Abstract
A constructive approach has been adopted to build B-spline like basis for cubic spline curves with the same continuity constraints as those for interpolatory weighted v-splines. These are local basis functions with local support and having the property of being positive everywhere. The design curves and surfaces, constructed through these functions, possess all the ideal geometric properties like partition of unity, convex hull, and variation diminishing. The method provides not only a variety of very interesting shape control like point, and interval tensions but, as a special case, also recovers the cubic B-spline method. In addition, it also provides B-spline like design curves and surfaces for weighted splines, v-splines and weighted v-splines. The method for evaluating these splines is suggested by a transformation to Bézier form.
| Original language | English |
|---|---|
| Pages (from-to) | 539-549 |
| Number of pages | 11 |
| Journal | Computers and Graphics |
| Volume | 28 |
| Issue number | 4 |
| DOIs | |
| State | Published - Aug 2004 |
Bibliographical note
Funding Information:The author is grateful to anonymous referees for their helpful and constructive comments in the construction of the paper. This work has been supported by the King Fahd University of Petroleum and Minerals under Project No. FT/2001-18.
Keywords
- B-spline
- Bézier
- Cubic spline
- Curves and surfaces
- Interpolation
ASJC Scopus subject areas
- Software
- Signal Processing
- General Engineering
- Human-Computer Interaction
- Computer Vision and Pattern Recognition
- Computer Graphics and Computer-Aided Design