void Intermediate ( Quaternion* q0, Quaternion* q1, Quaternion* q2,
Quaternion* a, Quaternion* b)
{
/* assert: q0, q1, q2 are unit quaternions */
/*Quaternion q0inv = q0.UnitInverse();
Quaternion q1inv = q1.UnitInverse();
Quaternion p0 = q0inv*q1;
Quaternion p1 = q1inv*q2;
Quaternion arg = 0.25*(p0.Log()-p1.Log());
Quaternion marg = -arg;
a = q1*arg.Exp();
b = q1*marg.Exp();
*/
Quaternion p0, p1;
UnitInverse(&p0, q0);
UnitInverse(&p1, q1);
MulSelf(&p0, q1);
MulSelf(&p1, q2);
LogSelf(&p0);
LogSelf(&p1);
Sub(a,&p0, &p1);
MulScalSelf(a, 0.25);
Neg(b, a);
ExpSelf(a);
ExpSelf(b);
Mul(a, q1, a);
Mul(b, q1, b);
}
/*-------------------------------------------------------------------------*/
void* KB_RotInitialize (int numKeys, RotationKey* key)
{
double omt0, omc0, opc0, omb0, opb0, adj0, out0, out1;
double omt1, omc1, opc1, omb1, opb1, adj1, in0, in1;
int i0 = 0, i1 = 1, i2 = 2, i3 = 3;
Quaternion q0, q1, q2, q3;
Quaternion prod;
Quaternion logdq, Tout, Tin, arg0, arg1;
/* assert: numKeys >= 4 */
SplineInfo* info = (SplineInfo*) calloc( 1, sizeof(SplineInfo));
info->numPolys = numKeys-3;
info->si = (SquadInfo*) calloc(info->numPolys, sizeof( SquadInfo ) );
for (/**/; i0 < info->numPolys; i0++, i1++, i2++, i3++)
{
FromAngleAxis(&q0, key[i0].Rot.angle,key[i0].Rot.x,key[i0].Rot.y,
key[i0].Rot.z);
FromAngleAxis(&q1, key[i1].Rot.angle,key[i1].Rot.x,key[i1].Rot.y,
key[i1].Rot.z);
FromAngleAxis(&q2, key[i2].Rot.angle,key[i2].Rot.x,key[i2].Rot.y,
key[i2].Rot.z);
FromAngleAxis(&q3, key[i3].Rot.angle,key[i3].Rot.x,key[i3].Rot.y,
key[i3].Rot.z);
/* arrange for consecutive quaternions to have acute angle */
if ( Dot(&q1, &q2) < 0.0 )
{
/*q2 = -q2;*/
NegSelf(&q2);
ToAngleAxis(&q2, &(key[i2].Rot.angle),&(key[i2].Rot.x),&(key[i2].Rot.y),
&(key[i2].Rot.z));
}
/* build log(q[i1]^{-1}*q[i2]) */
/* prod = q1.UnitInverse()*q2; */
UnitInverse(&prod, &q1); MulSelf(&prod, &q2);
/* logdq = prod.Log(); */
Log(&logdq, &prod);
/* build multipliers at q[i1] */
omt0 = 1-key[i1].tension;
omc0 = 1-key[i1].continuity;
opc0 = 1+key[i1].continuity;
omb0 = 1-key[i1].bias;
opb0 = 1+key[i1].bias;
adj0 = 2*(key[i2].t-key[i1].t)/(key[i2].t-key[i0].t);
out0 = 0.5*adj0*omt0*opc0*opb0;
out1 = 0.5*adj0*omt0*omc0*omb0;
/* build outgoing tangent at q[i1] */
/* prod = q0.UnitInverse()*q1; */
UnitInverse(&prod, &q0); MulSelf(&prod, &q1);
/* Quaternion Tout = out1*logdq+out0*prod.Log(); */
MulScal(&Tout, &logdq, out1); LogSelf(&prod); MulScal(&prod, &prod, out0);
AddSelf(&Tout, &prod);
/* build multipliers at q[i2] */
omt1 = 1-key[i2].tension;
omc1 = 1-key[i2].continuity;
opc1 = 1+key[i2].continuity;
omb1 = 1-key[i2].bias;
opb1 = 1+key[i2].bias;
adj1 = 2*(key[i2].t-key[i1].t)/(key[i3].t-key[i1].t);
in0 = 0.5*adj1*omt1*omc1*opb1;
in1 = 0.5*adj1*omt1*opc1*omb1;
/* build incoming tangent at q[i2] */
/* prod = q2.UnitInverse()*q3; */
UnitInverse(&prod, &q2); MulSelf(&prod, &q3);
/* Quaternion Tin = in1*prod.Log()+in0*logdq; */
MulScal(&Tin, &logdq, in0); LogSelf(&prod); MulScal(&prod, &prod, in1);
AddSelf(&Tin, &prod);
/*info->si[i0].p = q1;*/
SetQuat(&(info->si[i0].p), &q1);
/*info->si[i0].q = q2; */
SetQuat(&(info->si[i0].q), &q2);
/* Quaternion arg0 = 0.5*(Tout-logdq); */
Sub(&arg0, &Tout, &logdq); MulScalSelf(&arg0, 0.5);
/* Quaternion arg1 = 0.5*(logdq-Tin); */
Sub(&arg1, &logdq, &Tin); MulScalSelf(&arg1, 0.5);
/* info->si[i0].a = q1*arg0.Exp(); */
/* info->si[i0].b = q2*arg1.Exp(); */
ExpSelf(&arg0); Mul(&(info->si[i0].a), &q1, &arg0);
ExpSelf(&arg1); Mul(&(info->si[i0].b), &q2, &arg1);
info->si[i0].tmin = key[i1].t;
info->si[i0].tmax = key[i2].t;
info->si[i0].trange = info->si[i0].tmax-info->si[i0].tmin;
}
return info;
}