Efficient Algorithm for B-Spline Curve Fitting by Using Feature Data Points

In order to obtain B-spline curve with fewer control points and higher precision, an efficient algorithm for B-spline curve fitting by using feature data points is proposed. During iterations of the proposed algorithm, the projected points, which are the nearest points on fitting curve to discrete data points, are calculated first, then maximal deviations between B-spline curve and connection lines of the data points are controlled, finally new feature points are determined and parameters of feature points are adjusted by parameters of projected points. According to these, B-spline curve with fewer control points and higher precision are obtained rapidly. Experimental result indicates that the proposed algorithm is feasible and effective.

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On the Modeling and Analysis of an Improved CNC Interpolation Algorithm

Materials Science Forum ◽

10.4028/www.scientific.net/msf.626-627.459 ◽

2009 ◽

Vol 626-627 ◽

pp. 459-464 ◽

Cited By ~ 1

Author(s):

Lei Luo ◽

L. Wang ◽

Jun Hu

Keyword(s):

Interpolation Method ◽

Control Points ◽

Interpolation Algorithm ◽

Modeling And Analysis ◽

B Spline ◽

Spline Curve ◽

Spline Surface ◽

Cnc Interpolation ◽

Data Points ◽

Back Calculation

An improved interpolation method is presented based on B-spline curve back calculation which regards data points as control points. First, a B-spline surface reconstruction is done, and a favorable condition for real-time interpolation can be provided for NC machining. Then, by prejudging the trajectory feedrate, the tangent vectors of spline curve junction can be calculated, which can be used to establish the spline curve equations based on time. At last, with the equations mentioned above, the trajectory and feedrate profile can be generated simultaneously by the improved interpolation algorithm. An error analysis is also discussed and the feasibility of the improved algorithm is verified by the simulation results.

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B-Spline Curve Fitting Based on Adaptive Particle Swarm Optimization Algorithm

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.20-23.1299 ◽

2010 ◽

Vol 20-23 ◽

pp. 1299-1304 ◽

Cited By ~ 5

Author(s):

Yue Hong Sun ◽

Zhao Ling Tao ◽

Jian Xiang Wei ◽

De Shen Xia

Keyword(s):

Genetic Algorithm ◽

Particle Swarm Optimization ◽

Curve Fitting ◽

Optimization Algorithm ◽

Particle Swarm Optimization Algorithm ◽

Particle Swarm ◽

Control Points ◽

Swarm Optimization ◽

B Spline ◽

Spline Curve

For fitting of ordered plane data by B-spline curve with the least squares, the genetic algorithm is generally used, accompanying the optimization on both the data parameter values and the knots to result in good robust, but easy to fall into local optimum, and without improved fitting precision by increasing the control points of the curve. So what we have done are: combining the particle swarm optimization algorithm into the B-spline curve fitting, taking full advantage of the distribution characteristic for the data, associating the data parameters with the knots, coding simultaneously the ordered data parameter and the number of the control points of the B-spline curve, proposing a new fitness function, dynamically adjusting the number of the control points for the B-spline curve. Experiments show the proposed particle swarm optimization method is able to adaptively reach the optimum curve much faster with much better accuracy accompanied less control points and less evolution times than the genetic algorithm.

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B-Spline Curve Approximation Using Feature Points

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.397-400.1093 ◽

2013 ◽

Vol 397-400 ◽

pp. 1093-1098

Author(s):

Xian Guo Cheng

Keyword(s):

Error Bound ◽

Least Squares Method ◽

Maximum Error ◽

Control Points ◽

Feature Points ◽

Shape Information ◽

B Spline ◽

Spline Curve ◽

Curve Approximation ◽

Curvature Information

This paper addresses the problem of B-spline curve approximating to a set of dense and ordered points. We choose local curvature maximum points based on the curvature information. The points and the two end points are viewed as initial feature points, constructing a B-spline curve approximating to the feature points by the least-squares method, refining the feature points according to the shape information of the curve, and updating the curve. This process is repeated until the maximum error is less than the given error bound. The approach adaptively placed fewer knots at flat regions but more at complex regions. Under the same error bound, experimental results showed that our approach can reduce more control points than Parks approach,Piegls approach and Lis approach. The numbers of control points of the curve is equal to that of the feature points after refinement.

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Trajectory Model of J-Type Groove and its Curve Fitting of B-Spline

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.58-60.1396 ◽

2011 ◽

Vol 58-60 ◽

pp. 1396-1401

Author(s):

Chang Liang Chen ◽

Sheng Sun Hu ◽

Dong Lin He

Keyword(s):

High Efficiency ◽

Control Points ◽

Mathematical Relationship ◽

Terminal Position ◽

C Language ◽

B Spline ◽

Spline Curve ◽

Accuracy And Precision ◽

Data Points ◽

Intersecting Curve

This paper describes the complexity and particularity of the trajectory of tube-sphere intersection and derives mathematical model of the track; according to characteristics of B-Spline curve, the track intersecting curve is partitioned ,and determine the mathematical relationship between the control points (deBoor point) and the data points of J-type groove; using cubic non-uniform irrational B-Spline theory, generate segments of approximation curves, then first and last point of each segment are constrained, so that combination curves can be seen as a whole curve with C1continuity; programming the trajectory of the preprocess module with C# language, it has advantages of approximate accuracy and high efficiency, thereby it can increase accuracy and precision of welding terminal position, so that the overall system has a metronomic characteristic.

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