Unifying C-curves and H-curves by extending the calculation to complex numbers
نویسندگان
چکیده
Recently, we found that the CB-splines that use basis {sin t, cos t, t,1} and the HB-splines that use basis {sinh t, cosh t, 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. 2005 Elsevier B.V. All rights reserved.
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ورودعنوان ژورنال:
- Computer Aided Geometric Design
دوره 22 شماره
صفحات -
تاریخ انتشار 2005