scholarly journals Incremental Delaunay Triangulation

2012 ◽  
Author(s):  
Stephane Rigaud ◽  
Alexandre Gouaillard
Keyword(s):  
Delaunay Triangulation ◽  
Robust Implementation

This document describes the implementation in ITK of the Incremental Delaunay Triangulation algorithm. Using the Straight Walk in Triangulation function, the exact discrete geometrical orientation predicate, and the itk::QuadEdgeMesh API of ITK , we propose a geometrically exact and robust implementation that, from a given 2-dimensional itk::PointSet, incrementally constructs the corresponding 2-dimensional Delaunay Triangulation as an itk::QuadEdgeMesh.

scholarly journals Exact Geometrical Predicate: Point in circle

2011 ◽  
Author(s):  
Bertrand Moreau ◽  
Alexandre Gouaillard
Keyword(s):  
Delaunay Triangulation ◽  
Public Domain ◽  
Floating Point ◽  
Separate Paper ◽  
The Public ◽  
Voronoi Tesselation ◽  
Robust Implementation ◽  
Point Types ◽  
Exact Version

This document describes the implementation in ITK of the “point in circle” geometrical predicate. Based on Jonathan Shewchuk’s work which implements an exact version of the predicate using standard floating point types and arithmetic, the implementation consist of an ITK wrapper around the public domain C routines made available by the author of the precedent paper. Wrapper using itk::PointSet, itk:CellInterface and itk:Mesh / itk:QuadEdgeMesh APIs are provided along with corresponding examples which should provide enough details for users to directly copy paste code in their application.The application in mind for us is an exact and robust implementation of a delaunay triangulation / voronoi tesselation in ITK, and will be presented in a separate paper.

scholarly journals Walk In A Triangulation : Straight Walk

2012 ◽  
Author(s):  
Stephane Rigaud ◽  
Alexandre Gouaillard
Keyword(s):  
Delaunay Triangulation ◽  
Source Code ◽  
Efficient Implementation ◽  
Mesh Structure ◽  
Separate Paper ◽  
Voronoi Tesselation ◽  
Robust Implementation

This document describes the implementation in ITK of the Straight Walk in a Triangulation algorithm proposed by Devillers et al. Using the exact discrete geometrical orientation predicate, and the itk::QuadEdgeMesh API of ITK, we propose an efficient implementation that locates a point in a triangulated mesh structure. This paper is accompanied with the source code and examples that should provide enough details for users. This work has for principal intended an exact and robust implementation of a Delaunay triangulation / Voronoi tesselation in ITK, which will be presented in a separate paper, once done.

Numerical implementation of finite-element method of control volume using irregular mesh

2010 ◽  
Vol 7 ◽  
pp. 98-108
Author(s):  
Yu.A. Gafarova
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Delaunay Triangulation ◽  
Complex Geometry ◽  
Control Volume ◽  
Test Case ◽  
The Finite Element Method ◽  
Irregular Mesh ◽  
Discrete Analogues ◽  
Element Method

To solve problems with complex geometry it is considered the possibility of application of irregular mesh and the use of various numerical methods using them. Discrete analogues of the Beltrami-Mitchell equations are obtained by the control volume method using the rectangular grid and the finite element method of control volume using the Delaunay triangulation. The efficiency of using the Delaunay triangulation, Voronoi diagrams and the finite element method of control volume in a test case is demonstrated.

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