Quadric-Based Polygonal Surface Simplification

Many applications in computer graphics and related fields can benefit from
automatic simplification of complex polygonal surface models. Applications are
often confronted with either very densely over-sampled surfaces or models too
complex for the limited available hardware capacity. An effective algorithm
for rapidly producing high-quality approximations of the original model is a
valuable tool for managing data complexity.

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.