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.

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.

Smooth B-Spline Curves Extension with Ordered Points Constraint

2011 ◽  
Vol 311-313 ◽  
pp. 1439-1445 ◽  
Author(s):  
Jin Xu
Keyword(s):  
Experimental Results ◽  
Maximum Deviation ◽  
Curve Segment ◽  
B Spline ◽  
Original Curve ◽  
Spline Curves ◽  
Minimum Number ◽  
The Given ◽  
Curve Extension ◽  
Extension Process

An algorithm for extending B-spline curves with a sequence of ordered points constraint is presented based on the curve unclamping algorithm. The ordered points are divided into two categories: interpolation points and approximation points. The number of interpolation points increases gradually during the curve extension process. The most important feature of this algorithm is the ability to optimize the knots of the extended curve segment according to the ordered points. Thus, with minimum number of interpolation points, the maximum deviation of the extended curve segment from the ordered points is less than the given tolerance. The extended curve segment connects to the original curve with maximum continuity intrinsically. Several experimental results have shown the validity and applicability of the proposed algorithm.

scholarly journals Conditions for regular $B$-spline curves and surfaces

1992 ◽  
Vol 26 (1) ◽  
pp. 177-190 ◽  
Author(s):  
N. Dyn ◽  
D. Levin ◽  
I. Yad-Shalom
Keyword(s):  
B Spline ◽  
Curves And Surfaces ◽  
Spline Curves

scholarly journals Interactive Modeling of 3D Tree with Ball B-Spline Curves

2009 ◽  
Vol 8 (2) ◽  
pp. 101-107 ◽  
Author(s):  
Zhongke Wu ◽  
Mingquan Zhou ◽  
Xingce Wang
Keyword(s):  
Iterated Function Systems ◽  
Interactive Methods ◽  
Tree Model ◽  
B Spline ◽  
Spline Curves ◽  
Novel Approach ◽  
Iterated Function ◽  
Tree Models ◽  
Generating Tree ◽  
L Systems

A novel approach to modeling realistic tree easily through interactive methods based on ball B-Spline Curves (BBSCs) and an efficient graph based data structure of tree model is proposed in the paper. As BBSCs are flexible for modifying, deforming and editing, these methods provide intuitive interaction and more freedom for users to model trees. If conjuncted with other methods like generating tree models through L-systems or iterated function systems (IFS), the models are more realistic and natural through modifying and editing. The method can be applied to the design of bonsai tree models.

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