Upgrading from:

Geometry`Rotations`

All the functionality in Geometry`Rotations` is now available in the built-in Mathematica kernel function RotationTransform.

Here is the matrix for rotation by θ degrees:

Version 5.2 << Geometry`Rotations`;
MatrixForm[RotationMatrix2D[\[Theta]]]

In Version 6, you get a TransformationFunction that represents a rotation in 2D by θ radians about the origin:

In[32]:=
Click for copyable input
Out[32]=

The point {0,0} is rotated about the point {1,1} by 60 degrees:

Version 5.2 << Geometry`Rotations`;
MatrixForm[RotationMatrix2D[N[Pi/3]]];
Rotate2D[{0., 0.}, N[Pi/3], {1., 1.}]
In[33]:=
Click for copyable input
Out[33]=
In[53]:=
Click for copyable input
Out[53]=

RotationMatrix rotates points in the opposite direction from RotationMatrix2D:

Version 5.2 << Geometry`Rotations`;
RotationMatrix2D[phi]
In[8]:=
Click for copyable input
Out[8]=

Similarly RotationTransform rotates points in the opposite direction from Rotate2D:

Version 5.2 << Geometry`Rotations`;
Rotate2D[{x, y}, phi, {x0, y0}]
In[9]:=
Click for copyable input
Out[9]=

RotationMatrix uses yaw-pitch-roll angles rather than the Euler angles used by RotationMatrix3D:

Version 5.2 << Geometry`Rotations`;
RotationMatrix3D[phi, theta, psi]
In[10]:=
Click for copyable input
Out[10]=