Acceleration and Energy Efficiency of a Geometric Algebra Computation using Reconfigurable Computers and GPUs

Geometric algebra (GA) is a mathematical framework that allows the compact description of geometric relationships and algorithms in many fields of science and engineering. The execution of these algorithms, however, requires significant computational power that made the use of GA impractical for many real-world applications. We describe how a GA-based formulation of the inverse kinematics problem from computer animation and robotics can be accelerated using reconfigurable FPGA-based computing and using a graphics processing unit (GPU). The practical evaluation covers not only the sheer compute performance, but also the energy efficiency.