scholarly journals Hybrid Fireworks Algorithm for the Conversion of Planar Curve to B-Spline Curve

2020 ◽  
Vol 9 (4) ◽  
pp. 786-790
Keyword(s):  
Feature Points ◽  
Sampling Algorithm ◽  
Parametric Curve ◽  
B Spline ◽  
Point Sampling ◽  
Planar Curves ◽  
Fireworks Algorithm ◽  
Spline Curve ◽  
Spline Curves ◽  
User Intervention

Point sampling is essential for the conversion of planar curves to B-spline curves in geometric modelling applications. Conversion of parametric curve to B-Spline curve is often required as the latter provides the flexibility sought by the designer. Sampling methods generally ignores the feature points, which indicates the curve profile intuitively and they require user intervention. There is a need for generalized point sampling algorithm to capture the original shape of the planar curves. Auxiliary points are also needed which helps to define the curve and gives the better conversion into B-Spline curve. In this work, we developed a generalized point sampling algorithm based on fireworks algorithm for the conversion of parametric curve to B-spline curves. It is used curvature-based information to identify the feature points, while Fireworks algorithm is used for the identification of the auxiliary points. Developed algorithm was tested against curves with irregular shapes and cusps with no need of user intervention to tune the algorithm for conversion.

T-B Spline Curves with a Shape Parameter

2012 ◽  
Vol 241-244 ◽  
pp. 2144-2148
Author(s):  
Li Juan Chen ◽  
Ming Zhu Li
Keyword(s):  
Shape Parameter ◽  
Simple Structure ◽  
Control Points ◽  
Curve Segment ◽  
Closed Curves ◽  
B Spline ◽  
Spline Curve ◽  
Spline Curves

A T-B spline curves with a shape parameter λ is presented in this paper, which has simple structure and can be used to design curves. Analogous to the four B-spline curves, each curve segment is generated by five consecutive control points. For equidistant knots, the curves are C^2 continuous, but when the shape parameter λ equals to 0 , the curves are C^3 continuous. Moreover, this spline curve can be used to construct open and closed curves and can express ellipses conveniently.

Approximate Merging B-Spline Curves via Least Square Approximation

2014 ◽  
Vol 556-562 ◽  
pp. 3496-3500 ◽  
Author(s):  
Si Hui Shu ◽  
Zi Zhi Lin
Keyword(s):  
Approximation Error ◽  
Least Square ◽  
Error Tolerance ◽  
Knot Insertion ◽  
Least Squares Approximation ◽  
B Spline ◽  
Spline Curve ◽  
Spline Curves ◽  
Insertion Algorithm ◽  
Approximate Merging

An algorithm of B-spline curve approximate merging of two adjacent B-spline curves is presented in this paper. In this algorithm, the approximation error between two curves is computed using norm which is known as best least square approximation. We develop a method based on weighed and constrained least squares approximation, which adds a weight function in object function to reduce error of merging. The knot insertion algorithm is also developed to meet the error tolerance.

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.

G1/C1 Matching of Spline Curves

2010 ◽  
Vol 20-23 ◽  
pp. 202-208
Author(s):  
Xu Min Liu ◽  
Wei Xiang Xu ◽  
Jing Xu ◽  
Yong Guan
Keyword(s):  
Matching Condition ◽  
Basic Function ◽  
B Spline ◽  
Spline Curve ◽  
Spline Curves

The research is mainly made on the G1/C1 matching condition of spline curves. On the basis of the analysis on the basic function of T-B spline curves and the features of curve endpoints, we proposed the n+1 order T-B spline basic function and the solving method. The G1/C1 matching condition of C-B spline curves and T-B spline curves is put forward in this paper. On this condition, when matching C-B spline curves and T-B spline curves, the controlling vertexes can be added to make C-B spline curve tangent with the first and last edge by the first and last vertex of controlling polygon. Application instances were put up in this paper which illustrated that the G1/C1 matching between T-B spline curve and C-B spline curve using the feature of T-B spline curve which can represents semiellipse arc (semicircle arc) precisely can solve the problem that C-B spline curve cannot represents semiellipse arc (semicircle arc) precisely.

Internal Contour Extraction Algorithm Based on Quadratic B-spline for Images of Hot Long Shaft Forgings

2012 ◽  
Vol 472-475 ◽  
pp. 2274-2278
Author(s):  
Zhe Lin Li ◽  
Qin Xiang Xia ◽  
Yong Pan ◽  
Zhi Wu
Keyword(s):  
3D Reconstruction ◽  
Measurement Method ◽  
Hot Forging ◽  
Feature Points ◽  
Contour Extraction ◽  
Maximum Correlation ◽  
Internal Contour ◽  
B Spline ◽  
Spline Curve ◽  
Extraction Algorithm

It is necessary that the internal and external contours are extracted from the image of hot long shaft forgings, while the forgings are measured by CCD measurement method. In the light of the blurry internal edges in the image of the hot forging, a method based on quadratic B-spline curve is employed to extract feature points. In order to remove the pseudo features, a method based on maximum correlation is presented. In accordance with continuity of the internal contours, quadratic B-spline curve is used to fit the internal contours. Experiments show that this algorithm can effectively extract accurate internal contours for images of hot squaring and chamfering forgings. The extracted contours could provide basic data for subsequent 3D reconstruction and geometric measurements.

scholarly journals Interpolating Industrial Robot Orientation with Hermite Spline Curve Based on Logarithmic Quaternion

2019 ◽  
Vol 37 (6) ◽  
pp. 1165-1173
Author(s):  
Yasong Pu ◽  
Yaoyao Shi ◽  
Xiaojun Lin ◽  
Jian Guo
Keyword(s):  
Industrial Robot ◽  
B Spline ◽  
Spline Curve ◽  
Cartesian Space ◽  
Spline Curves ◽  
Detailed Method ◽  
Quaternion Space ◽  
Hermite Spline ◽  
Bézier Spline ◽  
Working Quality

Smooth orientation planning has an important influence on the working quality and service life as for industrial robot. Based on the logarithmic quaternion, a compact method to map a spline curve from Cartesian space to quaternion space is proposed, and consequently the multi-orientation smooth interpolation of quaternion is realized. Combining with the relevant example case, the detailed method and steps of multi-orientation interpolation are introduced for mapping Hermite spline curve into quaternion space, and the validity of the principle is verified by using the example case. The present multi-orientation smooth interpolation of quaternion has the characteristics of simple construction, easy implementation and intuitive understanding. The method is not only applicable to multi-orientation interpolation of quaternion with Hermite spline curve, but also can extended to the spline curves such as Bezier spline and B-spline.

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.

PIECEWISE QUARTIC TRIGONOMETRIC POLYNOMIAL B-SPLINE CURVES WITH TWO SHAPE PARAMETERS

2012 ◽  
Vol 12 (04) ◽  
pp. 1250028
Author(s):  
MRIDULA DUBE ◽  
REENU SHARMA
Keyword(s):  
Trigonometric Polynomial ◽  
Shape Parameters ◽  
B Spline ◽  
Spline Curve ◽  
Control Polygon ◽  
Spline Curves ◽  
Spline Surfaces ◽  
Polynomial Curve ◽  
Trigonometric Spline ◽  
The Given

Analogous to the quartic B-splines curve, a piecewise quartic trigonometric polynomial B-spline curve with two shape parameters is presented in this paper. Each curve segment is generated by three consecutive control points. The given curve posses many properties of the B-spline curve. These curves are closer to the control polygon than the different other curves considered in this paper, for different values of shape parameters for each curve. With the increase of the value of shape parameters, the curve approach to the control polygon. For nonuniform and uniform knot vector the given curves have C0, G3; C1, G3; C1, G7; and C3 continuity for different choice of shape parameters. A quartic trigonometric Bézier curves are also introduced as a special case of the given trigonometric spline curves. A comparison of quartic trigonometric polynomial curve is made with different other curves. In the last, quartic trigonometric spline surfaces with two shape parameters are constructed. They have most properties of the corresponding curves.

Research on Modification Algorithm of Cubic B-Spline Curve Interpolation Technology

2014 ◽  
Vol 687-691 ◽  
pp. 1596-1599 ◽  
Author(s):  
Wan Jun Zhang ◽  
Feng Zhang ◽  
Jun Hai Zhao
Keyword(s):  
High Speed ◽  
Recursive Formula ◽  
B Spline ◽  
Spline Curve ◽  
Nc Machine Tool ◽  
Mathematical Properties ◽  
Spline Curves ◽  
Nc Machine ◽  
Speed Change ◽  
Order Derivation

Based on cubic B-Spline curve mathematical properties, theoretical analysis the cubic B-Spline curve recursive formula of Taylor development of first-order, derivation of two order in the interpolation cycle under the condition of certain interpolation increment only and interpolation speed, change the interpolation increments can be amended cubic times B-Spline curves purpose The simulation results show that meet the high-speed and high-accuracy NC machine tool require-ments of CNC systems.

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