A vectorial solver for free-form vector gradients

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.