Exponential |
Exponential Splines.
Inheritance HierarchyNamespace: Altaxo.Calc.Interpolation
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3448.0 (4.8.3448.0)
SyntaxC#
public class ExponentialSpline : CurveBase, IInterpolationFunction, IInterpolationCurve
The ExponentialSpline type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | ExponentialSpline | Initializes a new instance of the ExponentialSpline class with default boundary conditions and smoothing. |
Properties| Name | Description | |
|---|---|---|
 | BoundaryCondition | Gets or sets the boundary condition mode used for spline interpolation. |
| Smoothing | Gets or sets the smoothing parameter that controls the spline tension. |
Methods| Name | Description | |
|---|---|---|
| CubicSplineCoefficients |
Calculate the spline coefficients y2(i) and y3(i) for a natural cubic
spline, given the abscissa x(i), the ordinate y(i), and the 1st
derivative y1(i).
(Inherited from CurveBase) |
| CubicSplineHorner |
Return the interpolation value P(u) for a piecewise cubic curve determined
by the abscissa vector x, the ordinate vector y,
and derivative coefficient vectors y1, y2, and y3, using the Horner scheme.
(Inherited from CurveBase) |
| CubicSplineHorner1stDerivative |
Return the first derivative P'(u) of the piecewise cubic curve evaluated using Horner's scheme.
(Inherited from CurveBase) |
| 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) |
| GetBoundaryConditions | Gets the current boundary condition configuration along with endpoint derivatives. |
| GetCurvePoints |
Get curve points to draw an interpolation curve between the abscissa values xlo and xhi.
It calls the virtual methods MpCurveBase::GetXOfU() and GetYOfU() to obtain the
interpolation values. Note, that before method DrawCurve() can be called
the method Interpolate() must have been called. Otherwise, not interpolation
is available.
(Inherited from CurveBase) |
| GetHashCode | Serves as the default hash function. (Inherited from Object) |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| GetXOfU |
Get the abscissa value in dependence on parameter u.
(Overrides CurveBaseGetXOfU(Double)) |
| GetYOfU |
Gets the ordinate value on dependence on parameter u.
(Overrides CurveBaseGetYOfU(Double)) |
| GetYOfX | Returns the y value in dependence of a given x value. |
| Interpolate |
Interpolates a curve using abcissa x and ordinate y.
(Overrides CurveBaseInterpolate(IReadOnlyListDouble, IReadOnlyListDouble)) |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
| Parametrize |
Curve length parametrization. Returns the accumulated "distances"
between the points (x(i),y(i)) and (x(i+1),y(i+1)) in t(i+1)
for i = lo ... hi. t(lo) = 0.0 always.
(Inherited from CurveBase) |
| SetBoundaryConditions | Sets the boundary conditions and any supplied endpoint derivatives. |
| ToString | Returns a string that represents the current object. (Inherited from Object) |
Fields| Name | Description | |
|---|---|---|
 | boundary | |
| r1 | |
| r2 | |
| sigma | |
| tmp | |
| x | Reference to the vector of the independent variable. (Inherited from CurveBase) |
| y | Reference to the vector of the dependent variable. (Inherited from CurveBase) |
| y1 |
RemarksC#
References: ----------- (1) D.G. Schweikert, "An Interpolation Curve using a Spline in Tension" J. Math. Physics, 45, pp 312-317 (1966). (2) Dr.rer.nat. Helmuth Spaeth, "Spline-Algorithmen zur Konstruktion glatter Kurven und Flaechen", 3. Auflage, R. Oldenburg Verlag, Muenchen, Wien, 1983. (3) A. K. Cline, Commun. of the ACM, 17, 4, pp 218-223 (Apr 1974). (4) This algorithm is also implemented in the Unix spline tool by James R. Van Zandt (jrv@mitre-bedford), 1985.
See Also