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Computing Discrete Minimal Surfaces and Their Conjugates
Abstract
We present a new algorithm to compute stable discrete minimal surfaces bounded by a number of fixed or free boundary curves in R 3, S 3 and H 3. The algorithm makes no restr iction on the genus and can handl e singular triangulations. Additionally, we present an algorithm that, starting from a discrete harmonic map, gives a conjugate harmonic map. This can be applied to the identity map on a minimal surface to produce its conjugate minimal surface, a procedure that often yields unstable solutions to a free boundary value problem for minimal surfaces. Symmetry properties of boundary curves are respected during conjugation.
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Cited by
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Desbrun, M., Meyer, M., Schröder, P., & Barr, A. H. (1999) · Proceedings of the 26th annual conference on Computer graphics and interactive techniques - SIGGRAPH '99 · doi:10.1145/311535.311576 · Cited by 1,538
Geodesic Convolutional Neural Networks on Riemannian Manifolds
Masci, J., Boscaini, D., Bronstein, M. M., & Vandergheynst, P. (2015) · 2015 IEEE International Conference on Computer Vision Workshop (ICCVW) · doi:10.1109/iccvw.2015.112 · Cited by 721
Least squares conformal maps for automatic texture atlas generation
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Metadata
- Authors
- Pinkall, U., & Polthier, K.
- Venue
- Experimental Mathematics
- Publisher
- Informa UK Limited
- Published
- 1993-01
- Volume
- 2
- Issue
- 1
- Pages
- 15-36
- ISSN
- 1058-6458 (ISSN-L)
- 1944-950X
- OpenAlex
- W1974956622
- Cited by
- 1,249
- References
- 0
- FWCI
- 5.18
- Type
- journal article
- Language
- en
- Open access
- closed
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
