Colour Interpolants for Polygonal Gradient Meshes

The gradient mesh is a powerful vector graphics primitive capable of representing detailed and scalable images. Borrowing techniques from 3D graphics such as subdivision surfaces and generalised barycentric coordinates, it has been recently extended from its original form supporting only rectangular arrays to (gradient) meshes of arbitrary manifold topology. We investigate and compare several formulations of the polygonal gradient mesh primitive capable of interpolating colour and colour gradients specified at the vertices of a 2D mesh of arbitrary manifold topology. Our study includes the subdivision based, topologically unrestricted gradient meshes (Lieng et al., 2017) and the cubic mean value interpolant (Li et al., 2013), as well as two newly-proposed techniques based on multisided parametric patches building on the Gregory generalised Bézier patch and the Charrot-Gregory corner interpolator. We adjust these patches from their original geometric 3D setting such that they have the same colour interpolation capabilities as the existing polygonal gradient mesh primitives. We compare all four techniques with respect to visual quality, performance, mathematical continuity, and editability.