Adaptive knot placement using a GMM-based continuous optimization algorithm in B-spline curve approximation

2011 ◽  
Vol 43 (6) ◽  
pp. 598-604 ◽  
Author(s):  
Xiuyang Zhao ◽  
Caiming Zhang ◽  
Bo Yang ◽  
Pingping Li
Keyword(s):  
Optimization Algorithm ◽  
Continuous Optimization ◽  
B Spline ◽  
Spline Curve ◽  
Curve Approximation ◽  
Continuous Optimization Algorithm

Fast converging elitist genetic algorithm for knot adjustment in B-spline curve approximation

2019 ◽  
Vol 13 (4) ◽  
pp. 317-328
Author(s):  
Johannes Bureick ◽  
Hamza Alkhatib ◽  
Ingo Neumann
Keyword(s):  
Genetic Algorithm ◽  
Real Data ◽  
Adjustment Problem ◽  
Data Set ◽  
New Approach ◽  
B Spline ◽  
Spline Curve ◽  
Curve Approximation ◽  
Data Gaps

Abstract B-spline curve approximation is a crucial task in many applications and disciplines. The most challenging part of B-spline curve approximation is the determination of a suitable knot vector. The finding of a solution for this multimodal and multivariate continuous nonlinear optimization problem, known as knot adjustment problem, gets even more complicated when data gaps occur. We present a new approach in this paper called an elitist genetic algorithm, which solves the knot adjustment problem in a faster and more precise manner than existing approaches. We demonstrate the performance of our elitist genetic algorithm by applying it to two challenging test functions and a real data set. We demonstrate that our algorithm is more efficient and robust against data gaps than existing approaches.

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

2010 ◽  
Vol 20-23 ◽  
pp. 1299-1304 ◽  
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.

scholarly journals Control point adjustment for B-spline curve approximation

2004 ◽  
Vol 36 (7) ◽  
pp. 639-652 ◽  
Author(s):  
Huaiping Yang ◽  
Wenping Wang ◽  
Jiaguang Sun
Keyword(s):  
Control Point ◽  
B Spline ◽  
Spline Curve ◽  
Curve Approximation

B-Spline Curve Approximation Using Feature Points

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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