Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Construction of exponential tension B-splines of arbitrary order
Curves and surfaces
The geometry of Tchebycheffian splines
Selected papers of the international symposium on Free-form curves and free-form surfaces
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Symmetric Tchebycheffian B-spline schemes
Proceedings of the international conference on Curves and surfaces in geometric design
C-curves: an extension of cubic curves
Computer Aided Geometric Design
Two different forms of C-B-splines
Computer Aided Geometric Design
The NURBS book (2nd ed.)
Graphical Models and Image Processing
Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
Corner cutting algorithms associated with optimal shape preserving representations
Computer Aided Geometric Design
Shape preserving alternatives to the rational Bézier model
Computer Aided Geometric Design
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
Computer Aided Geometric Design
Unifying C-curves and H-curves by extending the calculation to complex numbers
Computer Aided Geometric Design
A general class of Bernstein-like bases
Computers & Mathematics with Applications
Unified and extended form of three types of splines
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
AHT Bézier curves and NUAHT B-spline curves
Journal of Computer Science and Technology
Unifying C-curves and H-curves by extending the calculation to complex numbers
Computer Aided Geometric Design
Control point based exact description of a class of closed curves and surfaces
Computer Aided Geometric Design
Optimal bases for a class of mixed spaces and their associated spline spaces
Computers & Mathematics with Applications
A generalized curve subdivision scheme of arbitrary order with a tension parameter
Computer Aided Geometric Design
A class of algebraic-trigonometric blended splines
Journal of Computational and Applied Mathematics
Mixed hyperbolic/trigonometric spaces for design
Computers & Mathematics with Applications
Explicit representations of changeable degree spline basis functions
Journal of Computational and Applied Mathematics
Numerical Algorithms
A generalized surface subdivision scheme of arbitrary order with a tension parameter
Computer-Aided Design
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This paper presents a new kind of uniform splines, called hyperbolic polynomial B-splines, generated over the space Ω = span{sinht, cosht, tk-3, tk-4 ...,t, 1} in which k is an arbitrary integer larger than or equal to 3. Hyperbolic polynomial B-splines share most of the properties as those of the B-splines in the polynomial space. We give the subdivision formulae for this new kind of curves and then prove that they have the variation dimishing properties and the control polygons of the subdivisions converge. Hyperbolic polynomial B-splines can take care of freeform curves as well as some remarkable curves such as the hyperbola and the catenary. The generation of tensor product surfaces by these new splines is straightforward. Examples of such tensor product surfaces: the saddle surface, the catenary cylinder, and a certain kind of ruled surface are given in this paper.