Low Distortion Shell Map Generation

Geometric details are often used in computer graphics to enhance the visual richness of a 3D surface. Detail is commonly represented by two-dimensional textures, bump mapping, or displacement mapping applied to objects, polygonal meshes or higher-level primitives. These methods cannot represent the fine-scale surface geometry that is an integral component of the appearance of many real-world materials and objects. Thus it is necessary to address shell map methods. Shell map is a bijective mapping between shell space (the space between a base surface and its offset) and texture space. It can be used to generate small-scale features on surfaces using a variety of modeling techniques. In this dissertation, we present an efficient algorithm, which reduces distortion by construction, for the offset surface generation of triangular meshes. The basic idea is to independently offset each triangle of the base mesh, and then stitch them together by solving Poisson equation. We then introduce the details for computation of a stretch metric, which measures the distortion of shell maps. Our results show a substantial improvement compared to the previous results.The main contributions of this dissertation are:Poisson Offset Surface Generation. We introduce a method for the construction of the low distortion offset surface simply by solving a Poisson equation on the thin layer of tetrahedral mesh.Tetrahedron Stretch Metric. We present the Tetrahedron Stretch Metric, and propose using the metric to measure the distortion in the mapping between the shell space and the texture space. Moreover, we use the same metric to optimize the texture space.Applications for Offset Surface. We provide several applications for our offset surface, such as shell space mapping, mesh simplification, mesh deformation and animated texture.