A plane view of geometric silhouettes

Geometric silhouettes are arcs on a surface representation that separate front-facing regions from back-facing regions with respect to a given viewpoint. These arcs are in general significantly less complex than the surface itself, and carry a great deal of information describing the surface. In this thesis, we take a plane view of geometric silhouettes, defining them in terms of the tangential planes of the surfaces on which they are defined rather than its local properties. We show that this perspective leads to efficient algorithms as well as a novel characterization of silhouettes based on a silhouette-generating set, or SGS. The low asymptotic complexity of mesh silhouettes, combined with their utility, justifies the development of silhouette extraction algorithms that are sublinear in the size of the input model. Many of these more efficient algorithms are based on tangential-plane representations of the input model. We present a novel silhouette extraction and update algorithm based on the 3D Hough transform, which combines the advantages of previous tangential-plane representations. We begin by presenting this algorithm on triangle meshes, then extend it to support point-set surfaces. In doing so, we generalize the double-wedge structure underlying mesh-edge silhouettes to an SGS applicable to arbitrary primitives. While our plane-based data representation allows us to identify silhouettes on distant parts of the input model when their SGSes coincide, it is nonetheless a local approach in 3D Hough space. However, by aggregating tangential plane information over the entire input mesh, we can perform a number of global optimizations effectively. We introduce the tangential distance field (TDF), a scalar function based on the SGSes of all triangles in a mesh. We develop a toolbox of weighting functions which embed different geometric information in the TDF. Depending on the function chosen, we can find a set of optimized origins for our silhouette extraction algorithm, a set of visually informative viewpoints around a given model, or a similarly informative light position based on a given viewpoint.