Finding Compact Coordinate Representations for Polygons and Polyhedra

Practical solid modeling systems are plagued by numerical problems that arise from using oatingpoint arithmetic. For example, polyhedral solids are often represented by a combination of geometric and combinatorial information. The geometric information might consist of explicit plane equations, with oating-point coe cients; the combinatorial information might consist of face, edge, and vertex adjacencies and orientations, with edges de ned by face-face adjacencies and vertices by edge-edge adjacencies. Problems arise when numerical error in geometric operations causes the geometric information to become inconsistent with the combinatorial information. These problems could be avoided by using exact arithmetic instead of oating-point arithmetic. However, some operations, like rotation, increase the number of bits required to represent the plane equation coe cients. Since the execution time of exact arithmetic operators increases with the number of bits in the operands, the increased num...

• Type: Conference
• Year: 1990
• Where: COMPGEOM
• Authors: Victor Milenkovic, Lee R. Nackman
• Keywords: Combinatorial Information, COMPGEOM 1990, Discrete Geometry, Plane Equation, Plane Equation Coe