LBRARi"tES

Many application programs driven from modern CAD/CAM systems often operate on approximate lower order representations of the exact geometric definition. These applications include visualization, fundamental geometric calculations such as inte-grals, finite element or boundary element meshing for analysis and data exchange between various geometric modelers or design and fabrication systems. For this rea-son, a robust piecewise linear approximation method of high order and procedural curves and surfaces is necessary. This thesis presents a piecewise linear approximation method of edges and faces of complicated boundary representation (B-rep) models within a user specified geo-metric tolerance. The proposed method uses numerically robust interval geometric definitions and computations and also addresses the problem of topological consis-tency between the exact geometry and its approximation. These are among the most important outstanding issues in geometry approximation problems. The possible in-appropriate intersections of the approximating elements are efficiently checked an