research-article

An algorithm for triangulating multiple 3D polygons

Authors:

Nathan CarrAuthors Info & Claims

SGP '13: Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing

Pages 157 - 166

https://doi.org/10.1111/cgf.12182

Published: 03 July 2013 Publication History

Abstract

We present an algorithm for obtaining a triangulation of multiple, non-planar 3D polygons. The output minimizes additive weights, such as the total triangle areas or the total dihedral angles between adjacent triangles. Our algorithm generalizes a classical method for optimally triangulating a single polygon. The key novelty is a mechanism for avoiding non-manifold outputs for two and more input polygons without compromising optimality. For better performance on real-world data, we also propose an approximate solution by feeding the algorithm with a reduced set of triangles. In particular, we demonstrate experimentally that the triangles in the Delaunay tetrahedralization of the polygon vertices offer a reasonable trade off between performance and optimality.

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Salvi PVaitkus MVárady T(2023)Constrained modeling of multi-sided patchesComputers and Graphics10.1016/j.cag.2023.05.020114:C(86-95)Online publication date: 1-Aug-2023
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Liu J(2023)On the Mating Between a Polygonal Curve and a Convex PolygonCombinatorial Optimization and Applications10.1007/978-3-031-49614-1_18(240-252)Online publication date: 15-Dec-2023
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Index Terms

An algorithm for triangulating multiple 3D polygons
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image ACM Conferences

SGP '13: Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing

July 2013

244 pages

Conference Chairs:
Bianca Falcidieno
Institute of Applied Mathematics and Information Technologies, CNR, Italy
,
Michela Spagnuolo
Institute of Applied Mathematics and Information Technologies, CNR, Italy
,
Program Chairs:
Yaron Lipman
Weizmann Institute of Science, Israel
,
Hao Zhang
Simon Fraser University, Canada

Sponsors

SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques
Disney Research: Disney Research
GeometryFactory: The Geometry Factory
Microsoft Reasearch: Microsoft Reasearch

Publisher

Eurographics Association

Goslar, Germany

Publication History

Published: 03 July 2013

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Overall Acceptance Rate 64 of 240 submissions, 27%

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Cited By

Várady TSalvi PVaitkus M(2024)Genuine multi-sided parametric surface patches – A surveyComputer Aided Geometric Design10.1016/j.cagd.2024.102286110:COnline publication date: 1-May-2024
https://dl.acm.org/doi/10.1016/j.cagd.2024.102286
Salvi PVaitkus MVárady T(2023)Constrained modeling of multi-sided patchesComputers and Graphics10.1016/j.cag.2023.05.020114:C(86-95)Online publication date: 1-Aug-2023
https://dl.acm.org/doi/10.1016/j.cag.2023.05.020
Liu J(2023)On the Mating Between a Polygonal Curve and a Convex PolygonCombinatorial Optimization and Applications10.1007/978-3-031-49614-1_18(240-252)Online publication date: 15-Dec-2023
https://dl.acm.org/doi/10.1007/978-3-031-49614-1_18
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Yu EArora RStanko TBærentzen JSingh KBousseau AKitamura YQuigley AIsbister KIgarashi TBjørn PDrucker S(2021)CASSIE: Curve and Surface Sketching in Immersive EnvironmentsProceedings of the 2021 CHI Conference on Human Factors in Computing Systems10.1145/3411764.3445158(1-14)Online publication date: 6-May-2021
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Lazar RDym NKushinsky YHuang ZJu TLipman Y(2018)Robust optimization for topological surface reconstructionACM Transactions on Graphics10.1145/3197517.320134837:4(1-10)Online publication date: 30-Jul-2018
https://dl.acm.org/doi/10.1145/3197517.3201348
Stanko THahmann SBonneau GSaguin-Sprynski NSantos LBashford-Rogers T(2016)Smooth interpolation of curve networks with surface normalsProceedings of the 37th Annual Conference of the European Association for Computer Graphics: Short Papers10.5555/3059107.3059115(21-24)Online publication date: 9-May-2016
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Pan HLiu YSheffer AVining NLi CWang W(2015)Flow aligned surfacing of curve networksACM Transactions on Graphics10.1145/276699034:4(1-10)Online publication date: 27-Jul-2015
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Cao YYan DWonka P(2015)Patch layout generation by detecting feature networksComputers and Graphics10.1016/j.cag.2014.09.02246:C(275-282)Online publication date: 1-Feb-2015
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Zhuang YZou MCarr NJu T(2013)A general and efficient method for finding cycles in 3D curve networksACM Transactions on Graphics10.1145/2508363.250842332:6(1-10)Online publication date: 1-Nov-2013
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