Rotation Transforms in the Plane

Abstract

This chapter starts by introducing 2D transforms and how homogeneous coordinates provide a mechanism to support translation. Matrix transforms are developed to rotate a point about the origin, and about an arbitrary point, as well as composite rotations. The chapter then covers the role inverse transforms play in either reversing a point rotation, or simulating a frame of reference rotation. After matrix transforms, the reader is introduced to 2D multivector transforms to translate a point, rotate a point about the origin, and rotate a point about an arbitrary point. Finally, the chapter concludes with a summary and all the associated transforms.