Polygon Properties Calculated from the Vertex Neighborhoods

Calculating properties of polyhedra given only the set of the locations and neighborhoods of the vertices is easy. Possible properties include volume, surface area, and point containment testing. No global topological information at all is explicitly needed (although the complete global topology could be recovered). The neighborhood of the vertex means the directions of the edges and I'accs on it but not their extents. These vertex-based formulae are dual to the usual formulae that use the facts. They have been implemented and the stability against inconsistent data tested. AiteI'native data struclures and formulae for polyhedron calculation are iniporlallt since special CFxW.S aV2 % function partly of the dRtk% structure, and because different methods have different nllmcricsl accuracy and error detection propertics. ACKNOWLEDGEMENTS This work was supported by the National Science Il'ouudation under PYI grant no. ECS-83.51942. It was partly pcrfolmed at the Center for ...

• Type: Conference
• Year: 1987
• Where: COMPGEOM
• Authors: Wm. Randolph Franklin
• Keywords: COMPGEOM 1987, Discrete Geometry, Formulae, Point Containment Testing, Properties Include Volume