Computer Science Department
School of Computer Science, Carnegie Mellon University
Quadric-Based Polygonal Surface Simplification
In this dissertation, I present my simplification algorithm, based on iterative vertex pair contraction. This technique provides an effective compromise between the fastest algorithms, which often produce poor quality results, and the highest-quality algorithms, which are generally very slow. For example, a 1000 face approximation of a 100,000 face model can be produced in about 10 seconds on a PentiumPro 200. The algorithm can simplify both the geometry and topology of manifold as well as non-manifold surfaces. In addition to producing single approximations, my algorithm can also be used to generate multiresolution representations such as progressive meshes and vertex hierarchies for view-dependent refinement.
The foundation of my simplification algorithm, is the quadric error metric which I have developed. It provides a useful and economical characterization of local surface shape, and I have proven a direct mathematical connection between the quadric metric and surface curvature. A generalized form of this metric can accommodate surfaces with material properties, such as RGB color or texture coordinates.
I have also developed a closely related technique for constructing a hierarchy of well-defined surface regions composed of disjoint sets of faces. This algorithm involves applying a dual form of my simplification algorithm to the dual graph of the input surface. The resulting structure is a hierarchy of face clusters which is an effective multiresolution representation for applications such as radiosity.