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

Solid NURBS Conforming Scaffolding for Isogeometric Analysis

This work introduces a scaffolding framework to compactly parametrise solid structures with conforming NURBS elements for isogeometric analysis. A novel formulation introduces a topological, geometrical and parametric subdivision of the space in a minimal plurality of conforming vectorial elements. These determine a multi-compartmental scaffolding for arbitrary branching patterns. A solid smoothing paradigm is devised for the conforming scaffolding achieving higher than positional geometrical and parametric continuity. Results are shown for synthetic shapes of varying complexity, for modular CAD geometries, for branching structures from tessellated meshes and for organic biological structures from imaging data. Representative simulations demonstrate the validity of the introduced scaffolding framework with scalable performance and groundbreaking applications for isogeometric analysis

Mesh Reduction Using an Angle Criterion Approach

Surface polygonization is the process by which a representative polygonal mesh of a surface is constructed for rendering or analysis purposes. This work presents a new surface polygonization algorithm specifically tailored to be applied to a large class of models which are created with parametric surfaces having triangular meshes. This method has particular application in the area of building virtual environments from computer-aided-design (CAD) models. The algorithm is based on an edge reduction scheme that collapses two vertices of a given triangular polygon edge onto one new vertex. A two step approach is implemented consisting of boundary edge reduction followed by interior edge reduction. A maximum optimization is used to determine the location of the new vertex. The criterion that is used to control how well the approximate surface represents the actual surface is based on examining the angle between surface normals. The advantage of this approach is that the surface discretization is a function of two, user-controlled variables, a boundary edge angle error and a surface edge angle error. The method presented here differs from existing methods in that it takes advantage of the fact that for many models, the exact surface representation of the model is known before the polygonization is attempted. Because the precise surface definition is known, a maximum optimization procedure, that uses the surface information, can be used to locate the new vertex. The algorithm attempts to overcome the deficiencies in existing techniques while minimizing the number of triangular polygons required to represent a surface and still maintaining surface integrity in the rendered model. This paper presents the algorithm and testing results

Practical quad mesh simplification

In this paper we present an innovative approach to incremental quad mesh simplification, i.e. the task of producing a low complexity quad mesh starting from a high complexity one. The process is based on a novel set of strictly local operations which preserve quad structure. We show how good tessellation quality (e.g. in terms of vertex valencies) can be achieved by pursuing uniform length and canonical proportions of edges and diagonals. The decimation process is interleaved with smoothing in tangent space. The latter strongly contributes to identify a suitable sequence of local modification operations. The method is naturally extended to manage preservation of feature lines (e.g. creases) and varying (e.g. adaptive) tessellation densities. We also present an original Triangle-to-Quad conversion algorithm that behaves well in terms of geometrical complexity and tessellation quality, which we use to obtain the initial quad mesh from a given triangle mesh

Practical quad mesh simplification

In this paper we present an innovative approach to incremental quad mesh simplification, i.e. the task of producing a low complexity quad mesh starting from a high complexity one. The process is based on a novel set of strictly local operations which preserve quad structure. We show how good tessellation quality (e.g. in terms of vertex valencies) can be achieved by pursuing uniform length and canonical proportions of edges and diagonals. The decimation process is interleaved with smoothing in tangent space. The latter strongly contributes to identify a suitable sequence of local modification operations. The method is naturally extended to manage preservation of feature lines (e.g. creases) and varying (e.g. adaptive) tessellation densities. We also present an original Triangle-to-Quad conversion algorithm that behaves well in terms of geometrical complexity and tessellation quality, which we use to obtain the initial quad mesh from a given triangle mesh

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