Flexible G1 Interpolation of Quad Meshes

International audienceTransforming an arbitrary mesh into a smooth G1 surface has been the subject of intensive research works. To get a visual pleasing shape without any imperfection even in the presence of extraordinary mesh vertices is still a challenging problem in particular when interpolation of the mesh vertices is required. We present a new local method, which produces visually smooth shapes while solving the interpolation problem. It consists of combining low degree biquartic Bézier patches with minimum number of pieces per mesh face, assembled together with G1-continuity. All surface control points are given explicitly. The construction is local and free of zero-twists. We further show that within this economical class of surfaces it is however possible to derive a sufficient number of meaningful degrees of freedom so that standard optimization techniques result in high quality surfaces

A unified approach to blending of constant and varying parametric surfaces with curvature continuity

In this paper, we develop a new approach to blending of constant and varying parametric surfaces with curvature continuity. We propose a new mathematical model consisting of a vector-valued sixth-order partial differential equation (PDE) and time-dependent blending boundary constraints, and develop an approximate analytical solution of the mathematical model. The good accuracy and high computational efficiency are demonstrated by comparing the new approximate analytical solution with the corresponding accurate closed form solution. We also investigate the influence of the second partial derivatives on the continuity at trimlines, and apply the new approximate analytical solution in blending of constant and varying parametric surfaces with curvature continuit

Computer-Aided Geometry Modeling

Techniques in computer-aided geometry modeling and their application are addressed. Mathematical modeling, solid geometry models, management of geometric data, development of geometry standards, and interactive and graphic procedures are discussed. The applications include aeronautical and aerospace structures design, fluid flow modeling, and gas turbine design

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

Global approach for fitting 2D interferometric data

The present paper describes a fitting procedure capable of providing a smooth approximation of experimental data distributed on a bi-dimensional domain, e.g. the typical output of an interferometric technique. The procedure is based on the optimization of an analytical model defined on the whole domain by the B-spline formulation. In the paper rectangular, circular and polygonal convex domains are considered in details, but, according to the need of the operating conditions, the procedure can be extended to domains of different shapes. The proposed procedure was initially calibrated by an analytical case study: a thin square plate simply supported along the edges and loaded by a uniform pressure. Subsequently, by the operative parameters defined by the analyses carried out on the analytic data, the fitting procedure was applied on experimental data obtained by phase shifting speckle interferometry

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

Conceptual free-form styling in virtual environments

This dissertation introduces the tools for designing complete models from scratch directly in a head-tracked, table-like virtual work environment. The models consist of free-form surfaces, and are constructed by drawing a network of curves directly in space. This is accomplished by using a tracked pen-like input device. Interactive deformation tools for curves and surfaces are proposed and are based on variational methods. By aligning the model with the left hand, editing is made possible with the right hand, corresponding to a natural distribution of tasks using both hands. Furthermore, in the emerging field of 3D interaction in virtual environments, particularly with regard to system control, this work uses novel methods to integrate system control tasks, such as selecting tools, and workflow of shape design. The aim of this work is to propose more suitable user interfaces to computersupported conceptual shape design applications. This would be beneficial since it is a field that lacks adequate support from standard desktop systems.Diese Dissertation beschreibtWerkzeuge zum Entwurf kompletter virtueller Modelle von Grund auf. Dies geschieht direkt in einer tischartigen, virtuellen Arbeitsumge-bung mit Hilfe von Tracking der Hände und der Kopfposition. Die Modelle sind aus Freiformlächen aufgebaut und werden als Netz von Kurven mit Hilfe eines getrack-ten, stiftartigen Eingabegerätes direkt im Raum gezeichnet. Es werden interaktive Deformationswerkzeuge für Kurven und Flächen vorgestellt, die auf Methoden des Variational Modeling basieren. Durch das Ausrichten des Modells mit der linken Hand wird das Editieren mit der rechten Hand erleichtert. Dies entspricht einer natürlichen Aufteilung von Aufgaben auf beide Hände. Zusätzlich stellt diese Arbeit neue Techniken für die 3D-Interaktion in virtuellen Umgebungen, insbesondere im Bereich Anwendungskontrolle, vor, die die Aufgabe der Werkzeugauswahl in den Arbeitsablauf der Formgestaltung integrieren. Das Ziel dieser Arbeit ist es, besser geeignete Schnittstellen für den computer-unterstützten, konzeptionellen Formentwurf zur Verfügung zu stellen; ein Gebiet, für das Standard-Desktop-Systeme wenig geeignete Unterstützung bieten