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.

See Also

D3DXQuaternionSquad