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.

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.

Rational Bézier and B-Spline Ruled Surface Patches

1996 ◽  
Author(s):  
Q. J. Ge ◽  
Donglai Kang
Keyword(s):  
Ruled Surfaces ◽  
Dual Numbers ◽  
Line Segments ◽  
B Spline ◽  
Surface Patches ◽  
Spline Curves ◽  
Oriented Line ◽  
Euclidean Three Space ◽  
Three Space ◽  
Projective Algorithms

Abstract This paper presents a geometric method for constructing bounded rational Bézier and B-spline ruled surfaces directly from line-segments. Oriented line-segments in a Euclidean three-space are represented by vectors with four homogeneous components over the ring of dual numbers. Projective algorithms for rational Bézier and B-spline curves are dualized to yield algorithms for rational Bézier and B-spline ruled surfaces.

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.

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.

Stimulus-Change Effects of Forcing in Alternation Behavior

1966 ◽  
Vol 19 (2) ◽  
pp. 515-518 ◽  
Author(s):  
R. N. Hughes
Keyword(s):  
Free Choice ◽  
Stimulus Change ◽  
Lower Degree ◽  
Alternation Behavior ◽  
Subsequent Removal ◽  
Transparent Barrier ◽  
Initial Attraction ◽  
High Degree

To test the hypothesis that forcing left or right in a T-maze produces more alternation because of the stimulus-change resulting from subsequent removal of the arm barrier, rats were given free-choice trials and forced trials with a wooden barrier (favouring a high degree of change) and with a transparent barrier (favouring a lower degree of change). Although alternation was unaffected by the three conditions, the percentage of first investigatory responses directed toward the alternate arm on Trial 2 was highest following forcing with the wooden barrier. It was concluded that a stimulus-change explanation for the effects of forcing was acceptable if these first investigatory responses were acknowledged as indices of initial attraction of attention by an arm.

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