1.0000
149.5000  138.0000    1.0000
150.5000  152.0000    1.0000
151.5000  155.0000    1.0000
152.5000  157.0000    1.0000
153.0000  157.5000    1.0000
155.0000  157.5000    1.0000
171.0000  151.5000    1.0000
188.0000  144.5000    1.0000
192.0000  142.5000    1.0000
192.5000  142.0000    1.0000
193.5000  140.0000    1.0000
193.5000  139.0000    1.0000
193.0000  138.5000    1.0000
185.0000  134.5000    1.0000
177.0000  131.5000    1.0000
155.0000  124.5000    1.0000

Can someone help me vectorize this loop so it runs faster? It doesn't run too slowly now but this is part of an ongoing effort to increase the efficiency of a VERY slow part of my image processing code. Any help would be greatly appreciated.

THANKS!

Answer 1

variant

[m n] = size(CH);
k = size(tmat,2);
out = CH*reshape(permute(reshape(tmat.',n,k,[]),[2 1 3]),3,[]);
TCH = reshape(permute(reshape(out,m,k,[]),[1 3 2]),[],k);