The objective of this thesis is to investigate the problem of boundary evaluation, which transforms the CSG model of a scene to its BRep corresponding model, for scenes defined by quadrics. This algorithm consists of four steps : (i) the parameterization of every intersection curve between quadrics ; (ii) the calculation of the intersection points between such curves and the quadrics ; (iii) th...

The triangulation of boundary representation geomet-ries (BRep geometries) is neccessary for display generation , stereo-lithography applications and also nite element mesh (FE mesh) generation. The accuracy of the tesselation is of great signiic-ance not only for stereo-lithography and rendering algorithms but also for FE mesh generation, since even minor simpliications of the geometry of the ...

The rst section will build some basics. It will contrast implicit and parametric methods, and overview the broad range of implicit surfaces used today. It will develop fundamental properties of quadratic implicit polynomial surfaces, and illustrate how these surfaces have been traditionally used in CAD systems for handling \prismatic" objects (e.g. piston rods), and how recent research on algeb...

This paper addresses the problem of CAD geometric model pre-processing, known as CAD repair. Three main components of the CAD model repair: global geometric continuity of the boundary, topological validity and model preparation are discussed. General definition and classification of CAD errors for geometric models, using the Boundary REPresentation (BREP) are given. Methods, invariant from the ...

Difficulties with part oriented solid modeling tools have motivated the development of a derivationbased solid modeling system to aid in preliminary submarine design tasks. The projected system is a graphically editable geometric rule system based on Extended Pattern Grammars with Variables (EPGVs). This paper reviews relevant characteristics of Boundary Representation Modelers, Featurebased Mo...

There are limitations to the current BRep based “model then animate” paradigm when animating time-dependent (dynamic) objects. This paper describes an approach to modeling dynamic objects directly in space-time or even higher dimensional space. The use of the function representation (FRep) is proposed due to the ease with which it handles higher dimensions. After creating a multidimensional FRe...

This paper aims to describe the methodology behind the computer aided design tool TopoVisu. The objective of this tool is to support analysts and designers in their work, mainly by helping detect errors in models and meshes. But the error detection is not the only feature of TopoVisu, it also provides a visualization environment to cope with data portability issues. The paper briefly describes ...

While almost all collision detection algorithms have been linked to a particular object representation scheme, few attempts have been made using hybrid methods to exploit the advantages of multiple representations of objects. In this paper we present a collision detection algorithm based on a dual b-rep/CSG representation of concave polyhedra initially represented in b-rep. Our method naturally...

The union of axis-aligned boxes results in a constrained structure that is advantageous for solving certain geometrical problems. A widely used scheme for solid modelling systems is the boundary representation (Brep). We present a method to obtain the B-rep of a union of axis-aligned boxes. Our method computes all boundary vertices, and additional information for each vertex that allows us to a...

We present the Combined BRep as a multiresolution data structure suitable for interactive modeling and visualization of models composed of both free-form and polygonal parts. It is based on a half-edge data structure combined with Catmull/Clark subdivision surfaces. In addition to displaying the curved parts of the surface at an adaptive levelof-detail, the control mesh itself can be changed in...