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#include "hamilton-tools.h"
#include <cmath>
double VectorLength(const tVector& v)
{
return(sqrt(v.v[0]*v.v[0] + v.v[1]*v.v[1] + v.v[2]*v.v[2]));
}
double sqr(const double v) { return(v*v); }
double VectorDistance(const double v1[], const tVector& v2)
{
return(sqrt(sqr(v2.v[0]-v1[0])+sqr(v2.v[1]-v1[1])+sqr(v2.v[2]-v1[2])));
}
tVector Lerp(const tVector& s, const double d[], const double alpha)
{
tVector V;
V.v[0] = s.v[0] + (d[0] - s.v[0]) * alpha;
V.v[1] = s.v[1] + (d[1] - s.v[1]) * alpha;
V.v[2] = s.v[2] + (d[2] - s.v[2]) * alpha;
return(V);
}
tQuat QuatFromAngleAxe(const double angle, const tVector& axe)
{
double a = TO_RAD * 0.5 * angle;
double d = sin(a) / VectorLength(axe);
return ( tQuat (
axe.v[0] * d,
axe.v[1] * d,
axe.v[2] * d,
cos(a)
)
);
}
tQuat QuatMultiply(const tQuat& qL, const tQuat& qR)
{
tQuat Q;
Q.x = qL.w*qR.x + qL.x*qR.w + qL.y*qR.z - qL.z*qR.y;
Q.y = qL.w*qR.y + qL.y*qR.w + qL.z*qR.x - qL.x*qR.z;
Q.z = qL.w*qR.z + qL.z*qR.w + qL.x*qR.y - qL.y*qR.x;
Q.w = qL.w*qR.w - qL.x*qR.x - qL.y*qR.y - qL.z*qR.z;
return(Q);
}
double AngleBetween(const tQuat& S, const tQuat& D)
{
return( TO_DEG * 2*acos(fabs(S.x*D.x + S.y*D.y + S.z*D.z + S.w*D.w)) );
}
tQuat QuatFromYPR(const double YPR[])
{
tQuat Q, Qp, Qy;
Q = QuatFromAngleAxe( -YPR[2], {0, 0, 1} ); //Roll, Z axe
Qp = QuatFromAngleAxe( -YPR[1], {1, 0, 0} ); //Pitch, X axe
Qy = QuatFromAngleAxe( -YPR[0], {0, 1, 0} ); //Yaw, Y axe
Q = QuatMultiply(Qp, Q);
return(QuatMultiply(Qy, Q));
}
void Normalize(tQuat& Q)
{
double m = sqrt(Q.x*Q.x + Q.y*Q.y + Q.z*Q.z + Q.w*Q.w);
if (m > EPSILON)
{
m = 1 / m;
Q.x = Q.x * m;
Q.y = Q.y * m;
Q.z = Q.z * m;
Q.w = Q.w * m;
}
else Q = tQuat(0, 0, 0, 1);
}
tQuat Slerp(const tQuat& S, const tQuat& D, const double alpha)
{
// calc cosine of half angle
double cosin = S.x*D.x + S.y*D.y + S.z*D.z + S.w*D.w;
// select nearest rotation direction
tQuat Q;
if (cosin < 0)
{
cosin = - cosin;
Q.x = - D.x;
Q.y = - D.y;
Q.z = - D.z;
Q.w = - D.w;
}
else Q = D;
// calculate coefficients
double scale0, scale1;
if ((1.0 - cosin) > EPSILON)
{
double omega = acos(cosin);
double sinus = 1 / sin(omega);
scale0 = sin((1.0 - alpha) * omega) * sinus;
scale1 = sin(alpha * omega)* sinus;
}
else
{
scale0 = 1.0 - alpha;
scale1 = alpha;
}
Q.x = scale0 * S.x + scale1 * Q.x;
Q.y = scale0 * S.y + scale1 * Q.y;
Q.z = scale0 * S.z + scale1 * Q.z;
Q.w = scale0 * S.w + scale1 * Q.w;
Normalize(Q);
return( Q );
}
void QuatToYPR(const tQuat& Q, double YPR[])
{
const double xx = Q.x * Q.x;
const double xy = Q.x * Q.y;
const double xz = Q.x * Q.z;
const double xw = Q.x * Q.w;
const double yy = Q.y * Q.y;
const double yz = Q.y * Q.z;
const double yw = Q.y * Q.w;
const double zz = Q.z * Q.z;
const double zw = Q.z * Q.w;
YPR[0] = TO_DEG * ( -atan2( 2 * ( xz + yw ), 1 - 2 * ( xx + yy ) ));
YPR[1] = TO_DEG * ( asin ( 2 * ( yz - xw ) ));
YPR[2] = TO_DEG * ( -atan2( 2 * ( xy + zw ), 1 - 2 * ( xx + zz ) ));
}
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