UnsafeNativeMethods.Vector2.Hermite(Vector2,Vector2,Vector2,Vector2,Vector2,Single) Method (Microsoft.DirectX)

Performs a Hermite spline interpolation using specified 2-D vectors.

Definition

Visual Basic	Public Shared Function Hermite( _     ByVal pOut As Vector2, _     ByVal pPosition As Vector2, _     ByVal pTangent As Vector2, _     ByVal pPosition2 As Vector2, _     ByVal pTangent2 As Vector2, _     ByVal weightingFactor As Single _ ) As Vector2
C#	public static Vector2 Hermite(     Vector2 pOut,     Vector2 pPosition,     Vector2 pTangent,     Vector2 pPosition2,     Vector2 pTangent2,     float weightingFactor );
C++	public: static Vector2 Hermite(     Vector2 pOut,     Vector2 pPosition,     Vector2 pTangent,     Vector2 pPosition2,     Vector2 pTangent2,     float weightingFactor );
JScript	public static function Hermite(     pOut : Vector2,     pPosition : Vector2,     pTangent : Vector2,     pPosition2 : Vector2,     pTangent2 : Vector2,     weightingFactor : float ) : Vector2;

Parameters

pOut	Microsoft.DirectX.Vector2 A Vector2 structure that is the result of the Hermite spline interpolation.
pPosition	Microsoft.DirectX.Vector2 Source Vector2 structure that is a position vector.
pTangent	Microsoft.DirectX.Vector2 Source Vector2 structure that is a tangent vector.
pPosition2	Microsoft.DirectX.Vector2 Source Vector2 structure that is a position vector.
pTangent2	Microsoft.DirectX.Vector2 Source Vector2 structure that is a tangent vector.
weightingFactor	System.Single Weighting factor. See Remarks.

Return Value

Microsoft.DirectX.Vector2
A Vector2 structure that is the result of the Hermite spline interpolation.

Remarks

The Hermite method interpolates from (pPosition, pTangent) to (pPosition2, pTangent2) using Hermite spline interpolation.

The spline interpolation is a generalization of ease-in, ease-out spline interpolation. The ramp is a function of Q(s) with the following properties.

Q(s) = As³ + Bs² + Cs + D (and therefore, Q'(s) = 3As² + 2Bs + C)

a) Q(0) = v1, so Q'(0) = t1

b) Q(1) = v2, so Q'(1) = t2

In these properties, v1 is the contents of pPosition, v2 is the contents of pPosition2, t1 is the contents of pTangent, t2 is the contents of pTangent2, and s is the contents of weightingFactor.

These properties are used to solve for A, B, C, and D in the following example.

D = v1  (from a)
C = t1  (from a)
3A + 2B = t2 - t-1 (substituting for C)
A + B = v2 - v1 - t1 (substituting for C and D)

To generate Q(s), pass in the solutions for A, B, C, and D as follows.

A = 2v1 - 2v2 + t2 + t1 
B = 3v2 - 3v1 - 2t1 - t2
C = t1 
D = v1

The preceding example yields the following:

Q(s) = (2v1 - 2v2 + t2 + t1)s3 + (3v2 - 3v1 - 2t1 - t2)s2 + t1s + v1.

which can be rearranged as:

Q(s) = (2s3 - 3s2 + 1)v1 + (-2s3 + 3s2)v2 + (s3 - 2s2 + s)t1 + (s3 - s2)t2.

Hermite splines are useful for controlling animation because the curve runs through all of the control points. Also, because the position and tangent are explicitly specified at the ends of each segment, it is easy to create a continuous curve, provided that the starting position and tangent match the ending values of the last segment.

The return value for this method is the same value returned in the pOut parameter. This allows you to use the Hermite method as a parameter for another method.

See Also

• Hermite