B-Splines Geometric Modeling for Dynamic Analysis Behaviour in Offshore Systems

2006 ◽  
Author(s):  
Fa´bio G. T. de Menezes ◽  
Prota´sio Dutra Martins
Keyword(s):  
Geometric Modeling ◽  
Floating Body ◽  
Design Work ◽  
Oil Drilling ◽  
B Spline ◽  
B Splines ◽  
Hydrodynamic Behaviour ◽  
Spline Curves ◽  
Definition Of ◽  
Floating Systems

This work reports a study of B-Spline curves and surfaces applied to the geometric definition of hulls of ships and oil drilling and production platforms. The research aims at defining mathematically the floating body surface in suitable formats for the analysis of functional behaviour of the design object with sophisticated methods and tools. The WAMIT system was chosen as a reference in the research due to its reliability as a professional tool for hydrodynamic behaviour of floating systems in practice. The B-Spline model is input to the WAMIT system in the required format for the analysis of hull motion response to waves. The quality of the results obtained with B-Splines modeling was compared the ones obtained with flat panels. B-Splines have shown to be an effective approach, more efficient in computing terms when compared with the flat panels approach and suitable to optimization scripts. It revealed itself as a more adequate procedure to the design work as it simplifies the hull form mathematical definition of floating systems.

scholarly journals Hierarchical Genetic Algorithm for B-Spline Surface Approximation of Smooth Explicit Data

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
C. H. Garcia-Capulin ◽  
F. J. Cuevas ◽  
G. Trejo-Caballero ◽  
H. Rostro-Gonzalez
Keyword(s):  
Genetic Algorithm ◽  
Geometric Modeling ◽  
Data Set ◽  
Surface Approximation ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Surface Dimension ◽  
Hierarchical Genetic Algorithm

B-spline surface approximation has been widely used in many applications such as CAD, medical imaging, reverse engineering, and geometric modeling. Given a data set of measures, the surface approximation aims to find a surface that optimally fits the data set. One of the main problems associated with surface approximation by B-splines is the adequate selection of the number and location of the knots, as well as the solution of the system of equations generated by tensor product spline surfaces. In this work, we use a hierarchical genetic algorithm (HGA) to tackle the B-spline surface approximation of smooth explicit data. The proposed approach is based on a novel hierarchical gene structure for the chromosomal representation, which allows us to determine the number and location of the knots for each surface dimension and the B-spline coefficients simultaneously. The method is fully based on genetic algorithms and does not require subjective parameters like smooth factor or knot locations to perform the solution. In order to validate the efficacy of the proposed approach, simulation results from several tests on smooth surfaces and comparison with a successful method have been included.

Parametric Generation, Modeling, and Fairing of Simple Hull Lines With the Use of Nonuniform Rational B-Spline Surfaces

2008 ◽  
Vol 52 (01) ◽  
pp. 1-15
Author(s):  
F. L. Pérez ◽  
J. A. Clemente ◽  
J. A. Suárez ◽  
J. M. González
Keyword(s):  
Parametric Design ◽  
Design Method ◽  
Surface Modeling ◽  
Affine Transformations ◽  
Parametric Generation ◽  
B Spline ◽  
Ship Hulls ◽  
Spline Curves ◽  
Definition Of ◽  
Fairing Process

This paper deals with the use of a simple parametric design method applied to simple hull lines, such as sailing ship hulls and round bilge hulls. The described method allows the generation of hull lines that meet hydrodynamic coefficients imposed by the designer, obtaining more flexibility than with normal affine transformations of a parent hull. First, a wire model of the ship stations is made with the use of explicit curves. The method is completed with an automatic surface modeling of the previ¬ously generated offsets. The construction of spline curves and their application in the definition of ship lines are reviewed. Approximation of spline curves fitting the data on the stations is made, with special emphasis on the choice of parametrization, which is relevant to increasing the accuracy of the splines. B-spline surface modeling of the hull and the fairing process adapted to maintain certain ship characteristics are described. Some examples of the generation, lofting, and fairing process are pre¬sented.

On the Literature of B-Spline Interpolation Functions

2009 ◽  
pp. 214-222
Author(s):  
Carlo Ciulla
Keyword(s):  
Scientific Community ◽  
Polynomial Interpolation ◽  
Spline Interpolation ◽  
Spline Functions ◽  
Great Effort ◽  
Formal Definition ◽  
B Spline ◽  
B Splines ◽  
Scientific Disciplines ◽  
Definition Of

This chapter reviews the extensive and comprehensive literature on B-Splines. In the forthcoming text emphasis is given to hierarchy and formal definition of polynomial interpolation with specific focus to the subclass of functions that are called B-Splines. Also, the literature is reviewed with emphasis on methodologies and applications of B-Splines within a wide array of scientific disciplines. The review is conducted with the intent to inform the reader and also to acknowledge the merit of the scientific community for the great effort devoted to B-Splines. The chapter concludes emphasizing on the proposition that the unifying theory presented throughout this book has for what concerns two specific cases of B-Spline functions: univariate quadratic and cubic models.

Automatic Unstructured Mesh Generation Around Two-Dimensional Domains Described by B-Spline Curves

2001 ◽  
Author(s):  
Horacio Flórez Guzmán ◽  
Raúl Manzanilla Morillo
Keyword(s):  
Grid Generation ◽  
Computer Code ◽  
Two Dimensional ◽  
B Spline ◽  
Piecewise Polynomials ◽  
Spline Curves ◽  
Interpolation Problems ◽  
Interpolation Procedure ◽  
Definition Of ◽  
Unstructured Mesh Generation

Abstract A computer code for the generation of unstructured two-dimensional triangular meshes around arbitrary complex geometries has been developed. The code is based on Delaunay triangulation with an automatic point insertion scheme and a smoothing technique. The geometrical definition of the domain to be meshed is prescribed by means of B-spline curves obtained from two approaches of interest in Computer-Aided Geometric Design named inverse design and interpolation problems. The presented scheme is based on an interpolation procedure along a B-spline curve proposed by the author in a recent paper. This technique prevents that the resulting grid may overlap convex portions of the boundaries. The main goal is to study the possibility of extend the methodology of unstructured grid generation beginning with boundaries described by polylines to other in which they are prescribed by piecewise polynomials curves capable to drive more realistic problems. Several figures and examples from Computational Fluid Dynamics have been included to show the various steps of the algorithm. The results show that the code is able to solve the problem of automatic grid generation in a robust manner opening new perspectives for the development of a black-box grid generator.

scholarly journals Geometric Modeling Using New Cubic Trigonometric B-Spline Functions with Shape Parameter

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2102
Author(s):  
Abdul Majeed ◽  
Muhammad Abbas ◽  
Faiza Qayyum ◽  
Kenjiro T. Miura ◽  
Md Yushalify Misro ◽  
...  
Keyword(s):  
Geometric Modeling ◽  
Shape Parameter ◽  
3D Models ◽  
Basis Functions ◽  
Shape Parameters ◽  
B Spline ◽  
Spline Curves ◽  
Spline Basis ◽  
Cubic Polynomial ◽  
2D And 3D

Trigonometric B-spline curves with shape parameters are equally important and useful for modeling in Computer-Aided Geometric Design (CAGD) like classical B-spline curves. This paper introduces the cubic polynomial and rational cubic B-spline curves using new cubic basis functions with shape parameter ξ∈[0,4]. All geometric characteristics of the proposed Trigonometric B-spline curves are similar to the classical B-spline, but the shape-adjustable is additional quality that the classical B-spline curves does not hold. The properties of these bases are similar to classical B-spline basis and have been delineated. Furthermore, uniform and non-uniform rational B-spline basis are also presented. C3 and C5 continuities for trigonometric B-spline basis and C3 continuities for rational basis are derived. In order to legitimize our proposed scheme for both basis, floating and periodic curves are constructed. 2D and 3D models are also constructed using proposed curves.

BEZIER AND B-SPLINE CURVES WITH KNOTS IN THE COMPLEX PLANE

Fractals ◽  
2011 ◽  
Vol 19 (01) ◽  
pp. 67-86 ◽  
Author(s):  
KONSTANTINOS I. TSIANOS ◽  
RON GOLDMAN
Keyword(s):  
Complex Domain ◽  
Polynomial Algorithms ◽  
Control Points ◽  
Knot Insertion ◽  
Real Numbers ◽  
Koch Curve ◽  
Natural Manner ◽  
B Spline ◽  
B Splines ◽  
Spline Curves

We extend some well known algorithms for planar Bezier and B-spline curves, including the de Casteljau subdivision algorithm for Bezier curves and several standard knot insertion procedures (Boehm's algorithm, the Oslo algorithm, and Schaefer's algorithm) for B-splines, from the real numbers to the complex domain. We then show how to apply these polynomial and piecewise polynomial algorithms in a complex variable to generate many well known fractal shapes such as the Sierpinski gasket, the Koch curve, and the C-curve. Thus these fractals also have Bezier and B-spline representations, albeit in the complex domain. These representations allow us to change the shape of a fractal in a natural manner by adjusting their complex Bezier and B-spline control points. We also construct natural parameterizations for these fractal shapes from their Bezier and B-spline representations.

Parametric Design and Optimization of Sailing Yachts

1999 ◽  
Author(s):  
Stefan Harries ◽  
Claus Abt
Keyword(s):  
Geometric Modeling ◽  
Parametric Design ◽  
Generation Process ◽  
B Spline ◽  
Design And Optimization ◽  
Spline Curves ◽  
Design Variables ◽  
Hull Forms ◽  
High Level ◽  
Important Form

A new and flexible method for the geometric modeling of ship hull forms is presented. The underlying methodology is the parametric design of B-spline curves and surfaces. Important form parameters like displacement, center of buoyancy, waterplane area, center of flotation etc. are utilized as high-level descriptors of the intended shapes. Instead of interactively manipulating B-spline vertices, the generation process is viewed as a constrained optimization problem where fairness measures are applied as objective functions, vertices are treated as design variables and form parameters are preserved as equality constraints - making the approach a novelty in B­spline modeling. The new design methodology is discussed and mathematical principles are outlined. Examples are given to demonstrate the applicability of the parametric approach. They include the design of a 33ft IMS yacht with focus on the bare hull without rudder and keel.

Approximation of B-Spline Geometries With Lower Degree Representations

1990 ◽  
Vol 112 (3) ◽  
pp. 192-198
Author(s):  
N. M. Patrikalakis ◽  
L. Bardis ◽  
G. A. Kriezis
Keyword(s):  
Geometric Modeling ◽  
Lower Degree ◽  
Critical Feature ◽  
B Spline ◽  
Surface Patches ◽  
Spline Curves ◽  
Modeling Systems ◽  
High Degree ◽  
Reliable Methods ◽  
Prespecified Accuracy

Exchange of data between geometric modeling systems of different inherent capabilities frequently requires approximate conversion of high degree, piecewise, polynomial curves and surface patches to lower degree representations. The objective of this work is to provide reliable methods for the approximation of high-order B-spline curves and surface patches by low-order B-spline representations. Our method guarantees a prespecified accuracy at all isoparametric points of the curve and patch, a critical feature for accurate exchange of data.

A Multiresolution Fairing Approach for NURBS Curves

2012 ◽  
Vol 215-216 ◽  
pp. 1205-1208
Author(s):  
Ai Min Li ◽  
Hai Bo Tian
Keyword(s):  
Geometric Modeling ◽  
Important Influence ◽  
Nurbs Curve ◽  
B Spline ◽  
Nurbs Curves ◽  
Spline Curves ◽  
Spline Wavelets ◽  
Curve Fairing

Curve fairing has an important influence on curve editing and geometric modeling. Though there has been several different kinds of fairing methods, Multiresolution curve fairing has higher efficiency and simpler algorithms. Different from existing multiresolution curve fairing, a new multiresolution approach is presented based on non-uniform semiorthogonal B-spline wavelets, which can be applied for NURBS curve fairing. It has no restriction to B-spline curves’ knot sequence. This method effectively overcomes the limit of uniform or quasi-uniform B-spline wavelets for fairing. A detailed example is given to show the effectiveness of this multiresolution fairing method.

scholarly journals Application of Cubic B-Spline Curves for Hull Meshing

2021 ◽  
Vol 14 (28) ◽  
pp. 53-62
Author(s):  
César Augusto Salhua Moreno
Keyword(s):  
Quality Evaluation ◽  
Divergence Theorem ◽  
Mesh Quality ◽  
B Spline ◽  
Spline Curves ◽  
Definition Of ◽  
Discretization Procedure

This paper describes the development of a regular hull meshing code using cubic B-Spline curves. The discretization procedure begins by the definition of B-Spline curves over stations, bow and stern contours of the hull plan lines. Thus, new knots are created applying an equal spaced subdivision procedure on defined B-spline curves. Then, over these equal transversal space knots, longitudinal B-spline curves are defined and subdivided into equally spaced knots, too. Subsequently, new transversal knots are created using the longitudinal equally spaced knots. Finally, the hull mesh is composed by quadrilateral panels formed by these new transversal and longitudinal knots. This procedure is applied in the submerged Wigley hulls Series 60 Cb=0.60. Their mesh volumes are calculated using the divergence theorem, for mesh quality evaluation.

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