We develop a new method for segmentation of molecular surfaces. Topological analysis of a scalar function defined on the surface and its associated gradient field reveals the relationship between the features of interest and critical points of the scalar function. The segmentation is obtained by associating segments with local minima/maxima. Controlled simplification of the function merges segments resulting in a hierarchical segmentation of the molecular surface. This segmentation is used to identify rigid components of proteins molecules and to study the role of cavities and protrusions in protein-protein interactions.

In this paper we describe an approach for the parameterization and modeling of objects represented by adaptive distance fields (ADFs). ADF's allow the construction of powerful solid modeling tools. They can represent surfaces of arbitrary and even changing topology, while providing a more intuitive modeling interface than control point based structures such as splines. Using the octree structure of ADFs, we build an adaptively refined quadrilateral mesh that is topologically equivalent to the object's surface. We then project the mesh onto the object using multiple projection and smoothing steps. The resulting mesh serves as the user interface for modeling iperations and is used for high quality rendering of the resulting shape.

. We describe a method to approximate a closed surface triangulation using simulated annealing. Our approach guarantees that all vertices and triangles in an approximating surface triangulation are within a user-defined distance of the original surface triangulation. We introduce the idea of atomic envelopes to guarantee error bounds that are independent of the surface geometry. Atomic envelopes also allow approximation distance to be different for different parts of the surface. We start with the original triangulation and perturb it randomly and improve an approximating triangulation by locally changing the triangulation, using a simulated annealing algorithm. Our algorithm is not restricted to using only original vertices; the algorithm considers every point inside the envelope triangulation as a possible position. The algorithm attempts to minimize the total number of vertices needed to approximate the original surface triangulation within the prescribed error bound.

In this paper, we present a topological approach for simplifying continuous functions defined on volumetric domains. We introduce two atomic operations that remove pairs of critical points of the function and design a combinatorial algorithm that simplifies the Morse-Smale complex by repeated application of these operations. The Morse-Smale complex is a topological data structure that provides a compact representation of gradient flow between critical points of a function. Critical points paired by the Morse-Smale complex identify topological features and their importance. The simplification procedure leaves important critical points untouched, and is therefore useful for extracting desirable features. We also present a visualization of the simplified topology.

We describe a method to approximate a closed surface tri- angulation using simulated annealing. Our approach guarantees that all vertices and triangles in an approximating surface triangulation are within a user-defined distance of the original surface triangulation. We introduce the idea of atomic envelopes to guarantee error bounds that are independent of the surface geometry. Atomic envelopes also allow approximation distance to be di�erent for di�erent parts of the surface. We start with the original triangulation and perturb it randomly and improve an approximating triangulation by locally changing the triangulation, using a simulated annealing algorithm. Our algorithm is not restricted to using only original vertices; the algorithm considers every point inside the envelope triangulation as a possible position. The algorithm attempts to minimize the total number of vertices needed to approximate the original surface triangulation within the prescribed error bound.

In this paper, we present a topological approach for simplifying continuous functions defined on volumetric domains. We introduce two atomic operations that remove pairs of critical points of the function and design a combinator ial algorithm that simplifies the Morse-Smale complex by repeated applicatio n of these operations. The Morse-Smale complex is a topological data structu re that provides a compact representation of gradient flow between critical points of a function. Critical points paired by the Morse-Smale complex iden tify topological features and their importance. The simplification procedure leaves important critical points untouched, and is therefore useful for ext racting desirable features. We also present a visualization of the simplifie d topology.

This paper describes an efficient combinatorial method for simplification of topological features in a 3D scalar function. The Morse-Smale complex, which provides a succinct representation of a function's associated gradient flow field, is used to identify topological features and their significance. The simplification process, guided by the Morse-Smale complex, proceeds by repeatedly applying two atomic operations that each remove a pair of critical points from the complex. Efficient storage of the complex results in execution of these atomic operations at interactive rates. Visualization of the simplified complex shows that the simplification preserves significant topological features while removing small features and noise.