Geometric Uncertainty in Solid Modeling

Abstract

In solid modeling geometric uncertainty arises in several settings. For systems which use analytic solutions when possible, it is necessary to determine the type of surface so that the correct analytic solver will be used. In passing from 3-D space data to 2-D parametric data, the algorithms used are vulnerable to geometric uncertainty — examples and solutions from a project in a commercial solid modeler [ACIS, 2001] are presented. For any solid modeler, there is a fundamental uncertainty imposed by the use of exact logic for topology together with necessarily inexact logic for geometry.