CubicSpline Class

Visual Basic (Declaration)
Public Class CubicSpline _ Inherits PiecewiseCurve

C#
public class CubicSpline : PiecewiseCurve

C++
public ref class CubicSpline : public PiecewiseCurve

Icon	Type	Description
	Clone()	Constructs an exact copy of this instance.
	Equals(Object)	Determines whether the specified Object is equal to the current Object.
	Finalize()	Allows an Object to attempt to free resources and perform other cleanup operations before the Object is reclaimed by garbage collection.
	FindRoots()	Gets the set of X-coordinates where the curve crosses the X-axis.
	GetCurveFitter()	Returns a CurveFitter object that can be used to fit the curve to data.
	GetDataPoint(Int32)	Gets the data point with the specified index.
	GetDerivative()	Returns a Curve that represents the derivative of this Curve.
	GetHashCode()	Serves as a hash function for a particular type.
	GetType()	Gets the Type of the current instance.
	GetXValue(Int32)	Returns the X value of the data point with the specified index.
	GetYValue(Int32)	Returns the Y value of the data point with the specified index.
	IndexOf(Double)	Finds the index of the lower bound of the interval that contains the specfied value.
	Integral(Double, Double)	Gets the definite integral of the curve between the specified X-coordinates.
	IntegrateOnInterval(Int32, Double, Double)	Returns the integral of the curve over a single interval.
	IntegrateOnInterval(Int32)	Returns the value of the integral over the interval with the specified index.
	MemberwiseClone()	Creates a shallow copy of the current Object.
	OnParameterChanged(Int32, Double)	Called after a curve parameter has changed.
	OnParameterChanging(Int32, Double)	Called before the value of a curve parameter is changed.
	SetDataPoint(Int32, Point)	Sets the X value of the data point with the specified index.
	SetDataPoints(Int32[](), Point[]())	Sets the data points at the specified indexes.
	SetXValue(Int32, Double)	Sets the X value of the data point with the specified index.
	SetXValues(Int32[](), Double[]())	Sets the X values at the specified indexes.
	SetYValue(Int32, Double)	Sets the Y value of the data point with the specified index.
	SetYValues(Int32[](), Double[]())	Sets the Y values at the specified indexes.
	SlopeAt(Double)	Gets the slope of the curve at the specified X-coordinate.
	TangentAt(Double)	Gets the tangent Line to the curve at the specified X-coordinate.
	ToString()	Returns a String that represents the current Object.
	ValueAt(Double)	Gets the Y-value of the curve at the specified X-coordinate.

Icon	Type	Description
	CubicSplineNew(Double[](), Double[]())	Constructs the natural cubic spline through a set of points.
	CubicSplineNew(Vector, Vector)	Constructs the natural cubic spline through a set of points.
	CubicSplineNew(Point[]())	Constructs the natural cubic spline through a set of points.
	CubicSplineNew(Double[](), Double[](), Double, Double)	Constructs a clamped cubic spline through a set of points.
	CubicSplineNew(Vector, Vector, Double, Double)	Constructs a clamped cubic spline through a set of points.
	CubicSplineNew(Point[](), Double, Double)	Constructs a clamped cubic spline through a set of points.

Icon	Type	Description
	NumberOfIntervals	Gets the number of intervals that make up this PiecewiseCurve.
	Parameters	Gets the collection of parameters that determine the shape of this Curve.

Use the CubicSpline class to interpolate tabulated data, or to approximate a function defined in terms of tabulated data.

A cubic spline is a PiecewiseCurve defined by a third degree polynomial on each interval. In addition, the function value as well as the first and second derivatives are continuous.

Splines are defined by the data points and two additional conditions. Depending on the nature of these conditions, different types of spline curves arise. There are two main kinds of splines.

A natural spline is a spline curve whose second derivative at the end points are zero. This type of spline tends to minimize the overall curvature of the spline. There is only one natural spline for a given set of data points.

A clamped spline is a spline curve whose slope is fixed at both end points. There is a clamped spline curve for each pair of slopes. Therefore, two parameters must be defined in addition to the data points to specify a clamped spline completely.

System.Object
  Extreme.Mathematics.Curves.Curve
    Extreme.Mathematics.Curves.PiecewiseCurve
      Extreme.Mathematics.Curves.CubicSpline

Syntax

Methods

Constructors

Properties

Remarks

Inheritance Hierarchy