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Digital Differential Geometry Processing

Journal of Computer Science & Technology 2006年第5期21卷 847-860页

作者：刘新国鲍虎军彭群生 State Key Lab of CAD& CG Zhejiang University Hangzhou 310027 P.R. China

The theory and methods of digital geometry processing has been research area in computer graphics, as geometric models serves as the core data for 3D graphics applications. The purpose of this paper is to introduce some recent advances in digital geometry processing, particularly mesh fairing, surface parameterization and mesh editing, that heavily use differential geometry quantities. Some related concepts from differential geometry, such as normal, curvature, gradient, Laplacian and their counterparts on digital geometry are also reviewed for understanding the strength and weakness of various digital geometry processing methods.

关键词： digital geometry geometric algorithm mesh editing Laplacian parameterization

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geometric Properties of Ribs and Fans of a Bézier Curve

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Journal of Computer Science & Technology 2006年第2期21卷 279-283页

作者： Joo-Haeng Lee Hyungjun Park Electronics and Telecommunications Research Institute Daejeon 305-350 Korea Chosun University Gwangju 501-759 Korea

Ribs and fans are interesting geometric entities that are derived from a given Bézier curve or surface based on the recent theory of rib and fan decomposition. In this paper, we present some of new geometric properties of ribs and fans for a Bézier curve including composite fans, rib-invariant deformation, and fan-continuity in subdivision. We also give some examples for the presented properties.

关键词： geometric algorithm Bézier curve composite fan rib-invariance fan-continuity

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A Comparative Study of geometric algorithms for Real-Time Grasping Force Optimization

A Comparative Study of Geometric Algorithms for Real-Time Gr...

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第二十二届中国控制会议

作者： Liu G.F. Xu J.J. Li Z.X. Dept. of Electrical and Electronic Engineering Hong Kong University of Science and Technology Clear Water Bay, Kowloon, Hong Kong

＜正＞Real-time grasping force optimization problem can be naturally formulated as a convex optimization problem on the Riemannian manifold of positive definite matrices subject to linear constraints for which many algorithms, including gradient algorithms, Newton algorithms, and interior point algorithms, have been developed. In all these algorithms we need to specify a step size in every iteration and a valid initial point to start the recursion. In this paper we propose several strategies for selecting such a step size according to the properties of each algorithm. Simulation and experimental results show the different performances of these algorithms from computation time and convergence rates.

关键词： Real-time grasping force optimization geometric algorithm Step size Convergence rates

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