scholarly journals Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generation

2014 ◽  
Vol 36 (3) ◽  
pp. A930-A954 ◽  
Author(s):  
Zhonggui Chen ◽  
Wenping Wang ◽  
Bruno Lévy ◽  
Ligang Liu ◽  
Feng Sun
Keyword(s):  
Delaunay Triangulation ◽  
Mesh Generation ◽  
Graded Mesh

Triangulations and meshes in computational geometry

Acta Numerica ◽  
2000 ◽  
Vol 9 ◽  
pp. 133-213 ◽  
Author(s):  
Herbert Edelsbrunner
Keyword(s):  
Twentieth Century ◽  
Computational Geometry ◽  
Delaunay Triangulation ◽  
Mesh Generation ◽  
Three Dimensional ◽  
Central Theme ◽  
Physical Processes ◽  
Finite Point ◽  
Major Application ◽  
Point Set

The Delaunay triangulation of a finite point set is a central theme in computational geometry. It finds its major application in the generation of meshes used in the simulation of physical processes. This paper connects the predominantly combinatorial work in classical computational geometry with the numerical interest in mesh generation. It focuses on the two- and three-dimensional case and covers results obtained during the twentieth century.

DELAUNAY REFINEMENT ALGORITHMS FOR ESTIMATING LOCAL FEATURE SIZE IN 2D AND 3D

2011 ◽  
Vol 21 (05) ◽  
pp. 507-543
Author(s):  
ALEXANDER RAND ◽  
NOEL WALKINGTON
Keyword(s):  
Delaunay Triangulation ◽  
Mesh Generation ◽  
Piecewise Linear ◽  
Local Information ◽  
Local Feature ◽  
Delaunay Refinement ◽  
Linear Complex ◽  
Feature Size ◽  
2D And 3D ◽  
Local Feature Size

We present Delaunay refinement algorithms for estimating local feature size on the input vertices of a 2D piecewise linear complex and on the input vertices and segments of a 3D piecewise linear complex. These algorithms are designed to eliminate the need for a local feature size oracle during quality mesh generation of domains containing acute input angles. In keeping with Ruppert's algorithm, encroachment in these algorithms can be determined through only local information in the current Delaunay triangulation. The algorithms are practical to implement and several examples are given.

scholarly journals THE EXPECTED EXTREMES IN A DELAUNAY TRIANGULATION

1991 ◽  
Vol 01 (01) ◽  
pp. 79-91 ◽  
Author(s):  
MARSHALL BERN ◽  
DAVID EPPSTEIN ◽  
FRANCES YAO
Keyword(s):  
Aspect Ratio ◽  
Poisson Process ◽  
Delaunay Triangulation ◽  
Edge Effects ◽  
Mesh Generation ◽  
Case Analysis ◽  
Edge Length ◽  
Delaunay Triangulations ◽  
Fixed Dimension ◽  
Average Aspect Ratio

We give an expected-case analysis of Delaunay triangulations. To avoid edge effects we consider a unit-intensity Poisson process in Euclidean d-space, and then limit attention to the portion of the triangulation within a cube of side n1/d. For d equal to two, we calculate the expected maximum edge length, the expected minimum and maximum angles, and the average aspect ratio of a triangle. We also show that in any fixed dimension the expected maximum vertex degree is Θ( log n/ log log n). Altogether our results provide some measure of the suitability of the Delaunay triangulation for certain applications, such as interpolation and mesh generation.

Robust and Quality Boundary Constrained Tetrahedral Mesh Generation

2013 ◽  
Vol 14 (5) ◽  
pp. 1304-1321 ◽  
Author(s):  
Songhe Song ◽  
Min Wan ◽  
Shengxi Wang ◽  
Desheng Wang ◽  
Zhengping Zou
Keyword(s):  
Delaunay Triangulation ◽  
Mesh Generation ◽  
Tetrahedral Mesh ◽  
Mesh Optimization ◽  
Surface Mesh ◽  
Triangulated Surface ◽  
Advancing Front ◽  
Novel Method ◽  
Tetrahedral Mesh Generation

AbstractA novel method for boundary constrained tetrahedral mesh generation is proposed based on Advancing Front Technique (AFT) and conforming Delaunay triangulation. Given a triangulated surface mesh, AFT is firstly applied to mesh several layers of elements adjacent to the boundary. The rest of the domain is then meshed by the conforming Delaunay triangulation. The non-conformal interface between two parts of meshes are adjusted. Mesh refinement and mesh optimization are then preformed to obtain a more reasonable-sized mesh with better quality. Robustness and quality of the proposed method is shown. Convergence proof of each stage as well as the whole algorithm is provided. Various numerical examples are included as well as the quality of the meshes.

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