3-D geometric transformation of a matrix of 3-D points

I have a set of nine 3-D points, with the following form:

    e = 0.2;
    points3d = [-e -e 0
        -e 0 0
        -e e 0
        0 -e 0
        0 0 0
        0 e 0
        e -e 0
        e 0 0
        e e 0]';

I would like to apply a 3-D geometric transformation to this set of nine 3d points, so that they are rotated and translated to a random position. What is the easiest way to do this?

Thanks.

Answer 1

[Mike Garrity]

Probably the simplest is something like this:

mat = makehgtform('axisrotate',[1 1 1],pi/5, 'translate',[1 2 3]);
newpts = mat * [points3d; ones(1,9)];

See this blog post for background. The examples in that post are mostly 2D to keep things compact, but the theory is the same in 3D.

[Andrea Alberti]

Thanks, I like the makehgtform, very compact.