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Vector field processing on triangle meshes

de Goes, Fernando and Desbrun, Mathieu and Tong, Yiying (2015) Vector field processing on triangle meshes. In: SIGGRAPH Asia 2015 Courses. Association for Computing Machinery , New York, NY, Art. No. 17. ISBN 978-1-4503-3924-7.

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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 encoding 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 tradeoffs 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
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URLURL TypeDescription DOIArticle
Desbrun, Mathieu0000-0003-3424-6079
Additional Information:© 2015 is held by the owner/author(s).
Record Number:CaltechAUTHORS:20151123-155126691
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:62348
Deposited By: Tony Diaz
Deposited On:24 Nov 2015 00:08
Last Modified:10 Nov 2021 23:01

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