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

Superficies de Coons en el diseño geométrico

Este tipo de superficie se basa en la labor pionera de Steven Anson Coons, en la década de los 60’ del siglo pasado. Comenzamos con la superficie lineal de Coons, que es una generalización de las superficies lofted. Este tipo de superficie, también conocida como parche de Coons, se define por cuatro curvas frontera, donde ninguno de ellas es una línea recta. Naturalmente, las curvas frontera se cortan en las esquinas, por lo que estos puntos son conocidos implícitamente. La visualización de los resultados se realiza mediante el software científico Mathematica, en el cual se implementa una serie de comandos para su manipulación

NURBS enhanced virtual element methods for the spatial discretization of the multigroup neutron diffusion equation on curvilinear polygonal meshes

The Continuous Galerkin Virtual Element Method (CG-VEM) is a recent innovation in spatial discretization methods that can solve partial differential equations (PDEs) using polygonal (2D) and polyhedral (3D) meshes. Recently, a new formulation of CG-VEM was introduced which can construct VEM spaces on polygons with curvilinear edges. This paper presents the application of the curved VEM to the multigroup neutron diffusion equation and demonstrates its benefits over the conventional straight-sided VEM for a number of benchmark verification test cases with curvilinear domains. These domains were constructed using a topological data-structure developed as part of this paper, based on the doubly-connected edge list, with curves and surfaces both represented using non-uniform rational B-splines (NURBS). This data-structure is used both to specify the geometry of the reactor and to represent the curvilinear polygonal mesh. We also present two separate methods of performing integrations on curvilinear polygons, one for homogeneous functions and one for non-homogeneous functions

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

New strategies for curve and arbitrary-topology surface constructions for design

This dissertation presents some novel constructions for curves and surfaces with arbitrary topology in the context of geometric modeling. In particular, it deals mainly with three intimately connected topics that are of interest in both theoretical and applied research: subdivision surfaces, non-uniform local interpolation (in both univariate and bivariate cases), and spaces of generalized splines. Specifically, we describe a strategy for the integration of subdivision surfaces in computer-aided design systems and provide examples to show the effectiveness of its implementation. Moreover, we present a construction of locally supported, non-uniform, piecewise polynomial univariate interpolants of minimum degree with respect to other prescribed design parameters (such as support width, order of continuity and order of approximation). Still in the setting of non-uniform local interpolation, but in the case of surfaces, we devise a novel parameterization strategy that, together with a suitable patching technique, allows us to define composite surfaces that interpolate given arbitrary-topology meshes or curve networks and satisfy both requirements of regularity and aesthetic shape quality usually needed in the CAD modeling framework. Finally, in the context of generalized splines, we propose an approach for the construction of the optimal normalized totally positive (B-spline) basis, acknowledged as the best basis of representation for design purposes, as well as a numerical procedure for checking the existence of such a basis in a given generalized spline space. All the constructions presented here have been devised keeping in mind also the importance of application and implementation, and of the related requirements that numerical procedures must satisfy, in particular in the CAD context

Inferring Geodesic Cerebrovascular Graphs: Image Processing, Topological Alignment and Biomarkers Extraction

A vectorial representation of the vascular network that embodies quantitative features - location, direction, scale, and bifurcations - has many potential neuro-vascular applications. Patient-specific models support computer-assisted surgical procedures in neurovascular interventions, while analyses on multiple subjects are essential for group-level studies on which clinical prediction and therapeutic inference ultimately depend. This first motivated the development of a variety of methods to segment the cerebrovascular system. Nonetheless, a number of limitations, ranging from data-driven inhomogeneities, the anatomical intra- and inter-subject variability, the lack of exhaustive ground-truth, the need for operator-dependent processing pipelines, and the highly non-linear vascular domain, still make the automatic inference of the cerebrovascular topology an open problem. In this thesis, brain vessels’ topology is inferred by focusing on their connectedness. With a novel framework, the brain vasculature is recovered from 3D angiographies by solving a connectivity-optimised anisotropic level-set over a voxel-wise tensor field representing the orientation of the underlying vasculature. Assuming vessels joining by minimal paths, a connectivity paradigm is formulated to automatically determine the vascular topology as an over-connected geodesic graph. Ultimately, deep-brain vascular structures are extracted with geodesic minimum spanning trees. The inferred topologies are then aligned with similar ones for labelling and propagating information over a non-linear vectorial domain, where the branching pattern of a set of vessels transcends a subject-specific quantized grid. Using a multi-source embedding of a vascular graph, the pairwise registration of topologies is performed with the state-of-the-art graph matching techniques employed in computer vision. Functional biomarkers are determined over the neurovascular graphs with two complementary approaches. Efficient approximations of blood flow and pressure drop account for autoregulation and compensation mechanisms in the whole network in presence of perturbations, using lumped-parameters analog-equivalents from clinical angiographies. Also, a localised NURBS-based parametrisation of bifurcations is introduced to model fluid-solid interactions by means of hemodynamic simulations using an isogeometric analysis framework, where both geometry and solution profile at the interface share the same homogeneous domain. Experimental results on synthetic and clinical angiographies validated the proposed formulations. Perspectives and future works are discussed for the group-wise alignment of cerebrovascular topologies over a population, towards defining cerebrovascular atlases, and for further topological optimisation strategies and risk prediction models for therapeutic inference. Most of the algorithms presented in this work are available as part of the open-source package VTrails

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

Computer Aided Grid Interface: An Interactive CFD Pre-Processor

NASA maintains an applications oriented computational fluid dynamics (CFD) efforts complementary to and in support of the aerodynamic-propulsion design and test activities. This is especially true at NASA/MSFC where the goal is to advance and optimize present and future liquid-fueled rocket engines. Numerical grid generation plays a significant role in the fluid flow simulations utilizing CFD. An overall goal of the current project was to develop a geometry-grid generation tool that will help engineers, scientists and CFD practitioners to analyze design problems involving complex geometries in a timely fashion. This goal is accomplished by developing the Computer Aided Grid Interface system (CAGI). The CAGI system is developed by integrating CAD/CAM (Computer Aided Design/Computer Aided Manufacturing) geometric system output and / or Initial Graphics Exchange Specification (IGES) files (including all the NASA-IGES entities), geometry manipulations and generations associated with grid constructions, and robust grid generation methodologies. This report describes the development process of the CAGI system

Aeroelastic Modeling, Loads Analysis and Structural Design of a Fighter Aircraft

The DLR Future Fighter Demonstrator (FFD) is a highly agile, two-seated aircraft with twin-engines with reheat and a design flight speed extending into the supersonic regime up to Ma=2.0. Based on a given conceptual design, this work focuses on the aeroelastic modeling, including structures, masses and aerodynamics. With these models, a comprehensive loads analysis with 688 maneuver load cases, covering the whole flight envelope, is performed. Based on the resulting section and nodal loads, the structural model is subject to a structural optimization resulting in a preliminary, total primary structural mass of ~3.3t. To confirm the results, the aerodynamic panel methods (VLM and ZONA51) are compared to higher fidelity results obtained from CFD, showing a moderate agreement in terms of surface pressure distribution

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