Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
The geometry of Tchebycheffian splines
Selected papers of the international symposium on Free-form curves and free-form surfaces
C-curves: an extension of cubic curves
Computer Aided Geometric Design
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
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
A subdivision scheme for surfaces of revolution
Computer Aided Geometric Design
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
A class of algebraic-trigonometric blended splines
Journal of Computational and Applied Mathematics
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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-Bézier 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.