Engineering graphics in geometric algebra

Abstract

We illustrate the suitability of geometric algebra for representing structures and developing algorithms in computer graphics, especially for engineering applications. A number of example applications are reviewed. Geometric algebra unites many underpinning mathematical concepts in computer graphics such as vector algebra and vector fields, quaternions, kinematics and projective geometry, and it easily deals with geometric objects, operations, and transformations. Not only are these properties important for computational engineering, but also for the computational point-of-view they provide. We also include the potential of geometric algebra for optimizations and highly efficient implementations. © 2010 Springer-Verlag London Limited.