CaltechAUTHORS
  A Caltech Library Service

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 http://resolver.caltech.edu/CaltechAUTHORS:20151123-155126691

[img] PDF - Published Version
See Usage Policy.

16Mb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20151123-155126691

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 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
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1145/2818143.2818167 DOIArticle
http://dl.acm.org/citation.cfm?doid=2818143.2818167PublisherArticle
Additional Information:© 2015 is held by the owner/author(s).
Record Number:CaltechAUTHORS:20151123-155126691
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20151123-155126691
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:62348
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:24 Nov 2015 00:08
Last Modified:24 Nov 2015 00:08

Repository Staff Only: item control page