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.

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 Dynamic Centripetal Parameterization Method for B-Spline Curve Interpolation

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 589-598
Author(s):  
Cengiz Balta ◽  
Sitki Ozturk ◽  
Melih Kuncan ◽  
Ismet Kandilli
Keyword(s):  
B Spline ◽  
Spline Curve ◽  
Parameterization Method ◽  
Curve Interpolation

scholarly journals Parameterization Method on B-Spline Curve

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
H. Haron ◽  
A. Rehman ◽  
D. I. S. Adi ◽  
S. P. Lim ◽  
T. Saba
Keyword(s):  
Computer Model ◽  
Basis Function ◽  
Real Object ◽  
Reconstruction Process ◽  
B Spline ◽  
Parameterization Method ◽  
Spline Basis ◽  
Data Points ◽  
Data Point ◽  
2D And 3D

The use of computer graphics in many areas allows a real object to be transformed into a three-dimensional computer model (3D) by developing tools to improve the visualization of two-dimensional (2D) and 3D data from series of data point. The tools involved the representation of 2D and 3D primitive entities and parameterization method using B-spline interpolation. However, there is no parameterization method which can handle all types of data points such as collinear data points and large distance of two consecutive data points. Therefore, this paper presents a new parameterization method that is able to solve those drawbacks by visualizing the 2D primitive entity of scanned data point of a real object and construct 3D computer model. The new method has improved a hybrid method by introducing exponential parameterization method in the beginning of the reconstruction process, followed by computing B-spline basis function to find maximum value of the function. The improvement includes solving a linear system of the B-spline basis function using numerical method. Improper selection of the parameterization method may lead to the singularity matrix of the system linear equations. The experimental result on different datasets show that the proposed method performs better in constructing the collinear and two consecutive data points compared to few parameterization methods.

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.

Point-tangent/point-normal B-spline curve interpolation by geometric algorithms

2009 ◽  
Vol 41 (6) ◽  
pp. 412-422 ◽  
Author(s):  
Shu-ichi Gofuku ◽  
Shigefumi Tamura ◽  
Takashi Maekawa
Keyword(s):  
Geometric Algorithms ◽  
Tangent Point ◽  
B Spline ◽  
Spline Curve ◽  
Curve Interpolation

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.

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