An FPGA Implementation of a Quadruple-Based Multiplier for 4D Clifford Algebra

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4 Citazioni (Scopus)

Abstract

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.
Lingua originaleEnglish
Pagine743-751
Numero di pagine9
Stato di pubblicazionePublished - 2008

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Algebra
Field programmable gate arrays (FPGA)
Hardware
Computer graphics
Computer vision
Mathematical operators
Robotics

All Science Journal Classification (ASJC) codes

  • Hardware and Architecture
  • Control and Systems Engineering

Cita questo

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abstract = "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.",
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AU - Franchini, Silvia Giuseppina

AU - Gentile, Antonio

AU - Sorbello, Filippo

AU - Vitabile, Salvatore

AU - Vassallo, Giorgio

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

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KW - FPGA prototyping

KW - application-specific coprocessor

KW - computational geometry

UR - http://hdl.handle.net/10447/59412

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