Name
Abstract | ||
|---|---|---|
''The NURBS Book'' [L. Piegl, W. Tiller, The NURBS Book, second edn, Springer, 1997] is very popular in the fields of computer aided geometric design (CAGD) and geometric modeling. In Section 9.5.2 of the book, the well-known problem of the local cubic spline approximation is discussed. The key in local cubic spline approximation is cubic polynomial interpolation. In this short paper, we present the concept of single-side/double-side cubic curves and obtain the necessary and sufficient condition of a cubic curve being a single-side/double-side curve. Based on this result, for some cases of two end tangents being nearly parallel we present a new method for the problem of cubic polynomial interpolation. We also point out a flaw in Section 9.5.2 of the book and give the correction result. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.camwa.2008.02.032 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
correction result,double-side curve,double-side cubic curve,cagd,geometric design,geometric modeling,interpolation,cubic spline,nurbs book,cubic curve,local cubic spline approximation,cubic polynomial interpolation,data fitting,well-known problem,polynomial interpolation,geometric model | Mathematical optimization,Polynomial interpolation,Spline interpolation,Cubic form,Mathematical analysis,Interpolation,Bicubic interpolation,Monotone cubic interpolation,Cubic Hermite spline,Linear interpolation,Mathematics | Journal |
Volume | Issue | ISSN |
56 | 5 | Computers and Mathematics with Applications |
Citations | PageRank | References |
1 | 0.41 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Minghan Hu | 1 | 7 | 2.54 |
| Xiquan Shi | 2 | 93 | 12.31 |
| Tianjun Wang | 3 | 66 | 7.04 |
| Fengshan Liu | 4 | 76 | 11.78 |