An error-bounded B-spline curve approximation scheme using dominant points for CNC interpolation of micro-line toolpath

2020 ◽  
Vol 64 ◽  
pp. 101930 ◽  
Author(s):  
Xu Du ◽  
Jie Huang ◽  
Li-Min Zhu ◽  
Han Ding
Keyword(s):  
Approximation Scheme ◽  
B Spline ◽  
Spline Curve ◽  
Dominant Points ◽  
Curve Approximation ◽  
Cnc Interpolation

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.

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 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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