Search results for " Computational geometry"
showing 6 items of 16 documents
An Embedded, FPGA-based Computer Graphics Coprocessor with Native Geometric Algebra Support
2009
The representation of geometric objects and their transformation are the two key aspects in computer graphics applications. Traditionally, computer-intensive matrix calculations are involved in modeling and rendering three-dimensional (3D) scenery. Geometric algebra (aka Clifford algebra) is attracting attention as a natural way to model geometric facts and as a powerful analytical tool for symbolic calculations. In this paper, the architecture of Clifford coprocessor (CliffoSor) is introduced. CliffoSor is an embedded parallel coprocessing core that offers direct hardware support to Clifford algebra operators. A prototype implementation on a programmable gate array (FPGA) board is detailed…
Fixed-size Quadruples for a New, Hardware-Oriented Representation of the 4D Clifford Algebra
2010
Clifford algebra (geometric algebra) offers a natural and intuitive way to model geometry in fields as robotics, machine vision and computer graphics. This paper proposes a new representation based on fixed-size elements (quadruples) of 4D Clifford algebra and demonstrates that this choice leads to an algorithmic simplification which in turn leads to a simpler and more compact hardware implementation of the algebraic operations. In order to prove the advantages of the new, quadruple-based representation over the classical representation based on homogeneous elements, a coprocessing core supporting the new fixed-size Clifford operands, namely Quad-CliffoSor (Quadruple-based Clifford coproces…
Design Space Exploration of Parallel Embedded Architectures for Native Clifford Algebra Operations
2012
In the past few decades, Geometric or Clifford algebra (CA) has received a growing attention in many research fields, such as robotics, machine vision and computer graphics, as a natural and intuitive way to model geometric objects and their transformations. At the same time, the high dimensionality of Clifford algebra and its computational complexity demand specialized hardware architectures for the direct support of Clifford data types and operators. This paper presents the design space exploration of parallel embedded architectures for native execution of four-dimensional (4D) and five-dimensional (5D) Clifford algebra operations. The design space exploration has been described along wit…
An FPGA Implementation of a Quadruple-Based Multiplier for 4D Clifford Algebra
2008
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 s…
Modélisation géométrique de formes fractales pour la CAO
2020
International audience
An Optimized Architecture for CGA Operations and Its Application to a Simulated Robotic Arm
2022
Conformal geometric algebra (CGA) is a new geometric computation tool that is attracting growing attention in many research fields, such as computer graphics, robotics, and computer vision. Regarding the robotic applications, new approaches based on CGA have been proposed to efficiently solve problems as the inverse kinematics and grasping of a robotic arm. The hardware acceleration of CGA operations is required to meet real-time performance requirements in embedded robotic platforms. In this paper, we present a novel embedded coprocessor for accelerating CGA operations in robotic tasks. Two robotic algorithms, namely, inverse kinematics and grasping of a human-arm-like kinematics chain, ar…