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Mean value coordinates for closed triangular meshes

Authors:

Scott Schaefer,

Joe WarrenAuthors Info & Claims

SIGGRAPH '05: ACM SIGGRAPH 2005 Papers

Pages 561 - 566

https://doi.org/10.1145/1186822.1073229

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

Thiery JMichel �Chen J(2024)Biharmonic Coordinates and their Derivatives for Triangular 3D CagesACM Transactions on Graphics10.1145/365820843:4(1-17)Online publication date: 19-Jul-2024
https://doi.org/10.1145/3658208
Garbin SKowalski MEstellers VSzymanowicz SRezaeifar SShen JJohnson MValentin J(2024)VolTeMorph: Real‐time, Controllable and Generalizable Animation of Volumetric RepresentationsComputer Graphics Forum10.1111/cgf.1511743:6Online publication date: 29-May-2024
https://doi.org/10.1111/cgf.15117
Sun QNie YZhang QLi G(2024)Building Coarse to Fine Convex Hulls With Auxiliary Vertices for Palette-Based Image RecoloringIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.329638630:8(5581-5595)Online publication date: Aug-2024
https://doi.org/10.1109/TVCG.2023.3296386
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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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cover image ACM Conferences

SIGGRAPH '05: ACM SIGGRAPH 2005 Papers

July 2005

826 pages

ISBN:9781450378253

DOI:10.1145/1186822

Editor:
Markus Gross
Eidgen�ssische Technische Hochschule Z�rich

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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Published: 01 July 2005

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Cited By

Thiery JMichel �Chen J(2024)Biharmonic Coordinates and their Derivatives for Triangular 3D CagesACM Transactions on Graphics10.1145/365820843:4(1-17)Online publication date: 19-Jul-2024
https://doi.org/10.1145/3658208
Garbin SKowalski MEstellers VSzymanowicz SRezaeifar SShen JJohnson MValentin J(2024)VolTeMorph: Real‐time, Controllable and Generalizable Animation of Volumetric RepresentationsComputer Graphics Forum10.1111/cgf.1511743:6Online publication date: 29-May-2024
https://doi.org/10.1111/cgf.15117
Sun QNie YZhang QLi G(2024)Building Coarse to Fine Convex Hulls With Auxiliary Vertices for Palette-Based Image RecoloringIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2023.329638630:8(5581-5595)Online publication date: Aug-2024
https://doi.org/10.1109/TVCG.2023.3296386
Tian XGünther T(2024)A Survey of Smooth Vector Graphics: Recent Advances in Repr esentation, Creation, Rasterization, and Image VectorizationIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.322057530:3(1652-1671)Online publication date: Mar-2024
https://doi.org/10.1109/TVCG.2022.3220575
Jin LSong XLi JTu CQin X(2024)CSS-Net: Domain Generalization in Category-level Pose Estimation via Corresponding Structural Superpoints2024 IEEE International Conference on Multimedia and Expo (ICME)10.1109/ICME57554.2024.10687684(1-6)Online publication date: 15-Jul-2024
https://doi.org/10.1109/ICME57554.2024.10687684
Xia ZHao JLi KTian ADu Z(2024)Edit propagation via color palettesComputers & Graphics10.1016/j.cag.2024.01.002119(103875)Online publication date: Apr-2024
https://doi.org/10.1016/j.cag.2024.01.002
van de Ruit MEisemann E(2023)Metameric: Spectral Uplifting via Controllable Color ConstraintsSpecial Interest Group on Computer Graphics and Interactive Techniques Conference Conference Proceedings10.1145/3588432.3591565(1-10)Online publication date: 23-Jul-2023
https://doi.org/10.1145/3588432.3591565
Michel �Thiery J(2023)Polynomial 2D Green Coordinates for Polygonal CagesSpecial Interest Group on Computer Graphics and Interactive Techniques Conference Conference Proceedings10.1145/3588432.3591499(1-9)Online publication date: 23-Jul-2023
https://doi.org/10.1145/3588432.3591499
Liu RXiang JZhao BZhang RYu JZheng C(2023)Neural Impostor: Editing Neural Radiance Fields with Explicit Shape ManipulationComputer Graphics Forum10.1111/cgf.1498142:7Online publication date: 14-Nov-2023
https://doi.org/10.1111/cgf.14981
Chen KYin FDu BWu BNguyen T(2023)Efficient Registration for Human Surfaces via Isometric Regularization on Embedded DeformationIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.319738329:12(5020-5032)Online publication date: Dec-2023
https://doi.org/10.1109/TVCG.2022.3197383
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