Code covered by the BSD License

# 3D rotation of 3D image

09 Jan 2014 (Updated )

3D rotation of 3D image

rotationmat3D(r,Axis)
```function R= rotationmat3D(r,Axis)
%
% creates a rotation matrix such that R * x
% operates on x by rotating x around the origin r radians around line
% connecting the origin to the point "Axis"
%
% example:
% rotate around a random direction a random amount and then back
% the result should be an Identity matrix
%
%r = rand(4,1);
%rotationmat3D(r(1),[r(2),r(3),r(4)]) * rotationmat3D(-r(1),[r(2),r(3),r(4)])
%
% example2:
% rotate around z axis 45 degrees
% Rtest = rotationmat3D(pi/4,[0 0 1])
%
%Bileschi 2009

if nargin == 1
if(length(rotX) == 3)
rotY = rotX(2);
rotZ = rotZ(3);
rotX = rotX(1);
end
end

% useful intermediates
L = norm(Axis);
if (L < eps)
error('axis direction must be non-zero vector');
end
Axis = Axis / L;
L = 1;
u = Axis(1);
v = Axis(2);
w = Axis(3);
u2 = u^2;
v2 = v^2;
w2 = w^2;
c = cos(r);
s = sin(r);
%storage
R = nan(3);
%fill
R(1,1) =  u2 + (v2 + w2)*c;
R(1,2) = u*v*(1-c) - w*s;
R(1,3) = u*w*(1-c) + v*s;
R(2,1) = u*v*(1-c) + w*s;
R(2,2) = v2 + (u2+w2)*c;
R(2,3) = v*w*(1-c) - u*s;
R(3,1) = u*w*(1-c) - v*s;
R(3,2) = v*w*(1-c)+u*s;
R(3,3) = w2 + (u2+v2)*c;
```