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Stripe patterns on surfaces

Knöppel, Felix and Crane, Keenan and Pinkall, Ulrich and Schröder, Peter (2015) Stripe patterns on surfaces. ACM Transactions on Graphics, 34 (4). Art. No. 39. ISSN 0730-0301. doi:10.1145/2767000. https://resolver.caltech.edu/CaltechAUTHORS:20150814-144538364

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Abstract

Stripe patterns are ubiquitous in nature, describing macroscopic phenomena such as stripes on plants and animals, down to material impurities on the atomic scale. We propose a method for synthesizing stripe patterns on triangulated surfaces, where singularities are automatically inserted in order to achieve user-specified orientation and line spacing. Patterns are characterized as global minimizers of a convex-quadratic energy which is well-defined in the smooth setting. Computation amounts to finding the principal eigenvector of a symmetric positive-definite matrix with the same sparsity as the standard graph Laplacian. The resulting patterns are globally continuous, and can be applied to a variety of tasks in design and texture synthesis.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1145/2767000DOIArticle
http://dl.acm.org/citation.cfm?doid=2809654.2767000PublisherArticle
ORCID:
AuthorORCID
Schröder, Peter0000-0002-0323-7674
Additional Information:© 2015 Copyright is held by the owner/author(s). Publication rights licensed to ACM. This work was supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics,” an NSF Mathematical Sciences Postdoctoral Research Fellowship (Award #1304254), and Intel. Meshes in Figs. 2, 14, 18, 22 are courtesy the Stanford Computer Graphics Lab; in Figs. 5, 15, 16, 17 courtesy AIM@Shape; and in Fig. 21 courtesy Martin Newell.
Funders:
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)UNSPECIFIED
NSF Postdoctoral Fellowship1304254
IntelUNSPECIFIED
Subject Keywords:discrete differential geometry, digital geometry processing, texture synthesis, direction fields, singularities
Issue or Number:4
Classification Code:CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems
DOI:10.1145/2767000
Record Number:CaltechAUTHORS:20150814-144538364
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150814-144538364
Official Citation:Knöppel, F., Crane, K., Pinkall, U., Schröder, P. 2015. Stripe Patterns on Surfaces. ACM Trans. Graph. 34, 4, Article 39 (August 2015), 11 pages. DOI = 10.1145/2767000 http://doi.acm.org/10.1145/2767000
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:59562
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:14 Aug 2015 23:02
Last Modified:10 Nov 2021 22:22

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