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.

Parametric Generation of Planing Hulls with NURBS Surfaces

2013 ◽  
Vol 57 (04) ◽  
pp. 241-261
Author(s):  
Francisco L. Perez-Arribas ◽  
Erno Peter-Cosma
Keyword(s):  
Maximum Deviation ◽  
Geometric Features ◽  
Surface Geometry ◽  
Orthogonal Projections ◽  
Parametric Generation ◽  
B Spline ◽  
Spline Curves ◽  
Hull Design ◽  
Data Points ◽  
Control Curves

This article presents a mathematical method for producing hard-chine ship hulls based on a set of numerical parameters that are directly related to the geometric features of the hull and uniquely define a hull form for this type of ship. The term planing hull is used generically to describe the majority of hard-chine boats being built today. This article is focused on unstepped, single-chine hulls. B-spline curves and surfaces were combined with constraints on the significant ship curves to produce the final hull design. The hard-chine hull geometry was modeled by decomposing the surface geometry into boundary curves, which were defined by design constraints or parameters. In planing hull design, these control curves are the center, chine, and sheer lines as well as their geometric features including position, slope, and, in the case of the chine, enclosed area and centroid. These geometric parameters have physical, hydrodynamic, and stability implications from the design point of view. The proposed method uses two-dimensional orthogonal projections of the control curves and then produces three-dimensional (3-D) definitions using B-spline fitting of the 3-D data points. The fitting considers maximum deviation from the curve to the data points and is based on an original selection of the parameterization. A net of B-spline curves (stations) is then created to match the previously defined 3-D boundaries. A final set of lofting surfaces of the previous B-spline curves produces the hull surface.

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 Inverse-Problem-Based Accuracy Control for Arbitrary-Resolution Fairing of Quasiuniform Cubic B-Spline Curves

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Xiaogang Ji ◽  
Jie Xue ◽  
Yan Yang ◽  
Xueming He
Keyword(s):  
Inverse Problem ◽  
Approximation Algorithm ◽  
Linear Hypothesis ◽  
Accuracy Control ◽  
B Spline ◽  
Accuracy Requirement ◽  
Dyadic Wavelet ◽  
Spline Curves ◽  
Minimum Number ◽  
Fairing Process

In the process of curves and surfaces fairing with multiresolution analysis, fairing accuracy will be determined by final fairing scale. On the basis of Dyadic wavelet fairing algorithm (DWFA), arbitrary resolution wavelet fairing algorithm (ARWFA), and corresponding software, accuracy control of multiresolution fairing was studied for the uncertainty of fairing scale. Firstly, using the idea of inverse problem for reference, linear hypothesis was adopted to predict the corresponding wavelet scale for any given fairing error. Although linear hypothesis has error, it can be eliminated by multiple iterations. So faired curves can be determined by a minimum number of control vertexes and have the best faring effect under the requirement of accuracy. Secondly, in consideration of efficiency loss caused by iterative algorithm, inverse calculation of fairing scale was presented based on the least squares fitting. With the increase of order of curves, inverse calculation accuracy becomes higher and higher. Verification results show that inverse calculation scale can meet the accuracy requirement when fitting curve is sextic. In the whole fairing process, because there is no approximation algorithm such as interpolation and approximation, faired curves can be reconstructed again exactly. This algorithm meets the idea and essence of wavelet analysis well.

Blind digital watermarking of rational Bézier and B-spline curves and surfaces with robustness against affine transformations and Möbius reparameterization

2011 ◽  
Vol 43 (6) ◽  
pp. 629-638 ◽  
Author(s):  
Song-Hwa Kwon ◽  
Tae-wan Kim ◽  
Hyeong In Choi ◽  
Hwan Pyo Moon ◽  
Sung Ha Park ◽  
...  
Keyword(s):  
Digital Watermarking ◽  
Affine Transformations ◽  
B Spline ◽  
Curves And Surfaces ◽  
Spline Curves

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.

scholarly journals Sculptured Surface Design and Implementation by Lofting Design Method Using Cross-sectional B-Spline Curves

2019 ◽  
Vol 14 (2) ◽  
pp. 92-82
Author(s):  
Wisam Kadhum Hamdan ◽  
Mustafa Mohammed Abdulrazaq
Keyword(s):  
Design Method ◽  
Machining Process ◽  
Free Form ◽  
Cnc Machine ◽  
Cross Sectional ◽  
Surface Design ◽  
B Spline ◽  
Spline Curves ◽  
Interior Data ◽  
Scope Of Application

This research presents a particular designing strategy for a free form of surfaces, constructed by the lofting design method. The regarded surfaces were created by sliding a B-spline curves (profile curves), in addition to describing an automatic procedure for selective identification of sampling points in reverse engineering applications using Coordinate Measurement Machine. Two models have been implemented from (Ureol material) to represent the different cases of B-spline types to clarify its scope of application. The interior data of the desired surfaces was designed by MATLAB software, which then were transformed to UG-NX9 software for connecting the sections that were designed in MATLAB program and obtaining G-code programs for the models In addition, a virtual machining process was simulated to show the machining pitfalls, using VERICUT software.  The samples were machined using 3-axis vertical CNC machine (Isel) type.  Finally, the samples were measured using Faro arm (CMM inspection) and it was found that the average of errors was equal to (0.0589 mm) for the cross-sectional uniform B-spline model, and (0.1337 mm) for the lofted non-uniform B-spline model. It can be concluded that the whole steps task which built in the present research can be programmed in a single block of the part program where any surface at minimum designing time can be created from it.

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.

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.

Customized Saddle Design Method Based on Cubic B-Spline Surface

2014 ◽  
Vol 945-949 ◽  
pp. 151-155
Author(s):  
Qi Jun Yang ◽  
Shu Xian Zheng ◽  
Jia Li
Keyword(s):  
Parametric Design ◽  
Design Method ◽  
Control Point ◽  
Control Points ◽  
Outer Contour ◽  
Element Analysis ◽  
B Spline ◽  
Saddle Surface ◽  
Contour Control ◽  
Parameterized Model

Aimed to the comfort demand of people for the high-end bicycle saddle, a parametric design method of customized saddle is presented based on the Cubic B-spline theory. According to the relationship between Cubic B-spline control points and the saddle shape, the outer contour control points is determined firstly, then all control point positions on the saddle surface are calculated by these outer contour control points, and the parameterized model of the customized saddle is built and its overall surface is designed. On this basis, a more reasonable saddle surface is obtained by adjusting the control points. Finite element analysis (FEA) is carried out on customized saddle and common bicycle saddle respectively. Their stress distributions comparison result shows that customized saddle can minimize pressure to the anterior perineum and ischial tuberosity effectively. These verify that the saddle customized design method is feasible.

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