Chapter 2 MULTIRESOLUTION MODELING OF THREE-DIMENSIONAL SHAPES

Manipulation of models of complex three-dimensional shape s is common in computer graphics and virtual reality, computer-aidedsign, geographic information systems, medicine, etc. In this chapter, we deal with geometric models based on spati al decompositions, also known as geometric meshes . A mesh is an aggregate of a finite number of basic entities, called cells. When a mesh is used to describe the shape of an object, each cell represents a portion of the obje ct. The resolution of a mesh is related to the density of its cells, and it is a fund amental parameter for the accuracy of the object representation. Accurate rep resentations need high resolutions, and, thus, a high number of cells, which le ads to high costs for managing the mesh. Three-dimensional models are either fully synthetic or obt ained from sampling physical objects. In both cases, the models produced b y modern tools for either 3D acquisition and reconstruction, or computeraided shape design, become more and more accurate, with larger and larger sizes. Models at high resolution can provide very accurate object r presentations, but theycaneasilybecome too large tobe effectively used in tasks suchas rendering, recognition, classification, collision detection, an d manipulation planning. This problem cannot be simply solved by using more powerful m achines, since, while hardware and software technology improves, the resol ution of geometric models that we are able to construct increases at an even fast r r te. However, most applications tasks do not need a high resoluti on ineach parts of an object, at all times. Thus, we can reduce memory and computational costs