Abstract.
The paper proposes a new method for the boundary representation of three-dimensional (not necessarily convex) polyhedra, called a resolvable representation , in which small numerical errors do not violate the symbolic part of the representation. In this representation, numerical data are represented partly by the coordinates of vertices and partly by the coefficients of face equations in such a way that the polyhedron can be reconstructed from the representation in a step-by-step manner. It is proved that any polyhedron homeomorphic to a sphere has a resolvable representation, and an algorithm for finding such a representation is constructed.
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Received January 21, 1997, and in revised form April 29, 1998.
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Sugihara, K. Resolvable Representation of Polyhedra . Discrete Comput Geom 21, 243–255 (1999). https://doi.org/10.1007/PL00009419
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DOI: https://doi.org/10.1007/PL00009419