Multisided B-spline Patches Over Extraordinary Regions

We propose a generalised B-spline construction that extends uniform bi-degree B-splines to multisided regions spanned over extraordinary regions in quad-dominant meshes. We show how the structure of the existing cubic multisided B-spline patch can be generalised to work with B-spline basis functions of arbitrary degree and can be spanned over extraordinary vertices as well as extraordinary faces of quad-dominant meshes. The resulting multisided surfaces are Cd-1 continuous internally and connect with Gd-1 continuity to adjacent regular and other multisided B-splines patches. In addition, we design several specialised functions that increase the visual quality of the patches, in both the extraordinary vertex and face settings.<br/

Multisided generalisations of Gregory patches

We propose two generalisations of Gregory patches to faces of any valency by using generalised barycentric coordinates in combination with two kinds of multisided Bézier patches. Our first construction builds on S-patches to generalise triangular Gregory patches. The local construction of Chiyokura and Kimura providing G1 continuity between adjoining Bézier patches is generalised so that the novel Gregory S-patches of any valency can be smoothly joined to one another. Our second construction makes a minor adjustment to the generalised Bézier patch structure to allow for cross-boundary derivatives to be defined independently per side. We show that the corresponding blending functions have the inherent ability to blend ribbon data much like the rational blending functions of Gregory patches. Both constructions take as input a polygonal mesh with vertex normals and provide G1 surfaces interpolating the input vertices and normals. Due to the full locality of the methods, they are well suited for geometric modelling as well as computer graphics applications relying on hardware tessellation

A multisided C-2 B-spline patch over extraordinary vertices in quadrilateral meshes

We propose a generalised B-spline construction that extends uniform bicubic B-splines to multisided regions spanned over extraordinary vertices in quadrilateral meshes. We show how the structure of the generalised Bezier patch introduced by Varady et al. can be adjusted to work with B-spline basis functions. We create ribbon surfaces based on B-splines using special basis functions. The resulting multisided surfaces are C-2 continuous internally and connect with G(2) continuity to adjacent regular and other multisided B-splines patches. We visually assess the quality of these surfaces and compare them to Catmull-Clark limit surfaces on several challenging geometrical configurations. (C) 2020 The Author(s). Published by Elsevier Ltd

Mesh Colours for Gradient Meshes

We present an extension of the popular gradient mesh vector graphics primitive with the addition of mesh colours, aiming to reduce the mesh complexity needed to describe intricate colour gradients and textures. We present interesting applications to user-guided authoring of detailed vector graphics and image vectorisation

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

Noisy Gradient Meshes:Augmenting Gradient Meshes with Procedural Noise

We extend the gradient mesh vector graphics primitive with procedural noise functions. Specifically, we couple Perlin, Worley and Gabor noise to the gradient mesh. We allow local parameters controlling the noise functions to be defined at the vertices of the mesh. The parameters are interpolated along with the geometry similarly to how colour is interpolated in an ordinary gradient mesh, allowing for spatially varying noise patterns. These noisy gradient meshes facilitate a sparse representation of high frequency regions along with underlying smooth colour gradients. The meshes are easy to edit and efficient to evaluate on graphics hardware, making them a suitable candidate for inclusion in modern vector graphics authoring tools. We demonstrate the utility of our method on gradient meshes with added noise functions. Additionally, we show that the approach can be used in combination with regular surface meshes where noise functions are used to govern their displacement mapping