Universal attraction force-inspired freeform surface modeling for 3D sketching

This paper presents a novel freeform surface modeling method to construct a freeform surface from 3D sketch. The approach is inspired by Newton’s universal attraction force law to construct a surface model from rough boundary curves and unorganized interior characteristic curves which may cross the boundary curves or not. Based on these unorganized curves, an initial surface can be obtained for conceptual design and it can be improved later in a commercial package. The approach has been tested with examples and it is capable of dealing with unorganized design curves for surface modeling

AutoGraff: towards a computational understanding of graffiti writing and related art forms.

The aim of this thesis is to develop a system that generates letters and pictures with a style that is immediately recognizable as graffiti art or calligraphy. The proposed system can be used similarly to, and in tight integration with, conventional computer-aided geometric design tools and can be used to generate synthetic graffiti content for urban environments in games and in movies, and to guide robotic or fabrication systems that can materialise the output of the system with physical drawing media. The thesis is divided into two main parts. The first part describes a set of stroke primitives, building blocks that can be combined to generate different designs that resemble graffiti or calligraphy. These primitives mimic the process typically used to design graffiti letters and exploit well known principles of motor control to model the way in which an artist moves when incrementally tracing stylised letter forms. The second part demonstrates how these stroke primitives can be automatically recovered from input geometry defined in vector form, such as the digitised traces of writing made by a user, or the glyph outlines in a font. This procedure converts the input geometry into a seed that can be transformed into a variety of calligraphic and graffiti stylisations, which depend on parametric variations of the strokes

A code for surface modeling and grid generation coupled to a panel method for aerodynamic configuration design

An integrated platform has been developed which features a geometric, a grid generation and an aerodynamic analysis module. The main intent is to execute a quick though reliable preliminary aerodynamic analysis on a generic complex aerodynamic configuration and, at the same time, provide a mean of exporting the defined geometry or grid to leading CAE/CAD, meshing and analysis softwares, for deep detail modifications or more accurate, although time consuming, analysis. In the geometric module, the process of shape definition is easily and intuitively achieved with the aid of specific features and tools. The geometric description relies on NURBS, a flexible, accurate and efficient parametric form. Once the configuration has been defined, the user is ready to move on the grid generation module, or to export it to IGES standard format in order to use CAE/CAD, meshing or aerodynamic analysis programs. The grid generation module is capable to build structured or unstructured meshes. Both of the processes are automatized, even if the user can easily set and control grid parameters. The structured grid generator is oriented to LaWGS description standard, while the unstructured grid can be exported to different formats. The user is now ready to launch Pan Air, a panel method, as the aerodynamic solver. The preprocessor and postprocessor aid to the definition of the flow parameters and to the graphical visualization of the results. One of the strength of this code is the user friendly GUI organization of each module: the user is aided throughout all the steps. Besides this, every module relies on fast computational algorithms to speed up the overall process. For all these reasons, this code has a natural lean to be used in pair with an optimization tool

Controlling the interpolation of NURBS curves and surfaces

The primary focus of this thesis is to determine the best methods for controlling the interpolation of NURBS curves and surfaces. The various factors that affect the quality of the interpolant are described, and existing methods for controlling them are reviewed. Improved methods are presented for calculating the parameter values, derivative magnitudes, data point spacing and twist vectors, with the aim of producing high quality interpolants with minimal data requirements. A new technique for obtaining the parameter values and derivative magnitudes is evaluated, which constructs a C$^1$ cubic spline with orthogonal first and second derivatives at specified parametric locations. When this data is used to create a C$^2$ spline, the resulting interpolant is superior to those constructed using existing parameterisation and derivative magnitude estimation methods. Consideration is given to the spacing of data points, which has a significant impact on the quality of the interpolant. Existing methods are shown to produce poor results with curves that are not circles. Three new methods are proposed that significantly reduce the positional error between the interpolant and original geometry. For constrained surface interpolation, twist vectors must be estimated. A method is proposed that builds on the Adini method, and is shown to have improved error characteristics. In numerical tests, the new method consistently outperforms Adini. Interpolated surfaces are often required to join together smoothly along their boundaries. The constraints for joining surfaces with parametric and geometric continuity are discussed, and the problem of joining $N$ patches to form an $N$-sided region is considered. It is shown that regions with odd $N$ can be joined with G$^1$ continuity, but those with even $N$ or requiring G$^2$ continuity can only be obtained for specific geometries

Improving Realism of Facial Interpolation and Blendshapes with Analytical Partial Differential Equation-Represented Physics

How to create realistic shapes by interpolating two known shapes for facial blendshapes has not been investigated in the existing literature. In this paper, we propose a physics-based mathematical model and its analytical solutions to obtain more realistic facial shape changes. To this end, we first introduce the internal force of elastic beam bending into the equation of motion and integrate it with the constraints of two known shapes to develop the physics-based mathematical model represented with dynamic partial differential equations (PDEs). Second, we propose a unified mathematical expression of the external force represented with linear and various nonlinear time-dependent Fourier series, introduce it into the mathematical model to create linear and various nonlinear dynamic deformations of the curves defining a human face model, and derive analytical solutions of the mathematical model. Third, we evaluate the realism of the obtained analytical solutions in interpolating two known shapes to create new shape changes by comparing the shape changes calculated with the obtained analytical solutions and geometric linear interpolation to the ground-truth shape changes and conclude that among linear and various nonlinear PDE-based analytical solutions named as linear, quadratic, and cubic PDE-based interpolation, quadratic PDE-based interpolation creates the most realistic shape changes, which are more realistic than those obtained with the geometric linear interpolation. Finally, we use the quadratic PDE-based interpolation to develop a facial blendshape method and demonstrate that the proposed approach is more efficient than numerical physics-based facial blendshapes

Real-time parametric surface modeling for conceptual design

Conceptual design is the initial stage of the product design cycle. In this stage, the structural details of the products require less attention than the functionality and style. Designers need an environment where their creative inspiration and imagination can be expressed intuitively and instantaneously without limitations. Paper-pen based traditional tools are still common in the practice. However, pen and paper based methods limit the expression of ideas (conceptual design) in the form of 2D images. This thesis introduces a free-form 3D sketching technique with an objective to improve the conceptual design stage. Improvement comes from two characteristics: firstly, the designed system enables designers to use 3D digital space to summarize their imaginations; secondly, the toolkit provides an unconstrained environment where designers/artists can demonstrate their imaginations without dealing with details. Ultimate objective of this line of the research work is to develop a free-form sketching tool where users are not familiar with the system; rather they can naturally use the system in order to complete their initial design. In order to have a stereoscopic impression or called intuitive sensor of the designed products in the conceptual design stage, a direct 3D display is essential. Hence, in this research work, we introduce an unconstrained conceptual design environment that enables designers to display their ideas instantaneously and inspirationally without any constraints in computer in the form of 3D objects directly under the support of VR technology. The developed toolkit provides: a virtual space for designers to summarize their imaginations in 3D; a module to enable smooth connection of individual surface patches; finally, a method to give surface thickness to the images. Hence the resulting images are ready to be used within the existing CAD software, for design review purposes and manufacturing planning efforts

Interpolatory Catmull-Clark volumetric subdivision over unstructured hexahedral meshes for modeling and simulation applications

International audienceVolumetric modeling is an important topic for material modeling and isogeometric simulation. In this paper, two kinds of interpolatory Catmull-Clark volumetric subdivision approaches over unstructured hexahedral meshes are proposed based on the limit point formula of Catmull-Clark subdivision volume. The basic idea of the first method is to construct a new control lattice, whose limit volume by the CatmullClark subdivision scheme interpolates vertices of the original hexahedral mesh. The new control lattice is derived by the local push-back operation from one CatmullClark subdivision step with modified geometric rules. This interpolating method is simple and efficient, and several shape parameters are involved in adjusting the shape of the limit volume. The second method is based on progressive-iterative approximation using limit point formula. At each iteration step, we progressively modify vertices of an original hexahedral mesh to generate a new control lattice whose limit volume interpolates all vertices in the original hexahedral mesh. The convergence proof of the iterative process is also given. The interpolatory subdivision volume has C 2-smoothness at the regular region except around extraordinary vertices and edges. Furthermore, the proposed interpolatory volumetric subdivision methods can be used not only for geometry interpolation, but also for material attribute interpolation in the field of volumetric material modeling. The application of the proposed volumetric subdivision approaches on isogeometric analysis is also given with several examples

Discrete Geometric Methods for Surface Deformation and Visualisation

Industrial design has a long history. With the introduction of Computer-Aided Engineering, industrial design was revolutionised. Due to the newly found support, the design workflow changed, and with the introduction of virtual prototyping, new challenges arose. These new engineering problems have triggered new basic research questions in computer science. In this dissertation, I present a range of methods which support different components of the virtual design cycle, from modifications of a virtual prototype and optimisation of said prototype, to analysis of simulation results. Starting with a virtual prototype, I support engineers by supplying intuitive discrete normal vectors which can be used to interactively deform the control mesh of a surface. I provide and compare a variety of different normal definitions which have different strengths and weaknesses. The best choice depends on the specific model and on an engineer’s priorities. Some methods have higher accuracy, whereas other methods are faster. I further provide an automatic means of surface optimisation in the form of minimising total curvature. This minimisation reduces surface bending, and therefore, it reduces material expenses. The best results can be obtained for analytic surfaces, however, the technique can also be applied to real-world examples. Moreover, I provide engineers with a curvature-aware technique to optimise mesh quality. This helps to avoid degenerated triangles which can cause numerical issues. It can be applied to any component of the virtual design cycle: as a direct modification of the virtual prototype (depending on the surface defini- tion), during optimisation, or dynamically during simulation. Finally, I have developed two different particle relaxation techniques that both support two components of the virtual design cycle. The first component for which they can be used is discretisation. To run computer simulations on a model, it has to be discretised. Particle relaxation uses an initial sampling, and it improves it with the goal of uniform distances or curvature-awareness. The second component for which they can be used is the analysis of simulation results. Flow visualisation is a powerful tool in supporting the analysis of flow fields through the insertion of particles into the flow, and through tracing their movements. The particle seeding is usually uniform, e.g. for an integral surface, one could seed on a square. Integral surfaces undergo strong deformations, and they can have highly varying curvature. Particle relaxation redistributes the seeds on the surface depending on surface properties like local deformation or curvature.Industrielles Design ist ein traditionsreiches Gebiet, welches durch die Einführung computergestützter Ingenieurwissenschaft revolutioniert wurde. Durch die Computerunterstützung wurden Arbeitsweisen stark verändert und, im Rahmen der Einführung virtueller Prototypen, neue Herausforderungen geschaffen. Diese neuen Herausforderungen im Ingenieurwesen brachten auch neue Forschungsfragen für die Informatik mit sich. In dieser Dissertation präsentiere ich eine Reihe von Methoden, welche verschiedene Komponenten des virtuellen Designzykluses unterstützen, von der Modifikation von virtuellen Prototypen über ihre Optimierung bis hin zur Analyse von Simulationstechniken. Von einem virtuellen Prototypen ausgehend unterstütze ich Ingenieurinnen und Ingenieure dabei, diesen interaktiv mit Hilfe eines Kontrollgitters zu verformen, indem ich intuitive diskrete Normalenvektoren bereitstelle. Ich definiere und vergleiche unterschiedliche Normalendefinitionen, welche verschiedene Stärken und Schwächen besitzen. Die beste Wahl hängt hierbei davon ab, welche Eigenschaften ein Modell hat, und wie die Prioritäten der Ingenieurin oder des Ingenieurs gesetzt sind. Manche Methoden sind exakter, während andere schneller sind. Weiterhin liefere ich eine automatische Flächenoptimierung durch die Minimierung der Gesamtkrümmung einer Fläche. Diese Minimierung reduziert die Flächenkrümmung und reduziert hierdurch Materialkosten. Die besten Resultate lassen sich für analytische Flächen erzielen, jedoch kann die Technik auch auf praxisnahe Beispiele angewendet werden. Darüber hinaus biete ich Ingenieurinnen und Ingenieuren eine krümmungs\-basierte Technik, um die Qualität von Gittern zu verbessern. Dies vermeidet degenerierte Dreiecke, welche sonst zu numerischen Problemen führen würden. Diese Optimierung kann in jedem Schritt des virtuellen Designzykluses angewendet werden: Als direkte Modifikation des virtuellen Prototyps (abhängig von der Flächendefinition), zur Zeit der Optimierung, oder dynamisch während der Simulation. Schlussendlich habe ich zwei verschiedene Partikelrelaxierungstechniken entwickelt, welche jeweils zwei Komponenten des virtuellen Designzykluses unterstützen. Die erste Komponente ist die Diskretisierung, welche nötig ist, um Computersimulationen auf analytischen Modellen durchzuführen. Die Partikelrelaxierung nutzt eine initiale Verteilung und verbessert diese mit dem Ziel, entweder eine Gleichverteilung auf der Fläche oder eine krümmungsabhängige Verteilung zu erreichen. Die zweite Komponente, für die die Relaxierung genutzt werden kann, ist die Analyse der Simulationsergebnisse. Vektorfeldvisualisierung ist ein mächtiges Werkzeug zur Analyse von Flussfeldern durch Verfolgen von Partikeln, die in einen Fluss hinzugegeben wurden. Üblicherweise beginnt eine solche Simulation mit einer gleichverteilten Menge an Partikeln, die z.B. in einem Quadrat angeordnet sind. Die daraus entstehenden Integralflächen unterliegen starken Deformierungen und können sehr variable Krümmungen haben. Die Partikelrelaxierung verteilt die Partikel abhängig von Kriterien wie lokaler Deformierung oder Krümmung auf der Fläche um

An efficient active B-spline/nurbs model for virtual sculpting

This thesis presents an Efficient Active B-Spline/Nurbs Model for Virtual Sculpting. In spite of the on-going rapid development of computer graphics and computer-aided design tools, 3D graphics designers still rely on non-intuitive modelling procedures for the creation and manipulation of freeform virtual content. The ’Virtual Sculpting' paradigm is a well-established mechanism for shielding designers from the complex mathematics that underpin freeform shape design. The premise is to emulate familiar elements of traditional clay sculpting within the virtual design environment. Purely geometric techniques can mimic some physical properties. More exact energy-based approaches struggle to do so at interactive rates. This thesis establishes a unified approach for the representation of physically aware, energy-based, deformable models, across the domains of Computer Graphics, Computer-Aided Design and Computer Vision, and formalises the theoretical relationships between them. A novel reformulation of the computer vision approach of Active Contour Models (ACMs) is proposed for the domain of Virtual Sculpting. The proposed ACM-based model offers novel interaction behaviours and captures a compromise between purely geometric and more exact energy-based approaches, facilitating physically plausible results at interactive rates. Predefined shape primitives provide features of interest, acting like sculpting tools such that the overall deformation of an Active Surface Model is analogous to traditional clay modelling. The thesis develops a custom-approach to provide full support for B-Splines, the de facto standard industry representation of freeform surfaces, which have not previously benefited from the seamless embodiment of a true Virtual Sculpting metaphor. A novel generalised computationally efficient mathematical framework for the energy minimisation of an Active B-Spline Surface is established. The resulting algorithm is shown to significantly reduce computation times and has broader applications across the domains of Computer-Aided Design, Computer Graphics, and Computer Vision. A prototype ’Virtual Sculpting’ environment encapsulating each of the outlined approaches is presented that demonstrates their effectiveness towards addressing the long-standing need for a computationally efficient and intuitive solution to the problem of interactive computer-based freeform shape design