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Integrable PolyVector fields

Published: 27 July 2015 Publication History

Abstract

We present a framework for designing curl-free tangent vector fields on discrete surfaces. Such vector fields are gradients of locally-defined scalar functions, and this property is beneficial for creating surface parameterizations, since the gradients of the parameterization coordinate functions are then exactly aligned with the designed fields. We introduce a novel definition for discrete curl between unordered sets of vectors (PolyVectors), and devise a curl-eliminating continuous optimization that is independent of the matchings between them. Our algorithm naturally places the singularities required to satisfy the user-provided alignment constraints, and our fields are the gradients of an inversion-free parameterization by design.

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cover image ACM Transactions on Graphics
ACM Transactions on Graphics  Volume 34, Issue 4
August 2015
1307 pages
ISSN:0730-0301
EISSN:1557-7368
DOI:10.1145/2809654
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 27 July 2015
Published in TOG Volume 34, Issue 4

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Author Tags

  1. PolyVectors
  2. curl-free fields
  3. quad meshing

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