research-article

Weighted averages on surfaces

Authors:

Daniele Panozzo,

Olga Sorkine-HornungAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 32, Issue 4

Article No.: 60, Pages 1 - 12

https://doi.org/10.1145/2461912.2461935

Published: 21 July 2013 Publication History

Abstract

We consider the problem of generalizing affine combinations in Euclidean spaces to triangle meshes: computing weighted averages of points on surfaces. We address both the forward problem, namely computing an average of given anchor points on the mesh with given weights, and the inverse problem, which is computing the weights given anchor points and a target point. Solving the forward problem on a mesh enables applications such as splines on surfaces, Laplacian smoothing and remeshing. Combining the forward and inverse problems allows us to define a correspondence mapping between two different meshes based on provided corresponding point pairs, enabling texture transfer, compatible remeshing, morphing and more. Our algorithm solves a single instance of a forward or an inverse problem in a few microseconds. We demonstrate that anchor points in the above applications can be added/removed and moved around on the meshes at interactive framerates, giving the user an immediate result as feedback.

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Liu SJi YGuo JLiu LFu X(2024)Smooth Bijective Projection in a High-order ShellACM Transactions on Graphics10.1145/365820743:4(1-13)Online publication date: 19-Jul-2024
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Index Terms

Weighted averages on surfaces
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Image and video acquisition
        3D imaging
  2. Computer graphics
    1. Image manipulation
      1. Texturing
    2. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

Index terms have been assigned to the content through auto-classification.

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 32, Issue 4

July 2013

1215 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2461912

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Copyright © 2013 ACM.

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Publication History

Published: 21 July 2013

Published in TOG Volume 32, Issue 4

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Liu SJi YGuo JLiu LFu X(2024)Smooth Bijective Projection in a High-order ShellACM Transactions on Graphics10.1145/365820743:4(1-13)Online publication date: 19-Jul-2024
https://doi.org/10.1145/3658207
Mancinelli CPuppo E(2024)Splines on Manifolds: a SurveyComputer Aided Geometric Design10.1016/j.cagd.2024.102349(102349)Online publication date: May-2024
https://doi.org/10.1016/j.cagd.2024.102349
Pang BZheng ZWang GWang P(2023)Learning the Geodesic Embedding with Graph Neural NetworksACM Transactions on Graphics10.1145/361831742:6(1-12)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618317
Mancinelli CNazzaro GPellacini FPuppo E(2023)b/Surf: Interactive Bézier Splines on Surface MeshesIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.317117929:7(3419-3435)Online publication date: 1-Jul-2023
https://doi.org/10.1109/TVCG.2022.3171179
Mancinelli CPuppo E(2023)Computing the Riemannian center of mass on meshesComputer Aided Geometric Design10.1016/j.cagd.2023.102203103(102203)Online publication date: Jun-2023
https://doi.org/10.1016/j.cagd.2023.102203
Du XZhou QCarr NJu T(2022)Robust computation of implicit surface networks for piecewise linear functionsACM Transactions on Graphics10.1145/3528223.353017641:4(1-16)Online publication date: 22-Jul-2022
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Fouladi SShacklett BPoms FArora AOzdemir ARaghavan DHanrahan PFatahalian KWinstein K(2022)R2E2ACM Transactions on Graphics10.1145/3528223.353017141:4(1-12)Online publication date: 22-Jul-2022
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