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UnsafeNativeMethods.Vector3.CatmullRom(Vector3,Vector3,Vector3,Vector3,Vector3,Single) Method (Microsoft.DirectX)

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Performs a Catmull-Rom interpolation using specified 3-D vectors.

Note: For programming in Microsoft Visual Basic .NET or Microsoft JScript .NET, use the equivalent method in the Microsoft.DirectX structures.

Definition

Visual Basic Public Shared Function CatmullRom( _
    ByVal pOut As Vector3, _
    ByVal pPosition1 As Vector3, _
    ByVal pPosition2 As Vector3, _
    ByVal pPosition3 As Vector3, _
    ByVal pPosition4 As Vector3, _
    ByVal weightingFactor As Single _
) As Vector3
C# public static Vector3 CatmullRom(
    Vector3 pOut,
    Vector3 pPosition1,
    Vector3 pPosition2,
    Vector3 pPosition3,
    Vector3 pPosition4,
    float weightingFactor
);
C++ public:
static Vector3 CatmullRom(
    Vector3 pOut,
    Vector3 pPosition1,
    Vector3 pPosition2,
    Vector3 pPosition3,
    Vector3 pPosition4,
    float weightingFactor
);
JScript public static function CatmullRom(
    pOut : Vector3,
    pPosition1 : Vector3,
    pPosition2 : Vector3,
    pPosition3 : Vector3,
    pPosition4 : Vector3,
    weightingFactor : float
) : Vector3;

Parameters

pOut Microsoft.DirectX.Vector3
A Vector3 structure that is the result of the Catmull-Rom interpolation.
pPosition1 Microsoft.DirectX.Vector3
Source Vector3 structure that is a position vector.
pPosition2 Microsoft.DirectX.Vector3
Source Vector3 structure that is a position vector.
pPosition3 Microsoft.DirectX.Vector3
Source Vector3 structure that is a position vector.
pPosition4 Microsoft.DirectX.Vector3
Source Vector3 structure that is a position vector.
weightingFactor System.Single
Weighting factor. See Remarks.

Return Value

Microsoft.DirectX.Vector3
A Vector3 structure that is the result of the Catmull-Rom interpolation.

Remarks

To derive the Catmull-Rom spline from the Hermite spline, use the following settings. In this example, v1 is the contents of pPosition1, v2 is the contents of pPosition2, p3 is the contents of pPosition3, p4 is the contents of pPosition4, and s is the contents of weightingFactor.

v1 = p2
v2 = p3
t1 = (p3 - p1) / 2
t2 = (p4 - p2) / 2

Using the Hermite spline equation.

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

Substituting for v1, v2, t1, t2 yields the following result.

Q(s) = (2s3 - 3s2 + 1)p2 + (-2s3 + 3s2)p3 + (s3 - 2s2 + s)(p3 - p1) / 2 + (s3 - s2)(p4 - p2)/2

This result can be rearranged as follows:

Q(s) = [(-s3 + 2s2 - s)p1 + (3s3 - 5s2 + 2)p2 + (-3s3 + 4s2 + s)p3 + (s3 - s2)p4] / 2

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

See Also