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An O(n²log n) time algorithm for the MinMax angle triangulation

Authors:

Herbert Edelsbrunner,

Roman WaupotitschAuthors Info & Claims

SCG '90: Proceedings of the sixth annual symposium on Computational geometry

Pages 44 - 52

https://doi.org/10.1145/98524.98535

Published: 01 May 1990 Publication History

Abstract

We show that a triangulation of a set of n points in the plane that minimizes the maximum angle can be computed in time O(n² log n) and space O(n). In the same amount of time and space we can also handle the constrained case where edges are prescribed. The algorithm iteratively improves an arbitrary initial triangulation and is fairly easy to implement.

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Cited By

Tang WJia FWang X(2023)An improved adaptive triangular mesh-based image warping methodFrontiers in Neurorobotics10.3389/fnbot.2022.104242916Online publication date: 23-Jan-2023
https://doi.org/10.3389/fnbot.2022.1042429
Bogiatzis PRychert CHarmon N(2021)Multiple graph realizations method: improving the accuracy and the efficiency of the shortest path method through random samplingGeophysical Journal International10.1093/gji/ggab247227:1(669-679)Online publication date: 28-Jun-2021
https://doi.org/10.1093/gji/ggab247
Wang SHe KPan YXia M(2019)Rectangle Transformation ProblemAlgorithmica10.1007/s00453-019-00563-y81:7(2876-2898)Online publication date: 1-Jul-2019
https://dl.acm.org/doi/10.1007/s00453-019-00563-y
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Index Terms

An O(n²log n) time algorithm for the MinMax angle triangulation
1. Theory of computation
  1. Design and analysis of algorithms
  2. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Conferences

SCG '90: Proceedings of the sixth annual symposium on Computational geometry

May 1990

371 pages

ISBN:0897913620

DOI:10.1145/98524

Chairman:
Raimund Seidel

Copyright © 1990 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 01 May 1990

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SOCG: 6th Annual Conference on Computational Geometry

June 7 - 9, 1990

California, Berkley, USA

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Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Cited By

Tang WJia FWang X(2023)An improved adaptive triangular mesh-based image warping methodFrontiers in Neurorobotics10.3389/fnbot.2022.104242916Online publication date: 23-Jan-2023
https://doi.org/10.3389/fnbot.2022.1042429
Bogiatzis PRychert CHarmon N(2021)Multiple graph realizations method: improving the accuracy and the efficiency of the shortest path method through random samplingGeophysical Journal International10.1093/gji/ggab247227:1(669-679)Online publication date: 28-Jun-2021
https://doi.org/10.1093/gji/ggab247
Wang SHe KPan YXia M(2019)Rectangle Transformation ProblemAlgorithmica10.1007/s00453-019-00563-y81:7(2876-2898)Online publication date: 1-Jul-2019
https://dl.acm.org/doi/10.1007/s00453-019-00563-y
Johnson D(2005)The NP-completeness columnACM Transactions on Algorithms10.1145/1077464.10774761:1(160-176)Online publication date: 1-Jul-2005
https://dl.acm.org/doi/10.1145/1077464.1077476
Levcopoulos CLingas A(2005)C-sensitive triangulations approximate the minmax length triangulationFoundations of Software Technology and Theoretical Computer Science10.1007/3-540-56287-7_98(104-115)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-56287-7_98
Eppstein D(1994)Approximating the minimum weight steiner triangulationDiscrete & Computational Geometry10.1007/BF0257400211:2(163-191)Online publication date: 1-Dec-1994
https://dl.acm.org/doi/10.1007/BF02574002
Mitchell S(1993)Refining a triangulation of a planar straight-line graph to eliminate large anglesProceedings of the 1993 IEEE 34th Annual Foundations of Computer Science10.1109/SFCS.1993.366828(583-592)Online publication date: 3-Nov-1993
https://dl.acm.org/doi/10.1109/SFCS.1993.366828
Eppstein DFrederickson G(1992)Approximating the minimum weight triangulationProceedings of the third annual ACM-SIAM symposium on Discrete algorithms10.5555/139404.139415(48-57)Online publication date: 1-Sep-1992
https://dl.acm.org/doi/10.5555/139404.139415
Bern MDobkin DEppstein DAvis D(1992)Triangulating polygons without large anglesProceedings of the eighth annual symposium on Computational geometry10.1145/142675.142722(222-231)Online publication date: 1-Jul-1992
https://dl.acm.org/doi/10.1145/142675.142722
Melissaratos ESouvaine DAvis D(1992)Coping with inconsistenciesProceedings of the eighth annual symposium on Computational geometry10.1145/142675.142719(202-211)Online publication date: 1-Jul-1992
https://dl.acm.org/doi/10.1145/142675.142719
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