Arbitrary topology meshes in geometric design and vector graphics

Meshes are a powerful means to represent objects and shapes both in 2D and 3D, but the techniques based on meshes can only be used in certain regular settings and restrict their usage. Meshes with an arbitrary topology have many interesting applications in geometric design and (vector) graphics, and can give designers more freedom in designing complex objects. In the first part of the thesis we look at how these meshes can be used in computer aided design to represent objects that consist of multiple regular meshes that are constructed together. Then we extend the B-spline surface technique from the regular setting to work on extraordinary regions in meshes so that multisided B-spline patches are created. In addition, we show how to render multisided objects efficiently, through using the GPU and tessellation. In the second part of the thesis we look at how the gradient mesh vector graphics primitives can be combined with procedural noise functions to create expressive but sparsely defined vector graphic images. We also look at how the gradient mesh can be extended to arbitrary topology variants. Here, we compare existing work with two new formulations of a polygonal gradient mesh. Finally we show how we can turn any image into a vector graphics image in an efficient manner. This vectorisation process automatically extracts important image features and constructs a mesh around it. This automatic pipeline is very efficient and even facilitates interactive image vectorisation

Feature-Adaptive and Hierarchical Subdivision Gradient Meshes

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

Surface modelling for 2D imagery

Vector graphics provides powerful tools for drawing scalable 2D imagery. With the rise of mobile computers, of different types of displays and image resolutions, vector graphics is receiving an increasing amount of attention. However, vector graphics is not the leading framework for creating and manipulating 2D imagery. The reason for this reluctance of employing vector graphical frameworks is that it is difficult to handle complex behaviour of colour across the 2D domain. A challenging problem within vector graphics is to define smooth colour functions across the image. In previous work, two approaches exist. The first approach, known as diffusion curves, diffuses colours from a set of input curves and points. The second approach, known as gradient meshes, defines smooth colour functions from control meshes. These two approaches are incompatible: diffusion curves do not support the local behaviour provided by gradient meshes and gradient meshes do not support freeform curves as input. My research aims to narrow the gap between diffusion curves and gradient meshes. With this aim in mind, I propose solutions to create control meshes from freeform curves. I demonstrate that these control meshes can be used to render a vector primitive similar to diffusion curves using subdivision surfaces. With the use of subdivision surfaces, instead of a diffusion process, colour gradients can be locally controlled using colour-gradient curves associated with the input curves. The advantage of local control is further explored in the setting of vector-centric image processing. I demonstrate that a certain contrast enhancement profile, known as the Cornsweet profile, can be modelled via surfaces in images. This approach does not produce saturation artefacts related with previous filter-based methods. Additionally, I demonstrate various approaches to artistic filtering, where the artist locally models given artistic effects. Gradient meshes are restricted to rectangular topology of the control meshes. I argue that this restriction hinders the applicability of the approach and its potential to be used with control meshes extracted from freeform curves. To this end, I propose a mesh-based vector primitive that supports arbitrary manifold topology of the mesh

Local and Hierarchical Refinement for Subdivision Gradient Meshes

Gradient mesh design tools allow users to create detailed scalable images, traditionally through the creation and manipulation of a (dense) mesh with regular rectangular topology. Through recent advances it is now possible to allow gradient meshes to have arbitrary manifold topology, using a modified Catmull-Clark subdivision scheme to define the resultant geometry and colour [LKSD17]. We present two novel methods to allow local and hierarchical refinement of both colour and geometry for such subdivision gradient meshes. Our methods leverage the mesh properties that the particular subdivision scheme ensures. In both methods, the artists enjoy all the standard capabilities of manipulating the mesh and the associated colour gradients at the coarsest level as well as locally at refined levels. Further novel features include interpolation of both position and colour of the vertices of the input meshes, local detail follows coarser-level edits, and support for sharp colour transitions, all at any level in the hierarchy offered by subdivision

Locally refinable gradient meshes supporting branching and sharp colour transitions:Towards a more versatile vector graphics primitive

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