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BezierCubicSpline Class

Calculate the Bezier cubic spline interpolation for the given abscissa vector x and ordinate vector y. All vectors must have conformant dimensions.
Inheritance Hierarchy
SystemObject
  Altaxo.Calc.InterpolationCurveBase
    Altaxo.Calc.InterpolationBezierCubicSpline

Namespace: Altaxo.Calc.Interpolation
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
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public class BezierCubicSpline : CurveBase

The BezierCubicSpline type exposes the following members.

Constructors
 NameDescription
Public methodBezierCubicSplineInitializes a new instance of the BezierCubicSpline class
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Methods
 NameDescription
Public methodCubicSplineCoefficients 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)
Public methodCubicSplineHorner Return the interpolation value P(u) for a piecewise cubic curve determined by the abscissa vector x, the ordinate vector y, the 1st derivative vector y1, the 2nd derivative vector y2, and the 3rd derivative vector y3, using the Horner scheme.
(Inherited from CurveBase)
Public methodCubicSplineHorner1stDerivative
(Inherited from CurveBase)
Public methodEqualsDetermines whether the specified object is equal to the current object.
(Inherited from Object)
Protected methodFinalizeAllows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection.
(Inherited from Object)
Public methodGetCurvePoints 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)
Public methodGetHashCodeServes as the default hash function.
(Inherited from Object)
Public methodGetTypeGets the Type of the current instance.
(Inherited from Object)
Public methodGetXOfU
(Overrides CurveBaseGetXOfU(Double))
Public methodGetYOfU
(Overrides CurveBaseGetYOfU(Double))
Public methodInterpolate
(Overrides CurveBaseInterpolate(IReadOnlyListDouble, IReadOnlyListDouble))
Protected methodMemberwiseCloneCreates a shallow copy of the current Object.
(Inherited from Object)
Public methodParametrize 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)
Public methodToStringReturns a string that represents the current object.
(Inherited from Object)
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Fields
 NameDescription
Protected fieldxReference to the vector of the independent variable.
(Inherited from CurveBase)
Protected fieldyReference to the vector of the dependent variable.
(Inherited from CurveBase)
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Remarks
C#
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                            1   / -1.0  3.0 -3.0  1.0 \   / P1 \
BSpline(t) = (t^3 t^2 t 1) --- |   3.0 -6.0  3.0  0.0  | |  P2  | = T M G
                            6  |  -3.0  0.0  3.0  0.0  | |  P3  |
                                \  1.0  4.0  1.0  0.0 /   \ P4 /

T is the polynomial basis vector
M is the basis matrix of the Bezier spline
G is the geometry vector of the control points
See Also