Locally refinable gradient meshes supporting branching and sharp colour transitions

Abstract

We present a local refinement approach for gradient meshes, a primitive commonly used in the design of vector illustrations with complex colour propagation. Local refinement allows the artist to add more detail only in the regions where it is needed, as opposed to global refinement which often clutters the workspace with undesired detail and potentially slows down the workflow. Moreover, in contrast to existing implementations of gradient mesh refinement, our approach ensures mathematically exact refinement. Additionally, we introduce a branching feature that allows for a wider range of mesh topologies, as well as a feature that enables sharp colour transitions similar to diffusion curves, which turn the gradient mesh into a more versatile and expressive vector graphics primitive.

Noisy gradient meshes: Augmenting gradient meshes with procedural noise

“…The approach in this paper works directly only for quadrilateral meshes with regular topologies. It should be possible to support T-junctions similarly to locally refinable gradient meshes [3] as long as the gradient meshes remain rectangular and enforce C 1 continuity. For meshes with arbitrary manifold topology [13], the geometry should have at least C 1 continuity in order to avoid visible discontinuities or unexpected distortions in the generated noise fields.…”

“…Gradient meshes have also been used for image vectorisation [12,16]. More recent developments in gradient meshes include a colour interpolation scheme based on subdivision surfaces [13,18], and gradient meshes which allow T-junctions and hierarchical editing [3]. Nearly all of the research into gradient meshes has focused on extending the capabilities of the primitive to arbitrary meshes, or to use the meshes in a vectorisation process.…”

“…Traditionally, a Ferguson patch [7] is the underlying geometric primitive used for a gradient mesh. In this paper, we choose to represent each (quadrilateral) patch of the primitive as a bicubic Bézier patch instead; see [3] for an indepth discussion. The vertices v ij are defined as the tuple (x, y, r, g, b), where the first two components represent position, and the last three control its (RGB) colour.…”

Arbitrary topology meshes in geometric design and vector graphics

“…Traditionally, a Ferguson patch [Fer64] is the underlying geometric primitive used for a gradient mesh. However, since it is a bicubic patch we can also represent each (quadrilateral) patch as a bicubic Bézier patch instead; see [BLHK18] for an in-depth discussion. The vertices v i j are de ned as the quintuple (x, , r , , b), where the rst two components represent position, and the last three control its (RGB) colour.…”

“…The approach can be readily extended to locally re nable gradient meshes [BLHK18] as this still provides C 1 continuity across T-junctions and the parametrisation will stay intact. It cannot easily be extended to gradient meshes with arbitrary topology [LKSD17] as this requires a more elaborate assignment of texture coordinates to the mesh as this cannot be done through a rectangular subdivision of the u grid.…”