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Note
The D3DX utility library is deprecated. We recommend that you use DirectXMath instead.
Performs a Catmull-Rom interpolation, using the specified 3D vectors.
Syntax
D3DXVECTOR3* D3DXVec3CatmullRom(
_Inout_ D3DXVECTOR3 *pOut,
_In_ const D3DXVECTOR3 *pV0,
_In_ const D3DXVECTOR3 *pV1,
_In_ const D3DXVECTOR3 *pV2,
_In_ const D3DXVECTOR3 *pV3,
_In_ FLOAT s
);
Parameters
-
pOut [in, out]
-
Type: D3DXVECTOR3*
Pointer to the D3DXVECTOR3 structure that is the result of the operation.
-
pV0 [in]
-
Type: const D3DXVECTOR3*
Pointer to a source D3DXVECTOR3 structure, a position vector.
-
pV1 [in]
-
Type: const D3DXVECTOR3*
Pointer to a source D3DXVECTOR3 structure, a position vector.
-
pV2 [in]
-
Type: const D3DXVECTOR3*
Pointer to a source D3DXVECTOR3 structure, a position vector.
-
pV3 [in]
-
Type: const D3DXVECTOR3*
Pointer to a source D3DXVECTOR3 structure, a position vector.
-
s [in]
-
Type: FLOAT
Weighting factor. See Remarks.
Return value
Type: D3DXVECTOR3*
Pointer to a D3DXVECTOR3 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 is 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
| Requirement | Value |
|---|---|
| Header |
|
| Library |
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See also