Design Space Exploration of Parallel Embedded Architectures for Native Clifford Algebra Operations

摘要

THE COMPUTATIONAL SOLUTIONS used for computer graphics, including graphics processing units (GPUs) and stream processors, usually exploit linear algebra and matrix calculations for the formalization and implementation of geometric constructions. The main problem with this approach is that geometric objects and their transformations have to be represented by a very limited set of primitives (scalars, vectors, and matrices); at the same time, classical linear algebra does not provide universal geometric operations. The low representational power of linear algebra, as well as its limited geometric intuitiveness, result in a separation between geometric reasoning and low-level matrix-based algorithms, leading to implementation errors.