Computer Aided Geometric Design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Non-uniform recursive subdivision surfaces
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Curve and surface construction using variable degree polynomial splines
Computer Aided Geometric Design
On the degree elevation of B-spline curves and corner cutting
Computer Aided Geometric Design
A basis of multi-degree splines
Computer Aided Geometric Design
Changeable degree spline basis functions
Journal of Computational and Applied Mathematics
Explicit representations of changeable degree spline basis functions
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
This paper studies the merits of using knot interval notation for B-spline curves, and presents formulae in terms of knot intervals for common B-spline operations such as knot insertion, differentiation, and degree elevation. Using knot interval notation, the paper introduces MD-splines, which are B-spline-like curves that are comprised of polynomial segments of various degrees (MD stands for "multi-degree"). MD-splines are a generalization of B-spline curves in that if all curve segments in an MD-spline have the same degree, it reduces to a B-spline curve. The paper focuses on MD-splines of degree 1, 2, and 3, as well as degree 1 and n. MD-splines have local support, obey the convex hull and variation diminishing properties, and are at least Cn-1, where n is the smaller of the degrees of two adjoining curve segments.