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A Vectorial Solver for Free-form Vector Gradient

Simon Boyé 1, 2, 3 Pascal Barla 1, 2, 3 Gael Guennebaud 2, 3, 1
1 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
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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Contributor : Gaël Guennebaud Connect in order to contact the contributor
Submitted on : Monday, September 17, 2012 - 5:02:28 PM
Last modification on : Thursday, January 20, 2022 - 5:30:40 PM
Long-term archiving on: : Friday, March 31, 2017 - 1:14:56 PM



  • HAL Id : hal-00732992, version 2



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, p. ⟨hal-00732992v2⟩



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