Representing Rotations and Orientations in Geometric Computing

Geometric computing with three-dimensional rotations and orientations is a fundamental issue in three-dimensional computer graphics. Our approach was inspired by affine geometry and coordinatefree geometric programming. The basic idea of affine geometry is to make a distinction between points and vectors. The relation between orientations and rotations is analogous to the relation between points and vectors. Similarly to affine geometry, we argue that rotations and orientations should be represented differently in geometric computing. We show that, in three-dimensional space, unit quaternions (or rotation matrices) cannot parameterize rotations without singularity, but rotation vectors can. Conversely, rotation vectors cannot parameterize orientations without singularity, but unit quaternions (or rotation matrices) can. From these observations, we suggest that orientations should be represented by unit quaternions (or rotation matrices) and rotations should be represented by three-dim...

• Type: Journal
• Year: 2008
• Where: CGA
• Authors: Jehee Lee
• Keywords: CGA 2008, Computational Geometry, Geometric, Rotations, Three-dimensional