| We present two new parameterization techniques that solve modeling and rendering problems in computer graphics. The first parameterization, shell maps, is a novel near surface mapping that extends the notion of volumetric textures. These three dimension to three dimension shell maps easily map topologically complex geometry, procedural functions, and scalar fields to the space near an object. Unlike existing approaches, mapped geometry need not be converted to a volumetric grid. The general approach is based on the notions of two-dimensional texture mappings, offset surfaces, simple point location queries in two and three dimensions, and barycentric mappings. The second parameterization we explore involves conversion of an adaptive distance field (an implicit function) into parametric form. Volumetric representations such as distance fields are especially amenable to modeling operations that involve changes in surface topology. To obtain our parametric representation we develop new quadrilateral mesh extraction and mesh simplification techniques based on the special topological structure of an octree. The resulting mesh is semi-regular and is used as input to a B-spline construction algorithm. |
