CardinalSegment3F Class

Defines a single segment of a 3-dimensional cubic Cardinal spline (single-precision).

Inheritance Hierarchy

SystemObject
DigitalRune.Mathematics.InterpolationCardinalSegment3F

Namespace: DigitalRune.Mathematics.Interpolation
Assembly: DigitalRune.Mathematics (in DigitalRune.Mathematics.dll) Version: 1.14.0.0 (1.14.0.14427)

Syntax

C++

Copy

public class CardinalSegment3F : ICurve<float, Vector3F>, 
	IRecyclable

Public Class CardinalSegment3F
	Implements ICurve(Of Single, Vector3F), 
	IRecyclable

public ref class CardinalSegment3F : ICurve<float, Vector3F>, 
	IRecyclable

type CardinalSegment3F =  
    class
        interface ICurve<float32, Vector3F>
        interface IRecyclable
    end

The CardinalSegment3F type exposes the following members.

Constructors

	Name	Description
	CardinalSegment3F	Initializes a new instance of the CardinalSegment3F class

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Methods

	Name	Description
	Create	Creates an instance of the CardinalSegment3F class. (This method reuses a previously recycled instance or allocates a new instance if necessary.)
	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.)
	Flatten	Computes the points of a sequence of line segments which approximate the curve.
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetLength	Computes the approximated length of the curve for the parameter interval [start, end].
	GetPoint	Computes a point on the curve.
	GetTangent	Computes the tangent for a point on the curve.
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	Recycle	Recycles this instance.
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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Properties

	Name	Description
	Point1	Gets or sets the previous point.
	Point2	Gets or sets the start point.
	Point3	Gets or sets the end point.
	Point4	Gets or sets the subsequent point.
	Tension	Gets or sets the tension constant.

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Remarks

A CardinalSegment3F can be used to smoothly interpolate between two points.

Given a series of points (Point1, Point2, Point3, Point4) this method performs a smooth interpolation between the points Point2 and Point3. The interpolation curve is known as as Cardinal spline. The curve (spline) is a specialization of the cubic Hermit spline. The curve runs through the control points Point2 and Point3. The tangent at each point is computed from the previous point and the following point. The tangent t_i for point p_i is computed as:

t_i = 1/2 (1 - tension) (p_i+1 - p_i-1),

where tension is a parameter, which is a constant that modifies the length of the tangent. tension = 1 will yield zero tangents and tension = 0 yields a Catmull-Rom spline.

The curve function point = C(parameter) takes a scalar parameter and returns a point on the curve (see GetPoint(Single)). The curve parameter lies in the interval [0,1]; it is also known as interpolation parameter, interpolation factor or weight of the target point. C(0) returns the start point Point2; C(1) returns the end point Point3.

Reference

DigitalRune.Mathematics.Interpolation Namespace