scholarly journals Firefly Algorithm for Explicit B-Spline Curve Fitting to Data Points

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Akemi Gálvez ◽  
Andrés Iglesias
Keyword(s):  
Firefly Algorithm ◽  
Optimization Problem ◽  
Nonlinear Least Squares ◽  
Well Being ◽  
B Spline ◽  
Spline Curve ◽  
Spline Fitting ◽  
Nature Inspired Algorithm ◽  
Data Points ◽  
High Degree

This paper introduces a new method to compute the approximating explicit B-spline curve to a given set of noisy data points. The proposed method computes all parameters of the B-spline fitting curve of a given order. This requires to solve a difficult continuous, multimodal, and multivariate nonlinear least-squares optimization problem. In our approach, this optimization problem is solved by applying the firefly algorithm, a powerful metaheuristic nature-inspired algorithm well suited for optimization. The method has been applied to three illustrative real-world engineering examples from different fields. Our experimental results show that the presented method performs very well, being able to fit the data points with a high degree of accuracy. Furthermore, our scheme outperforms some popular previous approaches in terms of different fitting error criteria.

Kinematic Optimization of Transplanting Mechanism with B-Spline Curve Gear for Rice Pot Seedling Based on Matlab

2014 ◽  
Vol 624 ◽  
pp. 181-186
Author(s):  
Yan Jun Zuo ◽  
Xiao Xu Yu ◽  
Wen Ge Li ◽  
Hui Xuan Zhu ◽  
Hai Peng Ji
Keyword(s):  
Structural Parameters ◽  
Planetary Gear ◽  
Gear Train ◽  
Virtual Experiment ◽  
B Spline ◽  
Spline Curve ◽  
Data Points ◽  
Pitch Curve ◽  
Machine Interaction ◽  
Kinematic Optimization

In order to realize the mechanized transplanting of rice pot seedling and ensure our food security, The pitch curve of non-circular gear is fitted based on cubic, non-uniform and rational B-spline curve. The planetary gear train transplanting mechanism has been invented for ride type, and kinematics mathematical model has been built through the kinematics analysis of transplanting mechanism. The computer aided analytical and optimized software has been developed by using software platform of Matlab. Through tuning the data points by man-machine interaction, pitch curve of non-circular gear is optimized and structural parameters are obtained, which can meet the demand of track and attitude in the transplanting process for rice pot seedling. In condition of the parameters, the correctness of the established model is verified by the virtual experiment by software of Adams.

On the Modeling and Analysis of an Improved CNC Interpolation Algorithm

2009 ◽  
Vol 626-627 ◽  
pp. 459-464 ◽  
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.

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

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.

scholarly journals Firefly Algorithm for Polynomial Bézier Surface Parameterization

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Akemi Gálvez ◽  
Andrés Iglesias
Keyword(s):  
Computer Animation ◽  
Computer Aided Design ◽  
Firefly Algorithm ◽  
Optimization Problems ◽  
Continuous Optimization ◽  
Well Being ◽  
Optimization Techniques ◽  
Surface Parameterization ◽  
Cad Cam ◽  
Data Points

A classical issue in many applied fields is to obtain an approximating surface to a given set of data points. This problem arises in Computer-Aided Design and Manufacturing (CAD/CAM), virtual reality, medical imaging, computer graphics, computer animation, and many others. Very often, the preferred approximating surface is polynomial, usually described in parametric form. This leads to the problem of determining suitable parametric values for the data points, the so-called surface parameterization. In real-world settings, data points are generally irregularly sampled and subjected to measurement noise, leading to a very difficult nonlinear continuous optimization problem, unsolvable with standard optimization techniques. This paper solves the parameterization problem for polynomial Bézier surfaces by applying the firefly algorithm, a powerful nature-inspired metaheuristic algorithm introduced recently to address difficult optimization problems. The method has been successfully applied to some illustrative examples of open and closed surfaces, including shapes with singularities. Our results show that the method performs very well, being able to yield the best approximating surface with a high degree of accuracy.

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

2013 ◽  
Vol 411-414 ◽  
pp. 523-526
Author(s):  
Xiao Bing Chen ◽  
Kun Yu
Keyword(s):  
Curve Fitting ◽  
Efficient Algorithm ◽  
Experimental Result ◽  
Control Points ◽  
Feature Points ◽  
B Spline ◽  
Spline Curve ◽  
Data Points ◽  
New Feature ◽  
Nearest 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.

A Novel Adaptive GA-based B-spline Curve Interpolation Method

2019 ◽  
Vol 13 (3) ◽  
pp. 289-304
Author(s):  
Maozhen Shao ◽  
Liangchen Hu ◽  
Huahao Shou ◽  
Jie Shen
Keyword(s):  
Genetic Algorithm ◽  
Traditional Method ◽  
Interpolation Method ◽  
Tangent Vector ◽  
Adaptive Genetic Algorithm ◽  
B Spline ◽  
Spline Curve ◽  
Curve Interpolation ◽  
Data Points ◽  
Data Point

Background: Curve interpolation is very important in engineering such as computer aided design, image analysis and NC machining. Many patents on curve interpolation have been invented. Objective: Since different knot vector configuration and data point parameterization can generate different shapes of an interpolated B-spline curve, the goal of this paper is to propose a novel adaptive genetic algorithm (GA) based interpolation method of B-spline curve. Method: Relying on geometric features owned by the data points and the idea of genetic algorithm which liberalizes the knots of B-spline curve and the data point parameters, a new interpolation method of B-spline curve is proposed. In addition, the constraint of a tangent vector is also added to ensure that the obtained B-spline curve can approximately satisfy the tangential constraint while ensuring strict interpolation. Results: Compared with the traditional method, this method realizes the adaptive knot vector selection and data point parameterization. Therefore, the interpolation result was better than the traditional method to some extent, and the obtained curve was more natural. Conclusion: The proposed method is effective for the curve reconstruction of any scanned data point set under tangent constraints. Meanwhile, this paper put forward a kind of tangent calculation method of discrete data points, where users can also set the tangent of each data point in order to get more perfect interpolation results.

B-Spline Curve Approximation with Nearly Arc-Length Parameterization

2014 ◽  
Vol 513-517 ◽  
pp. 3372-3376 ◽  
Author(s):  
Si Hui Shu ◽  
Zi Zhi Lin ◽  
Yun Ding
Keyword(s):  
Three Dimensional ◽  
Smooth Curve ◽  
Least Square ◽  
Arc Length ◽  
Key Factors ◽  
B Spline ◽  
Spline Curve ◽  
Curve Approximation ◽  
Fitting Algorithm ◽  
Data Points

An algorithm of B-spline curve approximation with the three-dimensional data is presented in this paper. In this algorithm, we will get a smooth curve which is nearly arc-length parameterization. The smoothness and uniform parameterization are key factors of the approximating curve, specifically in skinning surface and surface approximation. Firstly, the data points are fitted using local interpolation, this local fitting algorithm yields n Bezier segments, each segment having speed equal to 1 at their end and midpoints. Then segments are composed of a C1 continuous cubic B-spline curve which named controlling curve. But the controlling curves control points are redundancy, so we find another curve to approximate the controlling curve using least square approximation with smoothness

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