research-article

Fast winding numbers for soups and clouds

Authors:

Neil G. Dickson,

David I. W. Levin,

Alec JacobsonAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 37, Issue 4

Article No.: 43, Pages 1 - 12

https://doi.org/10.1145/3197517.3201337

Published: 30 July 2018 Publication History

Abstract

Inside-outside determination is a basic building block for higher-level geometry processing operations. Generalized winding numbers provide a robust answer for triangle meshes, regardless of defects such as self-intersections, holes or degeneracies. In this paper, we further generalize the winding number to point clouds. Previous methods for evaluating the winding number are slow for completely disconnected surfaces, such as triangle soups or-in the extreme case- point clouds. We propose a tree-based algorithm to reduce the asymptotic complexity of generalized winding number computation, while closely approximating the exact value. Armed with a fast evaluation, we demonstrate the winding number in a variety of new applications: voxelization, signing distances, generating 3D printer paths, defect-tolerant mesh booleans and point set surfaces.

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Cited By

King NSu HAanjaneya MRuuth SBatty C(2024)A Closest Point Method for PDEs on Manifolds with Interior Boundary Conditions for Geometry ProcessingACM Transactions on Graphics10.1145/367365243:5(1-26)Online publication date: 9-Aug-2024
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Spainhour JGunderman DWeiss K(2024)Robust Containment Queries over Collections of Rational Parametric Curves via Generalized Winding NumbersACM Transactions on Graphics10.1145/365822843:4(1-14)Online publication date: 19-Jul-2024
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Index Terms

Fast winding numbers for soups and clouds
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling

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Published In

cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 37, Issue 4

August 2018

1670 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3197517

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Copyright © 2018 ACM.

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Publication History

Published: 30 July 2018

Published in TOG Volume 37, Issue 4

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Natural Sciences and Engineering Research Council of Canada
Adobe Systems
Connaught Fund
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Cited By

King NSu HAanjaneya MRuuth SBatty C(2024)A Closest Point Method for PDEs on Manifolds with Interior Boundary Conditions for Geometry ProcessingACM Transactions on Graphics10.1145/367365243:5(1-26)Online publication date: 9-Aug-2024
https://dl.acm.org/doi/10.1145/3673652
Spainhour JGunderman DWeiss K(2024)Robust Containment Queries over Collections of Rational Parametric Curves via Generalized Winding NumbersACM Transactions on Graphics10.1145/365822843:4(1-14)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658228
Heiss-Synak PKalinov AStrugaru MEtemadi AYang HWojtan C(2024)Multi-Material Mesh-Based Surface Tracking with Implicit Topology ChangesACM Transactions on Graphics10.1145/365822343:4(1-14)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658223
Gillespie MYang DBotsch MCrane K(2024)Ray Tracing Harmonic FunctionsACM Transactions on Graphics10.1145/365820143:4(1-18)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658201
Miller BSawhney RCrane KGkioulekas I(2024)Walkin’ Robin: Walk on Stars with Robin Boundary ConditionsACM Transactions on Graphics10.1145/365815343:4(1-18)Online publication date: 19-Jul-2024
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Liu WWang XZhao HXue XWu ZLu XHe Y(2024)Consistent Point Orientation for Manifold Surfaces via Boundary IntegrationACM SIGGRAPH 2024 Conference Papers10.1145/3641519.3657475(1-11)Online publication date: 13-Jul-2024
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Kim HPark J(2024)Vertebral segmentation without training using differentiable appearance modeling of a deformable spine templateMedical Imaging 2024: Image Processing10.1117/12.3006602(93)Online publication date: 2-Apr-2024
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Wang ZDou ZXu RLin CLiu YLong XXin SKomura TYuan XWang W(2024)Coverage Axis++: Efficient Inner Point Selection for 3D Shape SkeletonizationComputer Graphics Forum10.1111/cgf.15143Online publication date: 31-Jul-2024
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Scrivener DColdren EChien E(2024)Winding Number Features for Vector Sketch ColorizationComputer Graphics Forum10.1111/cgf.15141Online publication date: 31-Jul-2024
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