Spline2D Class |
Namespace: Imsl.Math
The Spline2D type exposes the following members.
Name | Description | |
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Derivative(Double, Double, Int32, Int32) | Returns the value of the partial derivative of the tensor-product spline
at the point (x, y).
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Derivative(Double, Double, Int32, Int32) | Returns the values of the partial derivative of the tensor-product spline
of an array of points.
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Equals | Determines whether the specified object is equal to the current object. (Inherited from Object.) | |
Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.) | |
GetCoefficients | Returns the coefficients for the tensor-product spline.
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GetHashCode | Serves as a hash function for a particular type. (Inherited from Object.) | |
GetType | Gets the Type of the current instance. (Inherited from Object.) | |
GetXKnots |
Returns the knot sequences in the x-direction.
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GetYKnots | Returns the knot sequences in the y-direction.
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Integral | Returns the value of an integral of a tensor-product spline
on a rectangular domain. | |
MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object.) | |
ToString | Returns a string that represents the current object. (Inherited from Object.) | |
Value(Double, Double) | Returns the value of the tensor-product spline at the point (x, y).
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Value(Double, Double) | Returns the values of the tensor-product spline of an array of points.
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The simplest method of obtaining multivariate interpolation and approximation functions is to take univariate methods and form a multivariate method via tensor products. In the case of two-dimensional spline interpolation, the derivation proceeds as follows: Let be a knot sequence for splines of order , and be a knot sequence for splines of order . Let be the length of , and be the length of . Then, the tensor-product spline has the following form:
Given two sets of points and for which the corresponding univariate interpolation problem can be solved, the tensor-product interpolation problem finds the coefficients so that This problem can be solved efficiently by repeatedly solving univariate interpolation problems as described in de Boor (1978, p. 347).