Titlebook: Interpolating Cubic Splines; Gary D. Knott Book 2000 Springer Science+Business Media New York 2000 Approximation.Approximation theory.Spli

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mechanical

,Λ-Spline Curves With Range Dimension ,nctions which map.to ., such that no two functions in Λ are identical on [. ., . .]. Given the real values . ≤ . ≤ … ≤ ., the parametric function .(.) defined on the interval [., .] is called a Λ- . ., .,…, . if .(.) = .(. ? .?1) for . ≤ . ≤ . and 1 ≤ . ≤ . ? 1, where each function . is a function i

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召集

鎮(zhèn)痛劑

Smoothing Splines,rom the graph of some unknown function . : . → . such that . = .(.) + ∈. for . = 1,… , .. If the form of the function . were known, except for some unknown parameter values, we could then determine those values by the least squares method, where the desired parameter values are those parameter value

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Geometrically Continuous Cubic Splines,try and exit tangent vectors at each point ., where each pair may have differing magnitudes, but the same direction. It is common to call a tangent vector geometrically continuous curve a . curve, in the same way that a tangent vector algebraically continuous curve is commonly called a . curve. A .

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Cubic Spline Vector Space Basis Functions,φ. where α.,… , α. ∈ .. For the case of a vector space of cubic spline functions, some basis sets can be developed by focusing on a representation of the cubic polynomial spline segments as component-wise linear combinations of fixed functions.

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Rational Cubic Splines,c polynomial cannot represent other conic section curves such as a circular arc, an elliptic arc, or a segment of an hyperbola. It is an interesting fact, however, that an elliptic or hyperbolic arc in . can be parametrically represented by three component functions .(.), .(.), and .(.), where each

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Tensor Product Surface Splines,ic surface splines analogous to the cubic space curve splines that we studied above. Again we want to construct spline surfaces that contain given points in 3-space, and, generally, that have specified directional derivatives or directional tangent vectors at these given interpolation points.