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.

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.

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.

Low-Degree B-Spline Approximation of Procedurally Defined Curves

1999 ◽  
Author(s):  
Jun Qu ◽  
Radha Sarma
Keyword(s):  
Spline Approximation ◽  
Optimality Criteria ◽  
Least Square ◽  
B Spline ◽  
Spline Curves ◽  
Low Degree ◽  
Integration Techniques ◽  
Error Metric ◽  
High Level ◽  
The Ideal

Abstract This paper outlines an algorithm for approximating procedurally defined curves with low-degree, integral b-spline curves. The algorithm is based on minimizing a least square error metric between the ideal and approximated curves. Expressions for optimality criteria using the least square error metric are derived from a combination of exact b-spline integration and numerical integration techniques, thereby eliminating the need for sampling the ideal curve. A high-level iterative procedure that doubles knots at each step is proposed to ensure that the deviations between the ideal and approximated curves are within user specified limits. Issues of computational complexity are addressed and several examples are presented that illustrate the effectiveness of the algorithm.

Freeform Deformation Versus B-Spline Representation in Inverse Airfoil Design

2008 ◽  
Vol 8 (2) ◽  
Author(s):  
Eleftherios I. Amoiralis ◽  
Ioannis K. Nikolos
Keyword(s):  
Three Dimensional ◽  
Differential Evolution Algorithm ◽  
3D Animation ◽  
B Spline ◽  
Spline Curves ◽  
Design Variables ◽  
Evolution Algorithm ◽  
Freeform Deformation ◽  
Reference Pressure ◽  
Insight Into

Freeform deformation (FFD) is a well established technique for 3D animation applications, used to deform two—or three-dimensional geometrical entities. Over the past few years, FFD technique has aroused growing interest in several scientific communities. In this work, an extensive bibliographic survey of the FFD technique is initially introduced, in order to explore its capabilities in shape parametrization. Moreover, FFD technique is compared to the classical parametrization technique using B-spline curves, in the context of the airfoil design optimization problem, by performing inverse airfoil design tests, with a differential evolution algorithm to serve as the optimizer. The criterion of the comparison between the two techniques is the achieved accuracy in the approximation of the reference pressure distribution. Experiments are presented, comparing FFD to B-spline techniques under the same flow conditions, for various numbers of design variables. Sensitivity analysis is applied for providing further insight into the differences in the performance of the two techniques.

Freeform Deformation vs. B-Spline Representation in Inverse Airfoil Design

2006 ◽  
Author(s):  
Eleftherios I. Amoiralis ◽  
Ioannis K. Nikolos
Keyword(s):  
Differential Evolution ◽  
Optimization Algorithm ◽  
Flow Conditions ◽  
B Spline ◽  
De Algorithm ◽  
Spline Curves ◽  
Design Variables ◽  
Spline Representation ◽  
Freeform Deformation ◽  
Reference Pressure

In this work FFD technique is compared to the classical parameterization technique using B-Spline curves by performing inverse airfoil design tests, with a Differential Evolution (DE) algorithm to serve as the optimizer. The criteria of the comparison between the two techniques are the achieved accuracy in the approximation of the reference pressure distribution and the convergence behavior of the optimization algorithm. Experiments are presented, comparing FFD to B-Spline techniques under the same flow conditions, for various numbers of design variables.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document