Ship Hull Representation by Non-Uniform Rational B-Spline Surface Patches

The purpose of this work is to propose a new method for representing the ship hull shape with mathematic surfaces so that geometric data can be generated for any point on the hull where required to assist the production process. An extensive survey of previous work is presented covering both the use of parametric curves and surfaces to model the ship hull and also the most relevant software systems developed for that purpose. The main methods and algorithms available for the generation and edition of curves and surfaces are presented and compared taking into consideration the intended application. From the analysis of the formulations available it was concluded that the most adequate one, which however had not yet been extensively used to model ship hulls was the Non-Uniform Rational B-Splines (NURBS), due to the potential of their capability to represent exactly conic curves and surfaces. Therefore these surfaces were selected as the basis of the method developed in this thesis. A procedure is proposed for the representation of a given hull form in a two step approach, creating first a wireframe model over which the surface patches are generated. Both curves and surfaces are based on the NURBS formulation. To create the wireframe model, first a set of longitudinal boundary lines is selected, dividing the surface into areas of similar shape. Then, these lines are fitted by curves and faired to some extent. Next, transverse sections are defined and split by the boundary lines. Surface patches are then generated over the transverse section curves within the limits of each patch. Finally, to obtain the traditional representation of the ship surface by transverse sections, buttocks and waterlines, contour lines are generated for constant values of x, y and z coordinates. A computer system has been developed incorporating an interface that allows the visualization of the curves and surfaces being modeled. The system incorporates several algorithms for generation and edition of curves and surfaces, in addition to the main contribution of this thesis which is the use of NURBS to represent the ship hull surface. The system also incorporates curve and surface analysis tools and some basic fairing algorithms so that during the several steps of the creation of the model, the fairness of the curves and surfaces can be evaluated and improved to some extent. The procedure is tested and compared with an existing commercial system through some application examples, of a complete hull and in more detail in the bow region, showing that good results can be obtained with the system presented here

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

Smooth Subdivision Surfaces: Mesh Blending and Local Interpolation

Subdivision surfaces are widely used in computer graphics and animation. Catmull-Clark subdivision (CCS) is one of the most popular subdivision schemes. It is capable of modeling and representing complex shape of arbitrary topology. Polar surface, working on a triangle-quad mixed mesh structure, is proposed to solve the inherent ripple problem of Catmull-Clark subdivision surface (CCSS). CCSS is known to be C1 continuous at extraordinary points. In this work, we present a G2 scheme at CCS extraordinary points. The work is done by revising CCS subdivision step with Extraordinary-Points-Avoidance model together with mesh blending technique which selects guiding control points from a set of regular sub-meshes (named dominative control meshes) iteratively at each subdivision level. A similar mesh blending technique is applied to Polar extraordinary faces of Polar surface as well. Both CCS and Polar subdivision schemes are approximating. Traditionally, one can obtain a CCS limit surface to interpolate given data mesh by iteratively solving a global linear system. In this work, we present a universal interpolating scheme for all quad subdivision surfaces, called Bezier Crust. Bezier Crust is a specially selected bi-quintic Bezier surface patch. With Bezier Crust, one can obtain a high quality interpolating surface on CCSS by parametrically adding CCSS and Bezier Crust. We also show that with a triangle/quad conversion process one can apply Bezier Crust on Polar surfaces as well. We further show that Bezier Crust can be used to generate hollowed 3D objects for applications in rapid prototyping. An alternative interpolating approach specifically designed for CCSS is developed. This new scheme, called One-Step Bi-cubic Interpolation, uses bicubic patches only. With lower degree polynomial, this scheme is appropriate for interpolating large-scale data sets. In sum, this work presents our research on improving surface smoothness at extraordinary points of both CCS and Polar surfaces and present two local interpolating approaches on approximating subdivision schemes. All examples included in this work show that the results of our research works on subdivision surfaces are of high quality and appropriate for high precision engineering and graphics usage

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

Designing aesthetically pleasing freeform surfaces in a computer environment

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, February 2001.Includes bibliographical references (p. 151-160).Statement: If computational tools are to be employed in the aesthetic design of freeform surfaces, these tools must better reflect the ways in which creative designers conceive of and develop such shapes. In this thesis, I studied the design of aesthetically constrained freeform surfaces in architecture and industrial design, formulated a requirements list for a computational system that would aid in the creative design of such surfaces, and implemented a subset of the tools that would comprise such a system. This work documents the clay modeling process at BMW AG., Munich. The study of that process has led to a list of tools that would make freeform surface modeling possible in a computer environment. And finally, three tools from this system specification have been developed into a proof-of-concept system. Two of these tools are sweep modification tools and the third allows a user to modify a surface by sketching a shading pattern desired for the surface. The proof-of-concept tools were necessary in order to test the validity of the tools being presented and they have been used to create a number of example objects. The underlying surface representation is a variational expression which is minimized using the finite element method over an irregular triangulated mesh.by Evan P. Smyth.Ph.D

Doctor of Philosophy

dissertationVolumetric parameterization is an emerging field in computer graphics, where volumetric representations that have a semi-regular tensor-product structure are desired in applications such as three-dimensional (3D) texture mapping and physically-based simulation. At the same time, volumetric parameterization is also needed in the Isogeometric Analysis (IA) paradigm, which uses the same parametric space for representing geometry, simulation attributes and solutions. One of the main advantages of the IA framework is that the user gets feedback directly as attributes of the NURBS model representation, which can represent geometry exactly, avoiding both the need to generate a finite element mesh and the need to reverse engineer the simulation results from the finite element mesh back into the model. Research in this area has largely been concerned with issues of the quality of the analysis and simulation results assuming the existence of a high quality volumetric NURBS model that is appropriate for simulation. However, there are currently no generally applicable approaches to generating such a model or visualizing the higher order smooth isosurfaces of the simulation attributes, either as a part of current Computer Aided Design or Reverse Engineering systems and methodologies. Furthermore, even though the mesh generation pipeline is circumvented in the concept of IA, the quality of the model still significantly influences the analysis result. This work presents a pipeline to create, analyze and visualize NURBS geometries. Based on the concept of analysis-aware modeling, this work focusses in particular on methodologies to decompose a volumetric domain into simpler pieces based on appropriate midstructures by respecting other relevant interior material attributes. The domain is decomposed such that a tensor-product style parameterization can be established on the subvolumes, where the parameterization matches along subvolume boundaries. The volumetric parameterization is optimized using gradient-based nonlinear optimization algorithms and datafitting methods are introduced to fit trivariate B-splines to the parameterized subvolumes with guaranteed order of accuracy. Then, a visualization method is proposed allowing to directly inspect isosurfaces of attributes, such as the results of analysis, embedded in the NURBS geometry. Finally, the various methodologies proposed in this work are demonstrated on complex representations arising in practice and research

New Techniques for the Modeling, Processing and Visualization of Surfaces and Volumes

With the advent of powerful 3D acquisition technology, there is a growing demand for the modeling, processing, and visualization of surfaces and volumes. The proposed methods must be efficient and robust, and they must be able to extract the essential structure of the data and to easily and quickly convey the most significant information to a human observer. Independent of the specific nature of the data, the following fundamental problems can be identified: shape reconstruction from discrete samples, data analysis, and data compression. This thesis presents several novel solutions to these problems for surfaces (Part I) and volumes (Part II). For surfaces, we adopt the well-known triangle mesh representation and develop new algorithms for discrete curvature estimation,detection of feature lines, and line-art rendering (Chapter 3), for connectivity encoding (Chapter 4), and for topology preserving compression of 2D vector fields (Chapter 5). For volumes, that are often given as discrete samples, we base our approach for reconstruction and visualization on the use of new trivariate spline spaces on a certain tetrahedral partition. We study the properties of the new spline spaces (Chapter 7) and present efficient algorithms for reconstruction and visualization by iso-surface rendering for both, regularly (Chapter 8) and irregularly (Chapter 9) distributed data samples