Efficient Degree Elevation and Knot Insertion for B-spline Curves using Derivatives

2004 ◽  
Vol 1 (1-4) ◽  
pp. 719-725
Author(s):  
Qi-Xing Huang ◽  
Shi-Min Hu ◽  
Ralph R Martin
Keyword(s):  
Knot Insertion ◽  
Degree Elevation ◽  
B Spline ◽  
Spline Curves

Fast degree elevation and knot insertion for B-spline curves

2005 ◽  
Vol 22 (2) ◽  
pp. 183-197 ◽  
Author(s):  
Qi-Xing Huang ◽  
Shi-Min Hu ◽  
Ralph R. Martin
Keyword(s):  
Knot Insertion ◽  
Degree Elevation ◽  
B Spline ◽  
Spline Curves

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.

Degree elevation of B-spline curves

1984 ◽  
Vol 1 (2) ◽  
pp. 193-198 ◽  
Author(s):  
Hartmut Prautzsch
Keyword(s):  
Degree Elevation ◽  
B Spline ◽  
Spline Curves

BEZIER AND B-SPLINE CURVES WITH KNOTS IN THE COMPLEX PLANE

Fractals ◽  
2011 ◽  
Vol 19 (01) ◽  
pp. 67-86 ◽  
Author(s):  
KONSTANTINOS I. TSIANOS ◽  
RON GOLDMAN
Keyword(s):  
Complex Domain ◽  
Polynomial Algorithms ◽  
Control Points ◽  
Knot Insertion ◽  
Real Numbers ◽  
Koch Curve ◽  
Natural Manner ◽  
B Spline ◽  
B Splines ◽  
Spline Curves

We extend some well known algorithms for planar Bezier and B-spline curves, including the de Casteljau subdivision algorithm for Bezier curves and several standard knot insertion procedures (Boehm's algorithm, the Oslo algorithm, and Schaefer's algorithm) for B-splines, from the real numbers to the complex domain. We then show how to apply these polynomial and piecewise polynomial algorithms in a complex variable to generate many well known fractal shapes such as the Sierpinski gasket, the Koch curve, and the C-curve. Thus these fractals also have Bezier and B-spline representations, albeit in the complex domain. These representations allow us to change the shape of a fractal in a natural manner by adjusting their complex Bezier and B-spline control points. We also construct natural parameterizations for these fractal shapes from their Bezier and B-spline representations.

Another knot insertion algorithm for B-spline curves

1992 ◽  
Vol 9 (3) ◽  
pp. 175-183 ◽  
Author(s):  
Phillip J. Barry ◽  
Rui-Feng Zhu
Keyword(s):  
Knot Insertion ◽  
B Spline ◽  
Spline Curves ◽  
Insertion Algorithm

Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces.

1994 ◽  
Vol 63 (208) ◽  
pp. 821
Author(s):  
Richard H. Bartels ◽  
Ronald N. Goldman ◽  
Tom Lyche
Keyword(s):  
Knot Insertion ◽  
B Spline ◽  
Curves And Surfaces ◽  
Insertion And Deletion ◽  
Spline Curves
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