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UBC Theses and Dissertations

An algorithm for polyhedron modelling and its implementation Yeung, Kwai-Biu Ricky


This thesis describes an algorithm for calculating the theoretic set operations union, intersection, and difference of two polyhedra. The polyhedra are in the Eulerian surface description format, specified by their vertices, edges, and faces. The representation of polyhedra is based on the unambiguous Boundary Representation scheme. The domain of this algorithm includes all flat-surfaced polyhedra; however, nested holes and curved surfaces are not permitted. The thesis is divided into three parts. The first part presents some mathematical definitions and the representation scheme for polygons and polyhedra. Since there are many similarities between 2-D polygon modelling and 3-D polyhedron modelling, the 2-D polygon modelling algorithm is presented next, followed by the 3-D polyhedron modelling algorithm.

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