Integrable PolyVector fields

Olga Diamanti; Amir Vaxman; Daniele Panozzo; Olga Sorkine-Hornung

doi:10.1145/2766906

Integrable PolyVector fields

Olga Diamanti, Amir Vaxman, Daniele Panozzo, Olga Sorkine-Hornung

Computer Science

Research output: Contribution to journal › Conference article › peer-review

Abstract

We present a framework for designing curl-free tangent vector fields on discrete surfaces. Such vector fields are gradients of locallydefined 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.

Original language	English (US)
Article number	38
Journal	ACM Transactions on Graphics
Volume	34
Issue number	4
DOIs	https://doi.org/10.1145/2766906
State	Published - Jul 27 2015
Event	ACM Special Interest Group on Computer Graphics and Interactive Techniques Conference, SIGGRAPH 2015 - Los Angeles, United States Duration: Aug 9 2015 → Aug 13 2015

Keywords

Curl-free fields
PolyVectors
Quad meshing

ASJC Scopus subject areas

Computer Graphics and Computer-Aided Design

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10.1145/2766906

Cite this

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title = "Integrable PolyVector fields",

abstract = "We present a framework for designing curl-free tangent vector fields on discrete surfaces. Such vector fields are gradients of locallydefined 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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AU - Diamanti, Olga

AU - Vaxman, Amir

AU - Panozzo, Daniele

AU - Sorkine-Hornung, Olga

PY - 2015/7/27

Y1 - 2015/7/27

N2 - We present a framework for designing curl-free tangent vector fields on discrete surfaces. Such vector fields are gradients of locallydefined 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.

AB - We present a framework for designing curl-free tangent vector fields on discrete surfaces. Such vector fields are gradients of locallydefined 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.

KW - Curl-free fields

KW - PolyVectors

KW - Quad meshing

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T2 - ACM Special Interest Group on Computer Graphics and Interactive Techniques Conference, SIGGRAPH 2015

Y2 - 9 August 2015 through 13 August 2015

ER -

Integrable PolyVector fields

Abstract

Keywords

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