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Figu re 7-A planar body and the four models associated with it
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... We are thus naturally led to consider polygonal arrangements, in which the curves are polygonal lines. In a previous paper [3], we studied such arrangements, and described EDP, a system for computing them. Another implementation is described in [8]. ...
... R. The simplest method for computing polygonal approximations of an implicit curve C = f ?1 (0) is full enumeration: The domain is subdivided uniformly into a mesh of small rectangles, and C is approximated by a linear segment within each rectangle for which the sign of f at its vertices is not the same. The segments thus obtained can then be fed into a system for computing polygonal arrangements [3,8]. ...
this paper is to find, whenever possible, the exact topology determined by a set of implicit curves, without having to resort to polygonal approximations. It is important to distinguish exact topology from exact geometry. In general, we cannot expect to obtain exact geometric results, such as vertex coordinates, since we must rely on numerical methods for curve sampling and intersection. Nevertheless, in many cases we can determine the exact topology of the arrangement. In this paper, we use range analysis [9] to find regions where the arrangement is locally simple. Even when it is not possible to find exactly the complete topology, we try to distinguish mathematically provable properties from those that depend on the adopted tolerance level for numerical approximations.
... This reenement can be done by inserting each curve segment into the appropriate faces. Since the geometrical support of a face is homeomorphic to < 2 , the method described in16], to include a simple segment in a (planar) face, can be readily adapted to deal with this case.If, at the end of this process, E l is empty, then we conclude that S was either disconnected from the CGC or weakly connected to it (linked only by vertices or wireframes). In both cases, R is the region containing an arbitrary point of an edge of S. If E l is not empty then, for each edge e i in E l , the face succeeding S in the ordered cycle of faces about e i must be found. ...
This paper deals with the problem of creating and maintaining a spatial subdivision, defined by a set of surface patches. The main goal is to create a set of functions which provides a layer of abstraction capable of hiding the geometric and topological problems which occur when one creates and manipulates spatial subdivisions. The study of arbitrary spatial subdivisions extends and unifies the techniques used in non-manifold solid modelling and allows the modelling of heterogeneous objects.
... The paper by Souza and Gattass [SOUZ92] introduces the use of graph theory data structures to support the generation of arbitrary shell meshes. Carvalho, Gattass and Martha [CARV90], Campos, Martha and Gattass [CAMP91] and Celes Filho, Martha and Gattass [CELE91] discuss the use of topological data structures to aid the processes of generating meshes and visualizing analysis results. ...
This paper deals with the problem of creating and maintaining a spatial
