Results 1  10
of
214
A Delaunay Refinement Algorithm for Quality 2Dimensional Mesh Generation
, 1995
"... We present a simple new algorithm for triangulating polygons and planar straightline graphs. It provides "shape" and "size" guarantees: All triangles have a bounded aspect ratio. The number of triangles is within a constant factor of optimal. Such "quality" triangulatio ..."
Abstract

Cited by 241 (0 self)
 Add to MetaCart
We present a simple new algorithm for triangulating polygons and planar straightline graphs. It provides "shape" and "size" guarantees: All triangles have a bounded aspect ratio. The number of triangles is within a constant factor of optimal. Such "quality" triangulations are desirable as meshes for the nite element method, in which the running time generally increases with the number of triangles, and where the convergence and stability may be hurt by very skinny triangles. The technique we use  successive refinement of a Delaunay triangulation  extends a mesh generation technique of Chew by allowing triangles of varying sizes. Compared with previous quadtreebased algorithms for quality mesh generation, the Delaunay refinement approach is much simpler and generally produces meshes with fewer triangles. We also discuss an implementation of the algorithm and evaluate its performance on a variety of inputs.
Survey of Polygonal Surface Simplification Algorithms
, 1997
"... This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewiselinear surface in 3D defined by a set of polygons ..."
Abstract

Cited by 227 (3 self)
 Add to MetaCart
This paper surveys methods for simplifying and approximating polygonal surfaces. A polygonal surface is a piecewiselinear surface in 3D defined by a set of polygons
Provably Good Mesh Generation
 J. COMPUT. SYST. SCI
, 1990
"... We study several versions of the problem of generating triangular meshes for finite element methods. We show how to triangulate a planar point set or polygonally bounded domain with triangles of bounded aspect ratio; how to triangulate a planar point set with triangles having no obtuse angles; how t ..."
Abstract

Cited by 214 (10 self)
 Add to MetaCart
We study several versions of the problem of generating triangular meshes for finite element methods. We show how to triangulate a planar point set or polygonally bounded domain with triangles of bounded aspect ratio; how to triangulate a planar point set with triangles having no obtuse angles; how to triangulate a point set in arbitrary dimension with simplices of bounded aspect ratio; and how to produce a linearsize Delaunay triangulation of a multidimensional point set by adding a linear number of extra points. All our triangulations have size (number of triangles) within a constant factor of optimal, and run in optimal time O(n log n+k) with input of size n and output of size k. No previous work on mesh generation simultaneously guarantees wellshaped elements and small total size.
Spectral partitioning works: planar graphs and finite element meshes, in:
 Proceedings of the 37th Annual Symposium on Foundations of Computer Science,
, 1996
"... Abstract Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to wo ..."
Abstract

Cited by 201 (10 self)
 Add to MetaCart
(Show Context)
Abstract Spectral partitioning methods use the Fiedler vectorthe eigenvector of the secondsmallest eigenvalue of the Laplacian matrixto find a small separator of a graph. These methods are important components of many scientific numerical algorithms and have been demonstrated by experiment to work extremely well. In this paper, we show that spectral partitioning methods work well on boundeddegree planar graphs and finite element meshesthe classes of graphs to which they are usually applied. While naive spectral bisection does not necessarily work, we prove that spectral partitioning techniques can be used to produce separators whose ratio of vertices removed to edges cut is O( √ n) for boundeddegree planar graphs and twodimensional meshes and O(n 1/d ) for wellshaped ddimensional meshes. The heart of our analysis is an upper bound on the secondsmallest eigenvalues of the Laplacian matrices of these graphs: we prove a bound of O(1/n) for boundeddegree planar graphs and O(1/n 2/d ) for wellshaped ddimensional meshes.
FreeForm Shape Design Using Triangulated Surfaces
, 1994
"... We present an approach to modeling with truly mutable yet completely controllable freeform surfaces of arbitrary topology. Surfaces may be pinned down at points and along curves, cut up and smoothly welded back together, and faired and reshaped in the large. This style of control is formulated as a ..."
Abstract

Cited by 163 (0 self)
 Add to MetaCart
(Show Context)
We present an approach to modeling with truly mutable yet completely controllable freeform surfaces of arbitrary topology. Surfaces may be pinned down at points and along curves, cut up and smoothly welded back together, and faired and reshaped in the large. This style of control is formulated as a constrained shape optimization, with minimization of squared principal curvatures yielding graceful shapes that are free of the parameterization worries accompanying many patchbased approaches. Triangulated point sets are used to approximate these smooth variational surfaces, bridging the gap between patchbased and particlebased representations. Automatic refinement, mesh smoothing, and retriangulation maintain a good computational mesh as the surface shape evolves, and give sample points and surface features much of the freedom to slide around in the surface that oriented particles enjoy. The resulting surface triangulations are constructed and maintained in real time. 1 Introduction ...
Spanning Trees and Spanners
, 1996
"... We survey results in geometric network design theory, including algorithms for constructing minimum spanning trees and lowdilation graphs. ..."
Abstract

Cited by 145 (2 self)
 Add to MetaCart
We survey results in geometric network design theory, including algorithms for constructing minimum spanning trees and lowdilation graphs.
General Object Reconstruction based on Simplex Meshes
, 1999
"... In this paper, we propose a general tridimensional reconstruction algorithm of range and volumetric images, based on deformable simplex meshes. Simplex meshes are topologically dual of triangulations and have the advantage of permitting smooth deformations in a simple and e cient manner. Our reconst ..."
Abstract

Cited by 134 (18 self)
 Add to MetaCart
In this paper, we propose a general tridimensional reconstruction algorithm of range and volumetric images, based on deformable simplex meshes. Simplex meshes are topologically dual of triangulations and have the advantage of permitting smooth deformations in a simple and e cient manner. Our reconstruction algorithm can handle surfaces without any restriction on their shape or topology. The di erent tasks performed during the reconstruction include the segmentation of given objects in the scene, the extrapolation of missing data, and the control of smoothness, density, and geometric quality of the reconstructed meshes. The reconstruction takes place in two stages. First, the initialization stage creates a simplex mesh in the vicinity of the data model either manually or using an automatic procedure. Then, after a few iterations, the mesh topology can be modi ed by creating holes or by increasing its genus. Finally, aniterativere nement algorithm decreases the distance of the mesh from the data while preserving high geometric and topological quality. Several reconstruction examples are provided with quantitative and qualitative results.
Combining Hierarchical Radiosity and Discontinuity Meshing
, 1993
"... We introduce a new approach for the computation of viewindependent solutions to the diffuse global illumination problem in polyhedral environments. The approach combines ideas from hierarchical radiosity and discontinuity meshing to yield solutions that are accurate both numerically and visually. Fi ..."
Abstract

Cited by 104 (9 self)
 Add to MetaCart
(Show Context)
We introduce a new approach for the computation of viewindependent solutions to the diffuse global illumination problem in polyhedral environments. The approach combines ideas from hierarchical radiosity and discontinuity meshing to yield solutions that are accurate both numerically and visually. First, we describe a modified hierarchical radiosity algorithm that uses a discontinuitydriven subdivision strategy to achieve better numerical accuracy and faster convergence. Second, we present a new algorithm based on discontinuity meshing that uses the hierarchical solution to reconstruct an objectspace approximation to the radiance function that is visually accurate. Our results show significant improvements over both hierarchical radiosity and discontinuity meshing algorithms.