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.

scholarly journals DELAUNAY STABILITY VIA PERTURBATIONS

2014 ◽  
Vol 24 (02) ◽  
pp. 125-152 ◽  
Author(s):  
JEAN-DANIEL BOISSONNAT ◽  
RAMSAY DYER ◽  
ARIJIT GHOSH
Keyword(s):  
Delaunay Triangulation ◽  
Arbitrary Dimension ◽  
Finite Point ◽  
Delaunay Triangulations ◽  
Point Set

We present an algorithm that takes as input a finite point set in ℝm, and performs a perturbation that guarantees that the Delaunay triangulation of the resulting perturbed point set has quantifiable stability with respect to the metric and the point positions. There is also a guarantee on the quality of the simplices: they cannot be too at. The algorithm provides an alternative tool to the weighting or refinement methods to re-move poorly shaped simplices in Delaunay triangulations of arbitrary dimension, but in addition it provides a guarantee of stability for the resulting triangulation.

Optimal tetrahedral mesh generation for three-dimensional point set

1997 ◽  
Vol 40 (2) ◽  
pp. 135-143
Author(s):  
Kaihuai Qin ◽  
Bian Wu ◽  
Youjiang Guan ◽  
Zhenzhou Ge
Keyword(s):  
Mesh Generation ◽  
Three Dimensional ◽  
Tetrahedral Mesh ◽  
Point Set ◽  
Tetrahedral Mesh Generation

Reading the Image of Race: Neurocriminology, Medical Imaging Technologies and Literary Intervention

2018 ◽  
Author(s):  
Lindsey Andrews ◽  
Jonathan M. Metzl
Keyword(s):  
Twentieth Century ◽  
Wall Street Journal ◽  
Genetic Basis ◽  
Three Dimensional ◽  
Criminal Behaviour ◽  
Dominant Model ◽  
Wall Street ◽  
Behavioural Genetics ◽  
Black And White ◽  
Brain Scan

On 26 April 2013, the Wall Street Journal published an essay by neurocriminologist Adrian Raine promoting his newest book, The Anatomy of Violence: The Biological Roots of Crime. On the newspaper’s website, an image of a black-and-white brain scan overlaid with handcuffs headed the essay. Clicking ‘play’ turned the image into a video filled with three-dimensional brain illustrations and Raine’s claims that some brains are simply more biologically prone to violence than others. Rejecting what he describes as ‘the dominant model for understanding criminal behaviour in the twentieth century’ – a model based ‘almost exclusively on social and sociological’ explanations – Raine wrote that ‘the genetic basis of criminal behaviour is now well established’ through molecular and behavioural genetics.

TRENDS IN AUTOMATIC THREE-DIMENSIONAL MESH GENERATION

1988 ◽  
pp. 421-429 ◽  
Author(s):  
M.S. SHEPHARD ◽  
K.R. GRICE ◽  
J.A. LOT ◽  
W.J. SCHROEDER
Keyword(s):  
Mesh Generation ◽  
Three Dimensional

A Constrained Delaunay Triangulation Algorithm Based on Incremental Points

2011 ◽  
Vol 90-93 ◽  
pp. 3277-3282 ◽  
Author(s):  
Bai Chao Wu ◽  
Ai Ping Tang ◽  
Lian Fa Wang
Keyword(s):  
Information System ◽  
Data Structures ◽  
Delaunay Triangulation ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Three Dimensional ◽  
Geographical Information ◽  
Two Dimensional ◽  
Data Set ◽  
Constrained Delaunay Triangulation

The foundation ofdelaunay triangulationandconstrained delaunay triangulationis the basis of three dimensional geographical information system which is one of hot issues of the contemporary era; moreover it is widely applied in finite element methods, terrain modeling and object reconstruction, euclidean minimum spanning tree and other applications. An algorithm for generatingconstrained delaunay triangulationin two dimensional planes is presented. The algorithm permits constrained edges and polygons (possibly with holes) to be specified in the triangulations, and describes some data structures related to constrained edges and polygons. In order to maintain the delaunay criterion largely，some new incremental points are added onto the constrained ones. After the data set is preprocessed, the foundation ofconstrained delaunay triangulationis showed as follows: firstly, the constrained edges and polygons generate initial triangulations，then the remained points completes the triangulation . Some pseudo-codes involved in the algorithm are provided. Finally, some conclusions and further studies are given.

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