6533b821fe1ef96bd127c502
RESEARCH PRODUCT
An FPGA Implementation of a Quadruple-Based Multiplier for 4D Clifford Algebra
Salvatore VitabileSilvia FranchiniFilippo SorbelloAntonio GentileGiorgio Vassallosubject
Settore ING-INF/05 - Sistemi Di Elaborazione Delle InformazioniTheoretical computer scienceComputer scienceClifford algebraClifford Algebra computational geometry application-specific coprocessor FPGA prototypingSolid modelingOperandData typeComputer graphicsGeometric algebraComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONLinear algebraArithmeticGeometric modelingdescription
Geometric or Clifford algebra is an interesting paradigm for geometric modeling in fields as computer graphics, machine vision and robotics. In these areas the research effort is actually aimed at finding an efficient implementation of geometric algebra. The best way to exploit the symbolic computing power of geometric algebra is to support its data types and operators directly in hardware. However the natural representation of the algebra elements as variable-length objects causes some problems in the case of a hardware implementation. This paper proposes a 4D Clifford algebra in which the variable-length elements are mapped into fixed-length elements (quadruples). This choice leads to a simpler and more compact hardware implementation of 4D geometric algebra. The paper also presents the architecture of CliffArchy, a coprocessing core supporting the new fixed-length Clifford operands. A prototype implementation on a FPGA board is described.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2008-01-01 |