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.

A New Method for Building B-Spline Curves and its Application to Geometry Design and Structured Grid Generation

2001 ◽  
Author(s):  
Horacio Flórez Guzmán
Keyword(s):  
Grid Generation ◽  
Iterative Refinement ◽  
Smooth Curves ◽  
B Spline ◽  
Linear System Of Equations ◽  
Structured Grid ◽  
Geometry Design ◽  
Spline Curves ◽  
Interpolation Problems ◽  
Structured Grid Generation

Abstract A new approach for building two-dimensional B-spline curves and its application to Computer-Aided Geometry Design is presented. The method constructs smooth curves based on a new knot sequence with an iterative refinement procedure suitable for the design of complex geometries. This knot sequence is applied to quadratic and cubic spline curves in two cases of interest, namely inverse design and interpolation problems. For the latter the linear system of equations is given, taking into account the appropriate end conditions. Several figures and examples from Computational Fluid Dynamics have been included to compare the proposed scheme with others. The results show that the method is a powerful and robust tool in curve design. Finally, an algorithm for solving the problem of interpolation along a B-spline curve is proposed and its potential application to 2-D structured grid generation is discussed.

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.

Collision-Free Path Planning by Using Nonperiodic B-Spline Curves

1993 ◽  
Vol 115 (3) ◽  
pp. 679-684 ◽  
Author(s):  
D. C. H. Yang
Keyword(s):  
Computational Complexity ◽  
Path Planning ◽  
Free Path ◽  
Computer Code ◽  
Control Points ◽  
B Spline ◽  
Spline Curves ◽  
End Effectors ◽  
Main Ideas ◽  
Fifth Order

This paper presents a method and an algorithm for the planning of collision-free paths through obstacles for robots end-effectors or autonomously guided vehicles. Fifth-order nonperiodic B-spline curves are chosen for this purpose. The main ideas are twofold: first, to avoid collision by moving around obstacles from the less blocking sides; and second, to assign two control points to all vertices of the control polygon. This method guarantees the generation of paths which have C3 continuity everywhere and satisfy the collision-free requirement. In addition, the obstacles can be of any shape, and the computational complexity and difficulty are relatively low. A computer code is developed for the implementation of this method. Case studies are given for illustration.

Collision-Free Path Planning by Using Non-Periodic B-Spline Curves

1990 ◽  
Author(s):  
D. C. H. Yang
Keyword(s):  
Computational Complexity ◽  
Path Planning ◽  
Computer Code ◽  
Control Points ◽  
A Algorithm ◽  
B Spline ◽  
Spline Curves ◽  
End Effectors ◽  
Main Ideas ◽  
Fifth Order

Abstract This paper presents a method and a algorithm for the planning of collision-free paths through obstacles for robots end-effectors or autonomously guided vehicles. Fifth-order non-periodic curves are chosen for this purpose. The main ideas are twofold: firstly, to avoid collision by moving around obstacles from the less blocking sides; and secondly, to assign two control points to all vertices of the control polygon. This method guarantees the generation of paths which have C3 continuity everywhere and satisfy the collision-free requirement. In addition, the obstacles can be of any shape, and the computational complexity and difficulty are relatively low. A computer code is developed for the implementation of this method. Cases study is given for illustration.

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.

Reconstruction of Sculptured Surface on Reverse Engineering

1997 ◽  
Author(s):  
Gou-Jen Wang ◽  
Chung-Chang Wang
Keyword(s):  
Data Structure ◽  
Reverse Engineering ◽  
Surface Reconstruction ◽  
Sparse Matrix ◽  
Computing Time ◽  
Cubic Spline ◽  
Surface Model ◽  
Two Dimensional ◽  
B Spline ◽  
Spline Curves

Abstract In this article, solutions for redundant measured data elimination and surface reconstruction on reverse engineering are presented. In redundant data elimination, we propose a simple algorithm that can efficiently discard those redundant measured points according to the required degree of accuracy. While in the surface reconstruction, we try first convert all eliminated column or row data into spline (B-Spline, Beizer and Cubic-Spline) curves. Methods for two dimensional spline (u, v directions) curve construction are described. Non-meshed two dimensional spline curves are then blended to a surface model by formatting data points into a sparse matrix data structure. Experimental results show that the proposed characteristic points extraction method can remarkably reduce the reconstruction time only on the cost of a little extracting time and minor modeling errors. Comparisons among B-spline, Beizer and Cubic-spline on data structure, computing time, and accuracy demonstrate that the B-spline algorithm is superior to other algorithms in surface reconstruction.

Collision-Free Trajectory Planning for a Two-Dimensional Mobile Robot by Optimizing Continuous Curves

1998 ◽  
Vol 10 (4) ◽  
pp. 364-369 ◽  
Author(s):  
Hiroaki Ozaki ◽  
◽  
Chang-jun Lin
Keyword(s):  
Mobile Robot ◽  
Trajectory Planning ◽  
Performance Index ◽  
Nonlinear Problems ◽  
Complex Method ◽  
Control Points ◽  
Two Dimensional ◽  
B Spline ◽  
Spline Curves ◽  
Continuous Curves

We propose a new algorithm for planning collision-free trajectories for a mobile robot. The trajectories of the mobile robot are described by uniform B-spline curves and these control points are optimized using the complex method. The complex method is very effective for this type of optimization of nonlinear problems because it does not require any computation of the gradient of performance index. B-spline curves have advantages for trajectory generation in that they guarantee the continuity of trajectories and the order of trajectories can be changed easily. Effectiveness is also confirmed by trajectory planning simulation of a two-dimensional mobile robot.

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

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