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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,...
In this paper, the trigonometric basis {sin t, cos t, t, 1} and the hyperbolic basis {sinh t, cosh t, t, 1} are unified by a shape parameter C (0≤C<∝). It yields the Functional B-splines (FB-splines) and its corresponding Subdivision B-splines (SB-splines). As well, a geometric proof of curvature continuity for SB-splines is provided. FB-splines and SB-splines inherited nearly all properties of...
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