Protein structure comparison is one of the most important problems in Bioinformatics. In this paper, we develop a convex hull expression of a protein and propose a grid method to evaluate similarity between two convex hulls. The purpose of introducing the convex hull expression is to investigate the relationship between the surface shape similarity and the protein function similarity. Extensive...

In this thesis we develop estimates for volumes of smooth boundary manifolds by deriving explicit relations between a heat flow across the surface and its volume. Applying these estimates together with existing results on randomised volume computation and rates of rapidly mixing chains on convex sets, we are able to derive a randomised algorithm for computing the surface volume of a smooth conv...

in this paper we introduce a sequential block iterative method and its simultaneous version with op-timal combination of weights (instead of convex combination) for solving convex feasibility problems.when the intersection of the given family of convex sets is nonempty, it is shown that any sequencegenerated by the given algorithms converges to a feasible point. additionally for linear feasibil...

It is proved that if C is a convex body in R" then C has an affine image C (of nonzero volume) so that if P is any 1-codimensional orthogonal projection, \PC\>\C\{tt~l)/n. It is also shown that there is a pathological body, K , all of whose orthogonal projections have volume about \fh~ times as large as |Ä"| . 0. Introduction The problems discussed in this paper concern the areas of shadows (or...

Given points in convex position in three dimensions, we want to find an approximating convex surface consisting of spherical patches, such that all points are within some specified tolerance bound ε of the approximating surface. We describe a greedy algorithm which constructs an approximating surface whose spherical patches are associated to the faces of an inscribed polytope formed from a subs...

We introduce a new and efficient approach for collision detection in point-based animations, based on the fast computation of tight surface bounds. Our approach is able to tightly bound a high-resolution surface with a cost linear in the number of simulation nodes, which is typically small. We extend concepts about bounds of convex sets to the point-based deformation setting, and we introduce a...

Given points in convex position in three dimensions, we want to find an approximating convex surface consisting of spherical patches, such that all points are within some specified tolerance bound ε of the approximating surface. We describe a greedy algorithm which constructs an approximating surface whose spherical patches are associated to the faces of an inscribed polytope formed from a subs...

This thesis demonstrates the feasibility of using a medial surface transformation as a tool to rapidly approximate the solidification patterns of convex faceted solid models of castings. The medial surface transformation is used to automate the greatest included sphere approach to solidification pattern approximation. The experimental software of this thesis extracts the medial surface transfor...

The affine surface area was introduced by Blaschke [B] for convex bodies in R with sufficently smooth boundary and by Leichtweiss [L1] for convex bodies in R with sufficently smooth boundary. As it occurs naturally in many important questions so for example in the approximation of convex bodies by polytopes ( see the survey article of Gruber [G] ) or in a priori estimates for PDEs [Lu2] one wan...

We first obtain some properties of a fundamentally nonexpansive self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the fixed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and con...