D3DXVec4CatmullRom

Performs a Catmull-Rom interpolation, using the specified 4D vectors.

D3DXVECTOR4 * D3DXVec4CatmullRom(
  D3DXVECTOR4 * pOut,
  CONST D3DXVECTOR4 * pV0,
  CONST D3DXVECTOR4 * pV1,
  CONST D3DXVECTOR4 * pV2,
  CONST D3DXVECTOR4 * pV3,
  FLOAT s
);

Parameters

pOut

[in, out] Pointer to the D3DXVECTOR4 structure that is the result of the operation.

pV0

[in] Pointer to a source D3DXVECTOR4 structure, a position vector.

pV1

[in] Pointer to a source D3DXVECTOR4 structure, a position vector.

pV2

[in] Pointer to a source D3DXVECTOR4 structure, a position vector.

pV3

[in] Pointer to a source D3DXVECTOR4 structure, a position vector.

s

[in] Weighting factor. See Remarks.

Return Values

Pointer to a D3DXVECTOR4 structure that is the result of the Catmull-Rom interpolation.

Remarks

Given four points (p1, p2, p3, p4), find a function Q(s) such that:

Q(s) is a cubic function. 
Q(s) interpolates between p2 and p3 as s ranges from 0 to 1. 
Q(s) is parallel to the line joining p1 to p3 when s is 0. 
Q(s) is parallel to the line joining p2 to p4 when s is 1. 

The Catmull-Rom spline can be derived from the Hermite spline by setting:

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

where:

v1 is the contents of pV0.

v2 in the contents of pV1.

p3 is the contents of pV2.

p4 is the contents of pV3.

Using the Hermite spline equation:

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

and substituting for v1, v2, t1, t2 yields:

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

This can be rearranged as:

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

Requirements

Header: Declared in D3dx9math.h.

See Also

D3DXVec2CatmullRom, D3DXVec3CatmullRom