Showing papers by "Herbert Edelsbrunner published in 1999"

Sliver exudation

Abstract: A sliver is a tetrahedron whose four vertices lie close to a plane and whose projection to that plane is a convex quadrilateral with no short edge. Slivers are notoriously common in 3-dimensional Delaunay triangulations even for well-spaced point sets. We show that if the Delaunay triangulation has the ratio property introduced in [15] then there is an assignment of weights so the weighted Delaunay triangulation contains no slivers. We also give an algorithm to compute such a weight assignment.

Deformable Smooth Surface Design

Abstract: A new paradigm for designing smooth surfaces is described. A finite set of points with weights specifies a closed surface in space referred to as skin . It consists of one or more components, each tangent continuous and free of self-intersections and intersections with other components. The skin varies continuously with the weights and locations of the points, and the variation includes the possibility of a topology change facilitated by the violation of tangent continuity at a single point in space and time. Applications of the skin to molecular modeling and to geometric deformation are discussed.

Methods of generating three-dimensional digital models of objects by wrapping point cloud data points

Abstract: A method of automatic conversion of a physical object into a three-dimensional digital model. The method acquires a set of measured data points on the surface of a physical model. From the measured data points, the method reconstructs a digital model of the physical object using a Delaunay complex of the points, a flow strcuture of the simplicies in the Delaunay complex and retracting the Delaunay complex into a digital model of the physical object using the flow structure. The method then outputs the digital model of the physical object.

Emerging Challenges in Computational Topology

Abstract: Here we present the results of the NSF-funded Workshop on Computational Topology, which met on June 11 and 12 in Miami Beach, Florida. This report identifies important problems involving both computation and topology.

Edgewise subdivision of a simplex

Abstract: In this paper we introduce the abacus model of a simplex and use it to subdivide a d-simplex into k d d-simplices all of the same volume and shape characteristics. The construction is an extension of the subdivision method of Freudenthal [3] and has been used by Goodman and Peters [4] to design smooth manifolds.

Mesh Association: Formulation and Algorithms.

Abstract: In computational simulation of coupled multicom ponent systems it is frequently necessary to transfer data between meshes that may di er in resolution structure and discretization methodology Typically nodes from one mesh must be associated with ele ments of another mesh In this paper we formulate mesh association as a geometric problem and intro duce two e cient mesh association algorithms One of these algorithms requires linear time in the worst case if the meshes are well shaped and geometrically well aligned Our formulation of the problem and our algorithms are more general than previous work and can be applied to surface meshes with curved elements