Isothetic polyhedra and monotone boolean formulae
We consider the problem of converting boundary representations of isothetic polyhedra into constructive solid geometry (CSG) representations. The CSG representation is a boolean formula based on the halfspaces supporting the faces of the polyhedron. This boolean formula exhibits two important featur...
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| Tipo de recurso: | informe técnico |
| Fecha de publicación: | 1994 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/96992 |
| Acceso en línea: | https://hdl.handle.net/2117/96992 |
| Access Level: | acceso abierto |
| Palabra clave: | Boundary representations Isothetic polyhedra Constructive solid geometry CSG |
| Sumario: | We consider the problem of converting boundary representations of isothetic polyhedra into constructive solid geometry (CSG) representations. The CSG representation is a boolean formula based on the halfspaces supporting the faces of the polyhedron. This boolean formula exhibits two important features: no term is complemented (it is monotone) and each supporting halfspace appears in the formula once and only once. In this work we prove that such a representation exists for those cyclic isothetic polyhedra such that for each cyclic deficiency set in the polyhedron it is possible to find out at least either a convex or a concave path of extremal edges which splits the cyclic deficiency set into two subsets. |
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