research-article

Unconventional patterns on surfaces

Authors:

Amir VaxmanAuthors Info & Claims

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

Article No.: 101, Pages 1 - 16

https://doi.org/10.1145/3450626.3459933

Published: 19 July 2021 Publication History

Abstract

We present a unified method to meshing surfaces with unconventional patterns, both periodic and aperiodic. These patterns, which have so far been studied on the plane, are patterns comprising a small number of tiles, that do not necessarily exhibit translational periodicity. Our method generalizes the de Bruijn multigrid method to the discrete setting, and thus reduces the problem to the computation of N-Directional fields on triangle meshes. We work with all cases of directional symmetries that have been little studied, including odd and high N. We address the properties of such patterns on surfaces and the challenges in their construction, including order-preservation, seamlessness, duality, and singularities. We show how our method allows for the design of original and unconventional meshes that can be applied to architectural, industrial, and recreational design.

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Cited By

Segall ARen JVaxman ASorkine-Hornung O(2024)Fabric Tessellation: Realizing Freeform Surfaces by SmockingACM Transactions on Graphics10.1145/365815143:4(1-20)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658151
Ebert MKim DAkleman EKrishnamurthy V(2024)Handlebody Plesiohedra Unchained: Topologically Interlocked Cell-Transitive 3-HoneycombsComputer-Aided Design10.1016/j.cad.2024.103779177(103779)Online publication date: Dec-2024
https://doi.org/10.1016/j.cad.2024.103779
Mitropoulou IVaxman ADiamanti ODillenburger B(2024)Fabrication-aware strip-decomposable quadrilateral meshesComputer-Aided Design10.1016/j.cad.2023.103666168:COnline publication date: 12-Apr-2024
https://dl.acm.org/doi/10.1016/j.cad.2023.103666
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Index Terms

Unconventional patterns on surfaces
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling

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- Theoretical foundation: discrete optimal mass transportation and surface Ricci flow.

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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 ACM.

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Publication History

Published: 19 July 2021

Published in TOG Volume 40, Issue 4

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Cited By

Segall ARen JVaxman ASorkine-Hornung O(2024)Fabric Tessellation: Realizing Freeform Surfaces by SmockingACM Transactions on Graphics10.1145/365815143:4(1-20)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658151
Ebert MKim DAkleman EKrishnamurthy V(2024)Handlebody Plesiohedra Unchained: Topologically Interlocked Cell-Transitive 3-HoneycombsComputer-Aided Design10.1016/j.cad.2024.103779177(103779)Online publication date: Dec-2024
https://doi.org/10.1016/j.cad.2024.103779
Mitropoulou IVaxman ADiamanti ODillenburger B(2024)Fabrication-aware strip-decomposable quadrilateral meshesComputer-Aided Design10.1016/j.cad.2023.103666168:COnline publication date: 12-Apr-2024
https://dl.acm.org/doi/10.1016/j.cad.2023.103666
Liu YLee TRezaee Javan APietroni NXie Y(2024)Reducing the Number of Different Faces in Free-Form Surface Approximations Through Clustering and OptimizationComputer-Aided Design10.1016/j.cad.2023.103633166:COnline publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1016/j.cad.2023.103633
Guţan OHegde SBerumen EBessmeltsev MChien E(2023)Singularity‐Free Frame Fields for Line Drawing VectorizationComputer Graphics Forum10.1111/cgf.1490142:5Online publication date: 10-Aug-2023
https://doi.org/10.1111/cgf.14901
Boksebeld IVaxman A(2022)High-Order Directional FieldsACM Transactions on Graphics10.1145/3550454.355545541:6(1-17)Online publication date: 30-Nov-2022
https://dl.acm.org/doi/10.1145/3550454.3555455
Damiand GNivoliers V(2022)Query-replace operations for topologically controlled 3D mesh editing▪Computers and Graphics10.1016/j.cag.2022.06.008106:C(187-199)Online publication date: 1-Aug-2022
https://dl.acm.org/doi/10.1016/j.cag.2022.06.008

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