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Mean value coordinates for closed triangular meshes

Authors:

Scott Schaefer,

Joe WarrenAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 24, Issue 3

Pages 561 - 566

https://doi.org/10.1145/1073204.1073229

Published: 01 July 2005 Publication History

Abstract

Constructing a function that interpolates a set of values defined at vertices of a mesh is a fundamental operation in computer graphics. Such an interpolant has many uses in applications such as shading, parameterization and deformation. For closed polygons, mean value coordinates have been proven to be an excellent method for constructing such an interpolant. In this paper, we generalize mean value coordinates from closed 2D polygons to closed triangular meshes. Given such a mesh P, we show that these coordinates are continuous everywhere and smooth on the interior of P. The coordinates are linear on the triangles of P and can reproduce linear functions on the interior of P. To illustrate their usefulness, we conclude by considering several interesting applications including constructing volumetric textures and surface deformation.

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Cited By

Nikolos ILygidakis GLeloudas STavla S(2024)Application of B-spline basis functions as harmonic functions for the concurrent shape and mesh morphing of airfoilsJournal of the Global Power and Propulsion Society10.33737/jgpps/1924478(360-369)Online publication date: 8-Oct-2024
https://doi.org/10.33737/jgpps/192447
de Goes FDesbrun M(2024)Stochastic Computation of Barycentric CoordinatesACM Transactions on Graphics10.1145/365813143:4(1-13)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658131
Hu JHui KLiu ZZhang HFu C(2024)CNS-Edit: 3D Shape Editing via Coupled Neural Shape OptimizationACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657412(1-12)Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1145/3641519.3657412
Show More Cited By

Index Terms

Mean value coordinates for closed triangular meshes
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 Transactions on Graphics

ACM Transactions on Graphics Volume 24, Issue 3

July 2005

826 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/1073204

Issue’s Table of Contents

Seminal Graphics Papers: Pushing the Boundaries, Volume 2
August 2023
893 pages
ISBN:9798400708978
DOI:10.1145/3596711
Editor:
Mary C. Whitton
Department of Computer Science, UNC Chapel Hill, USA

Copyright © 2005 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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Association for Computing Machinery

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Publication History

Published: 01 July 2005

Published in TOG Volume 24, Issue 3

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Cited By

Nikolos ILygidakis GLeloudas STavla S(2024)Application of B-spline basis functions as harmonic functions for the concurrent shape and mesh morphing of airfoilsJournal of the Global Power and Propulsion Society10.33737/jgpps/1924478(360-369)Online publication date: 8-Oct-2024
https://doi.org/10.33737/jgpps/192447
de Goes FDesbrun M(2024)Stochastic Computation of Barycentric CoordinatesACM Transactions on Graphics10.1145/365813143:4(1-13)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658131
Hu JHui KLiu ZZhang HFu C(2024)CNS-Edit: 3D Shape Editing via Coupled Neural Shape OptimizationACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657412(1-12)Online publication date: 13-Jul-2024
https://dl.acm.org/doi/10.1145/3641519.3657412
de la Houssaije WEchevarria JKosinka J(2024)Palette‐Based Recolouring of Gradient MeshesComputer Graphics Forum10.1111/cgf.1525843:7Online publication date: 7-Nov-2024
https://doi.org/10.1111/cgf.15258
Ströter DThiery JHormann KChen JChang QBesler SMueller‐Roemer JBoubekeur TStork AFellner D(2024)A Survey on Cage‐based Deformation of 3D ModelsComputer Graphics Forum10.1111/cgf.1506043:2Online publication date: 30-Apr-2024
https://doi.org/10.1111/cgf.15060
Bunge ABukenberger DWagner SAlexa MBotsch M(2024)Polygon Laplacian Made RobustComputer Graphics Forum10.1111/cgf.1502543:2Online publication date: 30-Apr-2024
https://doi.org/10.1111/cgf.15025
Guo JZhang WYe CFu X(2024)Robust Coarse Cage Construction With Small Approximation ErrorsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.325520730:7(4234-4245)Online publication date: 1-Jul-2024
https://dl.acm.org/doi/10.1109/TVCG.2023.3255207
Zhang RZhang CDi YManhardt FLiu XTombari FJi X(2024)KP-RED: Exploiting Semantic Keypoints for Joint 3D Shape Retrieval and Deformation2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR52733.2024.01941(20540-20550)Online publication date: 16-Jun-2024
https://doi.org/10.1109/CVPR52733.2024.01941
Das DWewer CYunus RIlg ELenssen J(2024)Neural Parametric Gaussians for Monocular Non-Rigid Object Reconstruction2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR52733.2024.01019(10715-10725)Online publication date: 16-Jun-2024
https://doi.org/10.1109/CVPR52733.2024.01019
Yenphraphai JPan XLiu SPanozzo DXie S(2024)Image Sculpting: Precise Object Editing with 3D Geometry Control2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)10.1109/CVPR52733.2024.00406(4241-4251)Online publication date: 16-Jun-2024
https://doi.org/10.1109/CVPR52733.2024.00406
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