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Surface multigrid via intrinsic prolongation

Authors:

Hsueh-Ti Derek Liu,

Jiayi Eris Zhang,

Mirela Ben-Chen,

Alec JacobsonAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 40, Issue 4

Article No.: 80, Pages 1 - 13

https://doi.org/10.1145/3450626.3459768

Published: 19 July 2021 Publication History

Abstract

This paper introduces a novel geometric multigrid solver for unstructured curved surfaces. Multigrid methods are highly efficient iterative methods for solving systems of linear equations. Despite the success in solving problems defined on structured domains, generalizing multigrid to unstructured curved domains remains a challenging problem. The critical missing ingredient is a prolongation operator to transfer functions across different multigrid levels. We propose a novel method for computing the prolongation for triangulated surfaces based on intrinsic geometry, enabling an efficient geometric multigrid solver for curved surfaces. Our surface multigrid solver achieves better convergence than existing multigrid methods. Compared to direct solvers, our solver is orders of magnitude faster. We evaluate our method on many geometry processing applications and a wide variety of complex shapes with and without boundaries. By simply replacing the direct solver, we upgrade existing algorithms to interactive frame rates, and shift the computational bottleneck away from solving linear systems.

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Index Terms

Surface multigrid via intrinsic prolongation
1. Applied computing
2. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Mesh models

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 40, Issue 4

August 2021

2170 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3450626

Editor:
Sylvain Paris
Adobe Inc.

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Copyright © 2021 Owner/Author.

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Published: 19 July 2021

Published in TOG Volume 40, Issue 4

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European Research Council
Canada Research Chairs Program
MESH Inc
New Frontiers of Research Fund
Ontario Early Research Award
Fields Centre for Quantitative Analysis and Modelling
Adobe Inc
Autodesk Inc
NSERC Discovery
German-Israeli Foundation for Scientific Research and Development
Israel Science Foundation

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https://dl.acm.org/doi/10.1145/3678002
Jia ZZhang ZWang LTan T(2024)Human Image Generation: A Comprehensive SurveyACM Computing Surveys10.1145/366586956:11(1-39)Online publication date: 28-Jun-2024
https://dl.acm.org/doi/10.1145/3665869
Li HJiang HLuo ATan PFan HZeng BLiu S(2024)DMHomo: Learning Homography with Diffusion ModelsACM Transactions on Graphics10.1145/365220743:3(1-16)Online publication date: 9-Apr-2024
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