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 prop...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.展开更多
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 so...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.展开更多
文摘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.
基金The research work of this paper is supported by the National Natural Science Foundation of China under Grant No. 60021201 the Cultivation Fund of the Key Scientific and Technical Innovation Project, Ministry of Education of China under Grant No. 705027 and the National Grand Fundamental Research 973 Program of China under Grant No. 2002CB312101.
文摘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.
