We propose the use of curved triangles and mesh colours as a vector primitive for image vectorisation. We show that our representation has clear benefits for rendering performance, texture detail, as well as further editing of the resulting vector images. The proposed method focuses on efficiency, but it still leads to results that compare favourably with those from previous work. We show results over a variety of input images ranging from photos, drawings, paintings, all the way to designs and cartoons. We implemented several editing workflows facilitated by our representation: interactive user-guided vectorisation, and novel raster-style feature-aware brushing capabilities.

Abstract Gradient meshes, an advanced vector graphics primitive, are widely used by designers for creating scalable vector graphics. Traditional variants require a regular rectangular topology, which is a severe design restriction. The more advanced subdivision gradient mesh allows for an arbitrary manifold topology and is based on subdivision techniques to define the resulting colour surface. This also allows the artists to manipulate the geometry and colours at various levels of subdivision. Recent advances allow for the interpolation of both geometry and colour, local detail following edits at coarser subdivision levels and sharp colour transitions. A shortcoming of all existing methods is their dependence on global refinement, which makes them unsuitable for real‐time (commercial) design applications. We present a novel method that incorporates the idea of feature‐adaptive subdivision and uses approximating patches suitable for hardware tessellation with real‐time performance. Further novel features include multiple interaction mechanisms and self‐intersection prevention during interactive design/editing.

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 Bézier patch introduced by Várady 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 C2 continuous internally and connect with G2 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.

Existing techniques that convert B-rep (boundary representation) patches into Clough-Tocher splines guarantee watertight, that is C0, conversion results across B-rep edges. In contrast, our approach ensures global tangent-plane, that is G1, continuity of the converted B-rep CAD models. We achieve this by careful boundary curve and normal vector management, and by converting the input models into Shirman-Séquin macro-elements near their (trimmed) B-rep edges. We propose several different variants and compare them with respect to their locality, visual quality, and difference with the input B-rep CAD model. Although the same global G1 continuity can also be achieved by conversion techniques based on subdivision surfaces, our approach uses triangular splines and thus enjoys full compatibility with CAD.

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.

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.