Question

Background:

  a = 0; b = 0; c = 0;
  Manipulate[Graphics3D[
    GeometricTransformation[
     {Cuboid[{0, 0, 0}, {1, 1, 1}]},
     {RotationTransform[x, {1, 1, 0}, {a, b, c}]}], 
    ViewPoint -> Left], {x, 0, 2 \[Pi]}]

My question concerns RotationTransform with the following signature:

  RotationTransform[x, {1, 1, 0}, {a, b, c}]

The documentation says: "gives a 3D rotation around the axis w anchored at the point p", in the example above w={1,1,0} and p={a,b,c}.

To my surprise the rotation acts the same no matter what values I assign to (a,b,c). I assume that I don’t understand the docs, made an error somewhere. I would have expected at least a different rotation for different values of a,b,c. Changing the vector w behaves as expected.

Please explain the purpose of p.

Answer 1

Consider the following example from the help:

gr={Cuboid[],AbsolutePointSize[10],Opacity[1],{Magenta,Point[{0,0,0}]},   
   {Green,Point[{1,1,1}]}};

p = {1,1,1};
Graphics3D[{{Opacity[.35], Blue, gr}, 
  GeometricTransformation[{Opacity[.85], Red, gr}, 
   RotationTransform[Pi/6, {0, 0, 1}, p]]}, Boxed -> False]

And now with :

p={1,0,0};