Many graphics and computer-aided design applications require that the polygonal meshes used in geometric computing have the properties of not only 2-manifold but also are orientable. In this paper, by collecting previ...
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Many graphics and computer-aided design applications require that the polygonal meshes used in geometric computing have the properties of not only 2-manifold but also are orientable. In this paper, by collecting previous work scattered in the topology and geometry literature, we rigorously present a theoretical basis for orientable polygonal surface representation from a modem point of view. Based on the presented basis, we propose a new combinatorial data structure that can guarantee the property of orientable 2-manifolds and is primal/dual efficient. Comparisons with other widely used datastructures are also presented in terms of time and space efficiency.
Software design solutions are presented for combinatorial data structures, such as polyhedral surfaces and planar maps, tailored for program libraries in computational geometry. Design issues considered are flexibilit...
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Software design solutions are presented for combinatorial data structures, such as polyhedral surfaces and planar maps, tailored for program libraries in computational geometry. Design issues considered are flexibility, time and space efficiency, and ease-of-use. We focus on topological aspects of polyhedral surfaces and evaluate edge-based representations with respect to our design goals. A design for polyhedral surfaces in a halfedge datastructure is developed following the generic programming paradigm known from the Standard Template Library STL for C++. Connections are shown to planar maps and face-based structures, (C) 1999 Elsevier Science B.V. All rights reserved.
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