Name
Abstract | ||
|---|---|---|
This paper presents a new kind of algebraic-trigonometric blended spline curve, called xyB curves, generated over the space {1,t,sint,cost,sin^2t,sin^3t,cos^3t}. The new curves not only inherit most properties of usual cubic B-spline curves in polynomial space, but also enjoy some other advantageous properties for modeling. For given control points, the shape of the new curves can be adjusted by using the parameters x and y. When the control points and the parameters are chosen appropriately, the new curves can represent some conics and transcendental curves. In addition, we present methods of constructing an interpolation xyB-spline curve and an xyB-spline curve which is tangent to the given control polygon. The generation of tensor product surfaces by these new spline curves is straightforward. Many properties of the curves can be easily extended to the surfaces. The new surfaces can exactly represent the rotation surfaces as well as the surfaces with elliptical or circular sections. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.cam.2010.09.016 | J. Computational Applied Mathematics |
Keywords | Field | DocType |
new kind,usual cubic b-spline curve,new curve,new spline curve,algebraic-trigonometric blended spline curve,control polygon,control point,transcendental curve,interpolation xyb-spline curve,new surface,tensor product,shape parameter,spline curve | Spline (mathematics),Mathematical optimization,Family of curves,Spline interpolation,Curve fitting,Mathematical analysis,Smoothing spline,Geometric design,Tangent,Flat spline,Mathematics | Journal |
Volume | Issue | ISSN |
235 | 6 | 0377-0427 |
Citations | PageRank | References |
4 | 0.53 | 11 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lanlan Yan | 1 | 17 | 2.68 |
| Jiongfeng Liang | 2 | 17 | 2.68 |