Microsoft DirectX 8.1 (C++) |
D3DXQuaternionSquadSetup
Setup control points for spherical quadrangle interpolation.
void D3DXQuaternionSquadSetup( D3DXQUATERNION* pAOut, D3DXQUATERNION* pBOut, D3DXQUATERNION* pCOut, CONST D3DXQUATERNION* pQ0, CONST D3DXQUATERNION* pQ1, CONST D3DXQUATERNION* pQ2, CONST D3DXQUATERNION* pQ3 );
Parameters
- pAOut
- [out] Pointer to AOut.
- pBOut
- [out] Pointer to BOut.
- pCOut
- [out] Pointer to COut.
- pQ0
- [in] Pointer to the input control point, Q0.
- pQ1
- [in] Pointer to the input control point, Q1.
- pQ2
- [in] Pointer to the input control point, Q2.
- pQ3
- [in] Pointer to the input control point, Q3.
Remarks
This function operates as shown below. It takes four control points (Q0, Q1, Q2, Q3), which are supplied to the inputs pQ0, pQ1, pQ2, and pQ3. The function then alters these values to find a curve that flows along the shortest path. The values of q0, q2, and q3 are calculated as shown below.
q0 = |Q0 + Q1| < |Q0 - Q1| ? -Q0 : Q0 q2 = |Q1 + Q2| < |Q1 - Q2| ? -Q2 : Q2 q3 = |Q2 + Q3| < |Q2 - Q3| ? -Q3 : Q3
Having calculated the new Q values, the values for AOut, BOut, and COut are calculated as shown below.
AOut = q1 * e[-0.25 *( Ln[Exp(q1)*q2] + Ln[Exp(q1)*q0] ) ] BOut = q2 * e[-0.25 *( Ln[Exp(q2)*q3] + Ln[Exp(q2)*q1] ) ] COut = q2 Note: Ln is the API method D3DXQuaternionLn Exp is the API method D3DXQuaternionExp
Example
The following example shows how to use a set of quaternion keys (Q0, Q1, Q2, Q3) to compute the inner quadrangle points (A, B, C). This ensures that the tangents are continuous across adjacent segments.
A B Q0 Q1 Q2 Q3
This is how you can interpolate between Q1 and Q2.
// rotation about the z axis D3DXQUATERNION Q0 = D3DXQUATERNION(0, 0, 0.707f, -.707f); D3DXQUATERNION Q1 = D3DXQUATERNION(0, 0, 0.000f, 1.000f); D3DXQUATERNION Q2 = D3DXQUATERNION(0, 0, 0.707f, 0.707f); D3DXQUATERNION Q3 = D3DXQUATERNION(0, 0, 1.000f, 0.000f); D3DXQUATERNION A, B, C, Qt; FLOAT time = 0.5f; D3DXQuaternionSquadSetup(&A;, &B;, &C;, &Q0;, &Q1;, &Q2;, &Q3;); D3DXQuaternionSquad(&Qt;, &Q1;, &A;, &B;, &C;, time); Note: C is +/- Q2 depending on the result of the function Qt is the result of the function The result is a rotation of 45 degrees around the z axis for time = 0.5.
Requirements
Header: Declared in D3dx8math.h.
Import Library: Use D3dx8.lib.