Problem
I understand that in general, if I define a 3D rotation matrix such as:
R = [
1,0,0;
0,cos(theta),-sin(theta);
0,sin(theta),cos(theta)
]
Then I can rotate a pointcloud pts where:
where x, y, z are datasets of arbitrary size and
by:
then:
[xp, yp, zp] = deal(pts(:,1), pts(:,2), pts(:,3))
I can then reshape the output vectors using
xp = reshape(xp, size(x))
yp = reshape(yp, size(y))
zp = reshape(zp, size(z))
Is there a more generalized way for matlab to apply a 3D rotation as described with R (3 x 3 matrix) such that I can for instance apply the rotation to an X, Y, Z volume (3 x m x n) in a single operation? For instance, say I define my X, Y, Z as a meshgrid so that each X, Y, Z is a m x n x p volume, can I do somethine like this
V = cat(3, X, Y, Z)
V = V*R
I would think an operation like this would be much faster and cleaner to implement than unloading into vectors and reshaping afterwards.
Attempt at Solution
[Lx,Ly, dL] = deal(10,20,1);
x = linspace(-Lx/2, Lx/2, Lx/dL);
y = linspace(-Ly/2, Ly/2, Ly/dL);
[X,Y] = meshgrid(x,y);
Z = zeros(size(X));
X = X(:);
Y = Y(:);
Z = Z(:);
V = cat(3, X, Y, Z);
TH = [pi/4, 0, 0];
Rx = [1,0,0; 0,cos(TH(1)),-sin(TH(1)); 0,sin(TH(1)),cos(TH(1))];
Ry = [cos(TH(2)),0,sin(TH(2)); 0,1,0; -sin(TH(2)),0,cos(TH(2))];
Rz = [cos(TH(3)),-sin(TH(3)),0; sin(TH(3)),cos(TH(3)),0; 0,0,1];
R = Rx*Ry*Rz;
V = V*R;
surf(V(:,:,1), V(:,:,2), V(:,:,3),'facecolor','none','edgecolor','black')
