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A Vectorial Solver for Free-form Vector Gradient

Simon Boyé 1, 2, 3 Pascal Barla 4, 5 Gael Guennebaud 1, 2, 4
3 IPARLA - Visualization and manipulation of complex data on wireless mobile devices
Université Sciences et Technologies - Bordeaux 1, Inria Bordeaux - Sud-Ouest, École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), CNRS - Centre National de la Recherche Scientifique : UMR5800
4 MANAO - Melting the frontiers between Light, Shape and Matter
LaBRI - Laboratoire Bordelais de Recherche en Informatique, Inria Bordeaux - Sud-Ouest, LP2N - Laboratoire Photonique, Numérique et Nanosciences
5 lp2n-05
LP2N - Laboratoire Photonique, Numérique et Nanosciences
Abstract : The creation of free-form vector drawings as been greatly improved in recent years with techniques based on harmonic or bi-harmonic interpolation. Such methods offer the best trade-off between spar- sity (keeping the number of control points small) and expressivity (achieving complex shapes and gradients). Unfortunately, the lack of a robust and versatile method to compute such images still lim- its their use in real-world applications. In this paper, we introduce a vectorial solver for the computation of free-form vector gradi- ents. 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 interme- diate representation is hidden from the user: it is dynamically up- dated using FEM during drawing when control points are edited. Since it is output-insensitive, our approach enables novel possibili- ties for (bi)-harmonic vector drawings such as instancing, layering, deformation, texture and environment mapping. Finally, in this pa- per we also generalize and extend the set of drawing possibilities. In particular, we show how to locally control vector gradients.
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Journal articles
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https://hal.inria.fr/hal-00732992
Contributor : Gaël Guennebaud <>
Submitted on : Monday, September 17, 2012 - 3:34:44 PM
Last modification on : Thursday, March 12, 2020 - 10:36:07 AM
Document(s) archivé(s) le : Friday, December 16, 2016 - 1:56:59 PM

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  • HAL Id : hal-00732992, version 1

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Simon Boyé, Pascal Barla, Gael Guennebaud. A Vectorial Solver for Free-form Vector Gradient. ACM Transactions on Graphics, Association for Computing Machinery, 2012, Proceedings of Siggraph Asia 2012. ⟨hal-00732992v1⟩

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