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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Index Terms

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

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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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https://doi.org/10.1016/j.jcp.2025.113744
Moon TRhee TKwon JYoon E(2025)Development of novel collision detection algorithms for the estimation of fast ion losses in tokamak fusion deviceComputer Physics Communications10.1016/j.cpc.2024.109490309(109490)Online publication date: Apr-2025
https://doi.org/10.1016/j.cpc.2024.109490
Renz RAlbers A(2024)Multi-Material Topology Optimization on Separate Tetrahedral Meshes with Explicit Design Resolution by Means of RemeshingAlgorithms10.3390/a1710046017:10(460)Online publication date: 16-Oct-2024
https://doi.org/10.3390/a17100460
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