The geometry of Tchebycheffian splines
Selected papers of the international symposium on Free-form curves and free-form surfaces
Two different forms of C-B-splines
Computer Aided Geometric Design
Graphical Models and Image Processing
Shape preserving alternatives to the rational Bézier model
Computer Aided Geometric Design
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
A basis of C-Bézier splines with optimal properties
Computer Aided Geometric Design
Uniform hyperbolic polynomial B-spline curves
Computer Aided Geometric Design
Computer Aided Geometric Design
C-curves: An extension of cubic curves
Computer Aided Geometric Design
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
Control point based exact description of a class of closed curves and surfaces
Computer Aided Geometric Design
Closed rational trigonometric curves and surfaces
Journal of Computational and Applied Mathematics
A generalized curve subdivision scheme of arbitrary order with a tension parameter
Computer Aided Geometric Design
Mixed hyperbolic/trigonometric spaces for design
Computers & Mathematics with Applications
Curves and Surfaces Construction Based on New Basis with Exponential Functions
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
A generalized surface subdivision scheme of arbitrary order with a tension parameter
Computer-Aided Design
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Recently, we found that the CB-splines that use basis {sint,cost,t,1} and the HB-splines that use basis {sinht,cosht,t,1} could be unified into a complete curve family, named FB-splines (Zhang and Krause, 2005). FB-splines are a scheme of what we call here F-curves. This paper explains that in the domain of complex numbers, the extended C-curves and extended H-curves are the same curves. Therefore, F-curves can be constructed in two identical styles, C and H. The C style is an extension of C-curves that uses sin and cos, and the H style is an extension of H-curves that uses sinh and cosh. Here the representations of F-curves are clearer and simpler. For real applications, the definitions, equations and main properties for the F-curves in different schemes (FB-splines, F-Bezier and F-Ferguson schemes) are introduced in details. F-curves are shape adjustable, and their curvatures on terminals can be any expected value between 0 and ~. They can represent the circular (or elliptical) arc, the cylinder, the helix, the cycloid, the hyperbola, the catenary, etc. precisely. Therefore, F-curves are more useful than C-curves or H-curves for the surface modeling in engineering.