## Discrete B-splines and subdivision techniques in computer aided geometric design and computer graphics

- E. Cohen, T. Lyche, R. Riesenfeld
- Computer Graphics & Image Processing,
- 1980

Highly Influential

4 Excerpts

- Published 2005

In order to fair and optimize rational cubic B-spline curves used frequently in engineering, and to improve design system function, some formulae on the degree and the knot vector, of the product of three B-spline functions, are presented; then Marsden’s identity is generalized, and by using discrete B-spline theory, the product of three B-spline functions is converted into a linear combination of B-splines. Consequently, a monotone curvature variation (MCV) discriminant for uniform planar rational cubic B-spline curves can be converted into a higher degree B-spline function. Applying the property of positive unit resolution of B-spline, an MCV sufficient condition for the curve segments is obtained. Theoretical reasoning and instance operation showed that the result is simple and applicable in curve design, especially in curve fair processing.

@inproceedings{Huixia2005NewMF,
title={New method for distinguishing planar rational cubic B-spline curve segments as monotone curvature variation},
author={XU Hui-xia and WANG Guo-jin},
year={2005}
}