Multiresolution mesh processing for triangular and tetrahedral meshes.
Ulf Labsik · OPUS FAU (Kooperativer Bibliotheksverbund Berlin-Brandenburg (KOBV), on behalf of the Universitätsbibliothek Erlangen-Nürnberg) · 2004
Technical advances in the field of 3D scanning technologies in the last years have resulted in more and more detailed three dimensional models of real world objects.Hence, the size of the models has grown enormously.Despite of increased performance of computers and graphics hardware, efficient algorithms for processing such models are required more than ever.The most commonly used technique for modeling three dimensional objects in Computer Graphics are triangle meshes.To exactly describe the complex geometry of real world objects, such triangle meshes often consist of millions of triangles.These large triangle meshes are difficult to render.Also, modifying or transmitting such meshes via computer networks, like the Internet, is difficult without efficient algorithms.To overcome the difficulties of processing large meshes, multiresolution methods can be used.The mesh is stored in different hierarchy levels, which can be used to solve a problem more efficiently.In the context of this work, we have developed and implemented different methods for the generation of multiresolution representations.We distinguish between two different types of meshes: triangle meshes and tetrahedral grids.At first, we discuss subdivision methods for triangle meshes.They are used to generate smooth surfaces from a given triangle mesh.In this context we have developed a new interpolating subdivision scheme based on √ 3 refinement of triangle meshes.Such methods have the advantage of a slower growth of the number of triangles per refinement step compared to standard schemes and enable a simpler adaptive refinement technique.Uniform subdivision generates triangle meshes with a special structure, so-called semi-regular meshes.Such meshes are especially well suited for various multiresolution algorithms.Hence, in this work we present different methods for generating semiregular triangles meshes from different types of input data.These are point clouds, arbitrary triangle meshes and volume data sets.In addition, an algorithm for the progressive transmission of semi-regular meshes is presented, which is based on inverse subdivision.This thesis also deals with a second type of meshes, tetrahedral grids.They are mainly used in the context of numerical simulations.A method is presented for generating a progressive representation of a given tetrahedral grid, which consists of a coarse base mesh and information for the refinement of the grid.The progressive representation is well suited for the transmission of grids via computer networks and remote iii Revision 1.1