Apply Rotation Matrix to a Set of Points

Hi all,

I have a set of 3D points (3 by N) to which I am applying a rotation (3 by 3) and translation (1 by 3). I can't figure out a way to get it out of a for-loop, and as you can guess, for loops are too slow.

I currently have:

for i=1:N
   rotPoints(:,i) = rotationMatrix*points(:,i)+translationVector;
end

giving me what I want. Tried using bsxfun() with it but no success.

Cheers guys, Andrew

Answer 1

[Matt J]

Two options:

(1) Loop over rows instead of columns (a much shorter loop)

rotPoints=rotationMatrix*points;

for i=1:3
   rotPoints(i,:) = rotPoints(i,:)+translationVector(i);
end

(2) using BSXFUN

   rotPoints=bsxfun(@plus, rotationMatrix*points,  translationVector);

Hard to say which will be faster...

[AndrewL]

Timed it for my problem, which is for a transform of 640x480 points (307200 operations off the top of my head). 1st method took 0.027217 seconds, 2nd method took 0.025025 seconds.

So 1st is marginally faster in this case. I imagine this could be different for much larger operations though.

Cheers by the way

[Matt J]

marginally slower, I think you mean. Your timings say that the 1st method took longer.

Answer 2

[Zihe Gao]

No need to use for loop.

translationMat = repmat(traslationVector,N,1); 

rotPoints = rotationMatrix*points+translationMat;

[Matt J]

BSXFUN will be faster and more memory-conservative than REPMAT in pre-R2016b Matlab (this question was from 2012...).

Post-R2016b you don't need either one! It's a one-liner

    rotPoints = rotationMatrix*points+translationVector;

[Zihe Gao]

Nice.

[Matt J]

Even in R2018a, I still see for-loops showing competitive speed for certain data sizes

N=1e6;

A=rand(3,N);
b=rand(3,1);

tic;
 for i=1:3
   A(i,:)=A(i,:)+b(i);
 end
toc
%Elapsed time is 0.014138 seconds.

tic;
 A=bsxfun(@plus, A,b);
toc;
%Elapsed time is 0.008340 seconds.

tic;
 A=A+b;
toc;
%Elapsed time is 0.011921 seconds.

tic;
  A=A+repmat(b,1,N);
toc;
%Elapsed time is 0.019553 seconds.