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authors Weiler, Kevin J.
year 1986
title Topological Structures for Geometric Modeling
source Computer and Systems Engineering, Rensselaer Polytechnic Institute
summary Geometric modeling technology for representing three-dimensional objects has progressed from early wireframe representations, through surface representations, to the most recent representation, solid modeling. Each of these forms has many possible representations. The boundary representation technique, where the surfaces, edges, and vertices of objects are represented explicitly, has found particularly wide application. Many of the more sophisticated versions of boundary representations explicitly store topological information about the positional relationships among surfaces, edges, and vertices. This thesis places emphasis on the use of topological information about the shape being modeled to provide a framework for geometric modeling boundary representations and their implementations, while placing little constraint on the actual geometric surface representations used. The major thrusts of the thesis fall into two areas of geometric modeling. First, a theoretical basis for two-manifold solid modeling boundary topology representation is developed. The minimum theoretical and minimum practical topological adjacency information required for the unambiguous topological representation of manifold solid objects is determined. This provides a basis for checking the correctness of existing and proposed representations. The correctness of the winged edge structure is also explored, and several new representations which have advantages over existing techniques are described and their sufficiency verified. Second, a non-two-manifold boundary geometric modeling topology representation is developed which allows the unified and simultaneous representation of wireframe, surface, and solid modeling forms, while featuring a representable range beyond what is achievable in any of the previous modeling forms. In addition to exterior surface features, interior features can be modeled, and non-manifold features can be represented directly. A new data structure, the Radial Edge structure, which provides access to all topological adjacencies in a non-manifold boundary representation, is described and its completeness is verified. A general set of non-manifold topology manipulation operators is also described which is independent of a specific data structure and is useful for insulating higher levels of geometric modeling functionality from the specifics and complexities of underlying data structures. The coordination of geometric and topological information in a geometric modeling system is also discussed.
series thesis:MSc
references Content-type: text/plain
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