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UnsafeNativeMethods.Vector3.CatmullRom Method |
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Performs a Catmull-Rom interpolation using specified 3-D vectors.
Visual Basic .NET 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 Vector3C# public static Vector3 CatmullRom(
Vector3 pOut,
Vector3 pPosition1,
Vector3 pPosition2,
Vector3 pPosition3,
Vector3 pPosition4,
float weightingFactor
);Managed C++ public: static Vector3 CatmullRom(
Vector3 pOut,
Vector3 pPosition1,
Vector3 pPosition2,
Vector3 pPosition3,
Vector3 pPosition4,
float weightingFactor
);JScript .NET public static function CatmullRom(
pOut : Vector3,
pPosition1 : Vector3,
pPosition2 : Vector3,
pPosition3 : Vector3,
pPosition4 : Vector3,
weightingFactor : float
) : Vector3;
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.
Microsoft.DirectX.Vector3 . A Vector3 structure that is the result of the Catmull-Rom interpolation.
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) / 2Using the Hermite spline equation.
Q(s) = (2s3 - 3s2 + 1)v1 + (-2s3 + 3s2)v2 + (s3 - 2s2 + s)t1 + (s3 - s2)t2Substituting 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)/2This result can be rearranged as follows:Q(s) = [(-s3 + 2s2 - s)p1 + (3s3 - 5s2 + 2)p2 + (-3s3 + 4s2 + s)p3 + (s3 - s2)p4] / 2The return value for this method is the same value returned in the pOut parameter. Resultantly, the CatmullRom method can be used as a parameter for another method.
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