This paper deals with the problem of creating and maintaining a spatial

Computer graphics is a defining application for computational geometry. The interaction between these fields is explored through two scenarios. Spatial subdivisions studied from the viewpoint of computational geometry are shown to have found application in computer graphics. Hidden surface removal problems of computer graphics have led to sweepline and area subdivision algorithms in computational geometry. The paper ends with two promising research areas with practical applications: precise computation and polyhedral decomposition. 1. Introduction Computational geometry and computer graphics both consider geometric phenomena as they relate to computing. Computational geometry provides a theoretical foundation involving the study of algorithms and data structures for doing geometric computations. Computer graphics concerns the practical development of the software, hardware and algorithms necessary to create graphics (i.e. to display geometry) on the computer screen. At the interface l...

Abstract: This paper presents an object-oriented approach for creating multi-region non-manifold models with NURBS. The main motivation is that the geometry and shape of realistic engineering objects are intrinsically complex, usually composed by several materials and regions. Therefore, automatic and/or adaptive meshing algorithms have become revealed themselves quite useful to increase the reliability of the procedures of a FEM numerical analysis. The present approach is concerned with two aspects of 3D FEM simulation: geometric modeling, with automatic multi-region detection, and support to automatic finite element mesh generation. The final objective is to use geometric models directly in numerical applications. 1

This paper deals with the problem of creating and maintaining a spa-tial subdivision, defined by a set of surface patches. The main goal is to create a set of functions which provides a layer of abstraction capable of hiding the geometric and topological problems which occur when one cre-ates and manipulates spatial subdivisions. The study of arbitrary spatial subdivisions extends and unifies the techniques used in nonmanifold solid modeling and allows the modeling of heterogeneous objects.