A Contribution to Triangulation Algorithms for Simple Polygons
Marko Lamot,Borut Žalik +1 more
- 30 Dec 2000
- Vol. 8, Iss: 4, pp 319-331
TL;DR: The paper briefly explains the most popular algorithms from each group and summarizes the common features of the groups, and examines the speed, the quality of the output triangles and the ability to handle holes of the algorithms.
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Abstract: Decomposing simple polygon into simpler components is one of the basic tasks in computational geometry and its applications. The most important simple polygon decomposition is triangulation. The known algorithms for polygon triangulation can be classified into three groups: algorithms based on diagonal inserting, algorithms based on Delaunay triangulation, and the algorithms using Steiner points. The paper briefly explains the most popular algorithms from each group and summarizes the common features of the groups. After that four algorithms based on diagonals insertion are tested: a recursive diagonal inserting algorithm, an ear cutting algorithm, Kong’s Graham scan algorithm, and Seidel’s randomized incremental algorithm. An analysis concerning speed, the quality of the output triangles and the ability to handle holes is done at the end.
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Citations
•Journal Article
Triangulating a simple polygon in linear time
TL;DR: A deterministic algorithm for triangulating a simple polygon in linear time is given, using the polygon-cutting theorem and the planar separator theorem, whose role is essential in the discovery of new diagonals.
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Polygon trapezoidation by sets of open trapezoids
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A fast polygon triangulation algorithm based on uniform plane subdivision
Marko Lamot,Borut Žalik +1 more
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•Dissertation
Mesh sensitivity investigation in the discrete adjoint framework
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References
•Book
Computational Geometry: Algorithms and Applications
Mark de Berg,Otfried Cheong,Marc van Kreveld,Mark H. Overmars +3 more
- 01 Jan 1997
TL;DR: In this article, an introduction to computational geometry focusing on algorithms is presented, which is related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems.
5.8K
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
Jonathan Richard Shewchuk
- 27 May 1996
TL;DR: Triangle as discussed by the authors is a robust implementation of two-dimensional constrained Delaunay triangulation and Ruppert's Delaunayer refinement algorithm for quality mesh generation, and it is shown that the problem of triangulating a planar straight line graph (PSLG) without introducing new small angles is impossible for some PSLGs.
A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation
Jim Ruppert
- 01 May 1995
TL;DR: Compared with previous quadtree-based algorithms for quality mesh generation, the Delaunay refinement approach is much simpler and generally produces meshes with fewer triangles.
814
Triangulating a simple polygon in linear time
TL;DR: In this paper, a deterministic algorithm for triangulating a simple polygon in linear time is presented. But the main tools used are the polygon-cutting theorem, which provides us with a balancing scheme, and the planar separator theorem, whose role is essential in the discovery of new diagonals.
•Journal Article
Triangulating a simple polygon in linear time
TL;DR: A deterministic algorithm for triangulating a simple polygon in linear time is given, using the polygon-cutting theorem and the planar separator theorem, whose role is essential in the discovery of new diagonals.
632