B-spline curve approximation to planar data points based on dominant points

2015 ◽  
pp. 225-228
Author(s):  
Z Lin ◽  
S Shu ◽  
Y Ding
Keyword(s):  
B Spline ◽  
Spline Curve ◽  
Dominant Points ◽  
Curve Approximation ◽  
Data Points

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

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.

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.

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.

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