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The fairing andG1continuity of quartic C-Bézier curves
- Source :
- Mathematical Methods in the Applied Sciences. 39:1336-1348
- Publication Year :
- 2015
- Publisher :
- Wiley, 2015.
-
Abstract
- Quartic C-Bezier curves possess similar properties with the traditional Bezier curves including terminal property, convex hull property, affine invariance, and approaching the shape of their control polygons as the shape parameter α decreases. In this paper, by adjusting the shape parameter α on the basis of the utilization of the least square approximation and nonlinear functional minimization together with fairing of a quartic C-Bezier curve with G1 continuity of quartic C-Bezier curve segments, we develop a fairing and G1 continuity algorithm for any given stitching coefficients λk(k = 1,2,…,n − 1). The shape parameters αi(i=1, 2, …, n) can be adjusted by the value of control points. The curvature of the resulting quartic C-Bezier curve segments after fairing is more uniform than before. Moreover, six examples are provided in the paper to demonstrate the efficacy of the algorithm and illustrate how to apply this algorithm to the computer-aided design/computer-aided manufacturing modeling systems. Copyright © 2015 John Wiley & Sons, Ltd.
- Subjects :
- Convex hull
Quartic plane curve
General Mathematics
Mathematical analysis
General Engineering
Bullet-nose curve
020207 software engineering
Bézier curve
02 engineering and technology
Curvature
01 natural sciences
Shape parameter
010101 applied mathematics
Quartic function
0202 electrical engineering, electronic engineering, information engineering
0101 mathematics
Quartic surface
Mathematics
Subjects
Details
- ISSN :
- 01704214
- Volume :
- 39
- Database :
- OpenAIRE
- Journal :
- Mathematical Methods in the Applied Sciences
- Accession number :
- edsair.doi...........a6e953ae4048a8bbefb3600ed535cc32