research-article

A vectorial solver for free-form vector gradients

Authors:

Gaël GuennebaudAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 31, Issue 6

Article No.: 173, Pages 1 - 9

https://doi.org/10.1145/2366145.2366192

Published: 01 November 2012 Publication History

Abstract

The creation of free-form vector drawings has been greatly improved in recent years with techniques based on (bi)-harmonic interpolation. Such methods offer the best trade-off between sparsity (keeping the number of control points small) and expressivity (achieving complex shapes and gradients). In this paper, we introduce a vectorial solver for the computation of free-form vector gradients. Based on Finite Element Methods (FEM), its key feature is to output a low-level vector representation suitable for very fast GPU accelerated rasterization and close-form evaluation. This intermediate representation is hidden from the user: it is dynamically updated using FEM during drawing when control points are edited. Since it is output-insensitive, our approach enables novel possibilities for (bi)-harmonic vector drawings such as instancing, layering, deformation, texture and environment mapping. Finally, in this paper we also generalize and extend the set of drawing possibilities. In particular, we show how to locally control vector gradients.

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Cited By

Tian XGünther T(2024)A Survey of Smooth Vector Graphics: Recent Advances in Repr esentation, Creation, Rasterization, and Image VectorizationIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.322057530:3(1652-1671)Online publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1109/TVCG.2022.3220575
Bang SSerkh KStein OJacobson A(2023)An Adaptive Fast-Multipole-Accelerated Hybrid Boundary Integral Equation Method for Accurate Diffusion CurvesACM Transactions on Graphics10.1145/361837442:6(1-28)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618374
Fu QLiu LHou FHe Y(2023)Hierarchical vectorization for facial imagesComputational Visual Media10.1007/s41095-022-0314-410:1(97-118)Online publication date: 30-Nov-2023
https://doi.org/10.1007/s41095-022-0314-4
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Index Terms

A vectorial solver for free-form vector gradients

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 31, Issue 6

November 2012

794 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2366145

Issue’s Table of Contents

Copyright © 2012 ACM.

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Publication History

Published: 01 November 2012

Published in TOG Volume 31, Issue 6

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Cited By

Tian XGünther T(2024)A Survey of Smooth Vector Graphics: Recent Advances in Repr esentation, Creation, Rasterization, and Image VectorizationIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.322057530:3(1652-1671)Online publication date: 1-Mar-2024
https://dl.acm.org/doi/10.1109/TVCG.2022.3220575
Bang SSerkh KStein OJacobson A(2023)An Adaptive Fast-Multipole-Accelerated Hybrid Boundary Integral Equation Method for Accurate Diffusion CurvesACM Transactions on Graphics10.1145/361837442:6(1-28)Online publication date: 5-Dec-2023
https://dl.acm.org/doi/10.1145/3618374
Fu QLiu LHou FHe Y(2023)Hierarchical vectorization for facial imagesComputational Visual Media10.1007/s41095-022-0314-410:1(97-118)Online publication date: 30-Nov-2023
https://doi.org/10.1007/s41095-022-0314-4
Bang SSerkh KStein OJacobson A(2022)A Hybrid Boundary Element and Boundary Integral Equation Method for Accurate Diffusion CurvesSIGGRAPH Asia 2022 Technical Communications10.1145/3550340.3564233(1-4)Online publication date: 6-Dec-2022
https://dl.acm.org/doi/10.1145/3550340.3564233
De Goes FSheffler WFleischer K(2022)Character articulation through profile curvesACM Transactions on Graphics10.1145/3528223.353006041:4(1-14)Online publication date: 22-Jul-2022
https://dl.acm.org/doi/10.1145/3528223.3530060
Hettinga GEchevarria JKosinka J(2022)Adaptive image vectorisation and brushing using mesh coloursComputers & Graphics10.1016/j.cag.2022.05.004105(119-130)Online publication date: Jun-2022
https://doi.org/10.1016/j.cag.2022.05.004
Hou FSun QFang ZLiu YHu SQin HHao AHe Y(2020)Poisson Vector Graphics (PVG)IEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2018.286747826:2(1361-1371)Online publication date: 1-Feb-2020
https://doi.org/10.1109/TVCG.2018.2867478
Chen KLuo YLai YChen YYao CChu HLee T(2020)Image Vectorization With Real-Time Thin-Plate SplineIEEE Transactions on Multimedia10.1109/TMM.2019.292212622:1(15-29)Online publication date: Jan-2020
https://doi.org/10.1109/TMM.2019.2922126
Lu SDing XGao FChen J(2020)Shape Manipulation of Diffusion Curves ImagesIEEE Access10.1109/ACCESS.2020.29824578(57158-57167)Online publication date: 2020
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Iu MTagliasacchi ATeather R(2019)DiffusionMeshProceedings of the 45th Graphics Interface Conference on Proceedings of Graphics Interface 201910.20380/GI2019.26(1-8)Online publication date: 1-Jun-2019
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