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Vector field processing on triangle meshes

de Goes, Fernando and Desbrun, Mathieu and Tong, Yiying (2016) Vector field processing on triangle meshes. In: SIGGRAPH '16 ACM SIGGRAPH 2016 Courses. ACM , New York, NY, Art. No. 27. ISBN 978-1-4503-4289-6. https://resolver.caltech.edu/CaltechAUTHORS:20170110-145123104

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Abstract

While scalar fields on surfaces have been staples of geometry processing, the use of tangent vector fields has steadily grown in geometry processing over the last two decades: they are crucial to encode both directions and sizing on surfaces as commonly required in tasks such as texture synthesis, non-photorealistic rendering, digital grooming, and meshing. There are, however, a variety of discrete representations of tangent vector fields on triangle meshes, and each approach offers different trade-offs among simplicity, efficiency, and accuracy depending on the targeted application. This course reviews the three main families of discretizations used to design computational tools for vector field processing on triangle meshes: face-based, edge-based, and vertex-based representations. In the process of reviewing the computational tools offered by these representations, we go over a large body of recent developments in vector field processing in the area of discrete differential geometry. We also discuss the theoretical and practical limitations of each type of discretization, and cover increasingly-common extensions such as n-direction and n-vector fields. While the course will focus on explaining the key approaches to practical encoding (including data structures) and manipulation (including discrete operators) of finite-dimensional vector fields, important differential geometric notions will also be covered: as often in Discrete Differential Geometry, the discrete picture will be used to illustrate deep continuous concepts such as covariant derivatives, metric connections, or Bochner Laplacians.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1145/2897826.2927303DOIArticle
http://dl.acm.org/citation.cfm?doid=2897826.2927303PublisherArticle
Additional Information:© 2016 Copyright held by the owner/author(s).
Record Number:CaltechAUTHORS:20170110-145123104
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170110-145123104
Official Citation:Fernando de Goes, Mathieu Desbrun, and Yiying Tong. 2016. Vector field processing on triangle meshes. In ACM SIGGRAPH 2016 Courses (SIGGRAPH '16). ACM, New York, NY, USA, , Article 27 , 49 pages. DOI: http://dx.doi.org/10.1145/2897826.2927303
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73395
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:10 Jan 2017 23:45
Last Modified:03 Oct 2019 16:27

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