A New Embedded Coprocessor for Clifford Algebra Based Software Intensive Systems

Abstract

Computer graphics applications require efficient tools to model geometric objects and their transformations. Clifford algebra (also known as geometric algebra) is receiving a growing attention in many research fields, such as computer graphics, machine vision and robotics, as a new, interesting computational paradigm that offers a natural and intuitive way to perform geometric calculations. At the same time, compute-intensive graphics algorithms require the execution of million Clifford operations. Clifford algebra based software intensive systems need therefore the support of specialized hardware architectures capable of accelerating Clifford operations execution. In this paper the architecture of CliffoSorII (Clifford coprocessor II), an embedded coprocessor that offers direct hardware support to Clifford algebra operations, is introduced. The coprocessor has been designed, implemented and tested on a Field Programmable Gate Array (FPGA) board. The experimental results show the potential to achieve a 20x speedup for Clifford sums and differences and a 5x speedup for Clifford products against the analogous operations in Gaigen, a standard geometric algebra software library generator for general purpose processors. An execution analysis of a ray tracing application is also presented.