quaternion.h~
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#include "rts/math/matrix.h"
#ifndef RTS_QUATERNION_H
#define RTS_QUATERNION_H
namespace rts{
template<typename T>
class quaternion
{
public:
T w;
T x;
T y;
T z;
void normalize();
void CreateRotation(T theta, T axis_x, T axis_y, T axis_z);
void CreateRotation(T theta, vector<T, 3> axis);
quaternion<T> operator*(quaternion<T> &rhs);
matrix<T, 3> toMatrix3();
matrix<T, 4> toMatrix4();
quaternion();
quaternion(T w, T x, T y, T z);
};
template<typename T>
void quaternion<T>::normalize()
{
double length=sqrt(w*w + x*x + y*y + z*z);
w=w/length;
x=x/length;
y=y/length;
z=z/length;
}
template<typename T>
void quaternion<T>::CreateRotation(T theta, T axis_x, T axis_y, T axis_z)
{
//assign the given Euler rotation to this quaternion
w = (T)cos(theta/2.0);
x = axis_x*(T)sin(theta/2.0);
y = axis_y*(T)sin(theta/2.0);
z = axis_z*(T)sin(theta/2.0);
}
template<typename T>
void quaternion<T>::CreateRotation(T theta, vector<T, 3> axis)
{
CreateRotation(theta, axis[0], axis[1], axis[2]);
}
template<typename T>
quaternion<T> quaternion<T>::operator *(quaternion<T> ¶m)
{
float A, B, C, D, E, F, G, H;
A = (w + x)*(param.w + param.x);
B = (z - y)*(param.y - param.z);
C = (w - x)*(param.y + param.z);
D = (y + z)*(param.w - param.x);
E = (x + z)*(param.x + param.y);
F = (x - z)*(param.x - param.y);
G = (w + y)*(param.w - param.z);
H = (w - y)*(param.w + param.z);
quaternion<T> result;
result.w = B + (-E - F + G + H) /2;
result.x = A - (E + F + G + H)/2;
result.y = C + (E - F + G - H)/2;
result.z = D + (E - F - G + H)/2;
return result;
}
template<typename T>
matrix<T, 3> quaternion<T>::toMatrix3()
{
matrix<T, 3> result;
T wx, wy, wz, xx, yy, yz, xy, xz, zz, x2, y2, z2;
// calculate coefficients
x2 = x + x; y2 = y + y;
z2 = z + z;
xx = x * x2; xy = x * y2; xz = x * z2;
yy = y * y2; yz = y * z2; zz = z * z2;
wx = w * x2; wy = w * y2; wz = w * z2;
result(0, 0) = (T)1.0 - (yy + zz);
result(0, 1) = xy - wz;
result(0, 2) = xz + wy;
result(1, 0) = xy + wz;
result(1, 1) = (T)1.0 - (xx + zz);
result(1, 2) = yz - wx;
result(2, 0) = xz - wy;
result(2, 1) = yz + wx;
result(2, 2) = (T)1.0 - (xx + yy);
return result;
}
template<typename T>
matrix<T, 4> quaternion<T>::toMatrix4()
{
matrix<T, 4> result;
T wx, wy, wz, xx, yy, yz, xy, xz, zz, x2, y2, z2;
// calculate coefficients
x2 = x + x; y2 = y + y;
z2 = z + z;
xx = x * x2; xy = x * y2; xz = x * z2;
yy = y * y2; yz = y * z2; zz = z * z2;
wx = w * x2; wy = w * y2; wz = w * z2;
result(0, 0) = (T)1.0 - (yy + zz);
result(0, 1) = xy - wz;
result(0, 2) = xz + wy;
result(1, 0) = xy + wz;
result(1, 1) = (T)1.0 - (xx + zz);
result(1, 2) = yz - wx;
result(2, 0) = xz - wy;
result(2, 1) = yz + wx;
result(2, 2) = (T)1.0 - (xx + yy);
result(3, 3) = (T)1.0;
return result;
}
template<typename T>
quaternion<T>::quaternion()
{
w=0.0; x=0.0; y=0.0; z=0.0;
}
template<typename T>
quaternion<T>::quaternion(T c, T i, T j, T k)
{
w=c; x=i; y=j; z=k;
}
} //end rts namespace
#if __GNUC__ > 3 && __GNUC_MINOR__ > 7
template<class T> using rtsQuaternion = rts::quaternion<T>;
#endif
#endif