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template<class T>
class quaternion_base
{
public:
T k[4];
/*void Unit()
{
k[0] = 0;
k[1] = 0;
k[2] = 0;
k[3] = 1;
}*/
inline quaternion_base(){}
inline quaternion_base(T x, T y, T z, T w)
{
k[0] = x;
k[1] = y;
k[2] = z;
k[3] = w;
}
inline quaternion_base(vector3_base<T> axis, T angle)
{
T sin_angle = sin(angle * (T)0.5);
T cos_angle = cos(angle * (T)0.5);
k[0] = axis.x * sin_angle;
k[1] = axis.y * sin_angle;
k[2] = axis.z * sin_angle;
k[3] = cos_angle;
}
T magnitude()
{
return sqrt(k[0] * k[0] + k[1] * k[1] + k[2] * k[2] + k[3] * k[3]);
}
matrix4_base<T> create_matrix() const
{
matrix4_base<T> mat;
T xx = k[0] * k[0];
T xy = k[0] * k[1];
T xz = k[0] * k[2];
T xw = k[0] * k[3];
T yy = k[1] * k[1];
T yz = k[1] * k[2];
T yw = k[1] * k[3];
T zz = k[2] * k[2];
T zw = k[2] * k[3];
mat.k[0][0] = 1 - 2 * (yy + zz);
mat.k[0][1] = 2 * (xy + zw);
mat.k[0][2] = 2 * (xz - yw);
mat.k[0][3] = 0;
mat.k[1][0] = 2 * (xy - zw);
mat.k[1][1] = 1 - 2 * (xx + zz);
mat.k[1][2] = 2 * (yz + xw);
mat.k[1][3] = 0;
mat.k[2][0] = 2 * (xz + yw);
mat.k[2][1] = 2 * (yz - xw);
mat.k[2][2] = 1 - 2 * (xx + yy);
mat.k[2][3] = 0;
mat.k[3][0] = 0;
mat.k[3][1] = 0;
mat.k[3][2] = 0;
mat.k[3][3] = 1;
}
/*
void CreateDOOM(T x, T y, T z)
{
k[0] = x;
k[1] = y;
k[2] = z;
T Term = 1 - (x * x) - (y * y) - (z * z);
if (Term < 0)
k[3] = 0;
else
k[3] = -sqrt(Term);
Normalize();
}
T DotProd(const TQuaternion<T>& Quat) const
{
return (k[0] * Quat.k[0] + k[1] * Quat.k[1] + k[2] * Quat.k[2] + k[3] * Quat.k[3]);
}
void Interpolate(const TQuaternion<T>& Quat, TQuaternion& Dest, T Scale)
{
T Separation = k[0] * Quat.k[0] + k[1] * Quat.k[1] + k[2] * Quat.k[2] + k[3] * Quat.k[3];
T Factor1,Factor2;
if (Separation > 1)
Separation = 1;
if (Separation < -1)
Separation = -1;
Separation = acos(Separation);
if (Separation == 0 || Separation == pi)
{
Factor1 = 1;
Factor2 = 0;
}
else
{
Factor1 = sin((1 - Scale)*Separation) / sin(Separation);
Factor2 = sin(Scale * Separation) / sin(Separation);
}
Dest.k[0] = k[0] * Factor1 + Quat.k[0] * Factor2;
Dest.k[1] = k[1] * Factor1 + Quat.k[1] * Factor2;
Dest.k[2] = k[2] * Factor1 + Quat.k[2] * Factor2;
Dest.k[3] = k[3] * Factor1 + Quat.k[3] * Factor2;
}
void Slerp(const TQuaternion<T>& Quat, TQuaternion& Dest, T Scale) const
{
T Sq1,Sq2;
T Dot = DotProd(Quat);
TQuaternion Temp;
if (Dot < 0.0f)
{
Dot = -Dot;
Temp.k[0] = -Quat.k[0];
Temp.k[1] = -Quat.k[1];
Temp.k[2] = -Quat.k[2];
Temp.k[3] = -Quat.k[3];
}
else
{
Temp = Quat;
}
if ((1.0 + Dot) > 0.00001)
{
if ((1.0 - Dot) > 0.00001)
{
T om = (T)acos(Dot);
T rsinom = (T)(1.0f / sin(om));
Sq1 = (T)sin(((T)1.0 - Scale) * om) * rsinom;
Sq2 = (T)sin(Scale * om) * rsinom;
}
else
{
Sq1 = (T)(1.0 - Scale);
Sq2 = Scale;
}
Dest.k[0] = Sq1 * k[0] + Sq2 * Temp[0];
Dest.k[1] = Sq1 * k[1] + Sq2 * Temp[1];
Dest.k[2] = Sq1 * k[2] + Sq2 * Temp[2];
Dest.k[3] = Sq1 * k[3] + Sq2 * Temp[3];
}
else
{
Sq1 = (T)sin(((T)1.0 - Scale) * (T)0.5 * pi);
Sq2 = (T)sin(Scale * (T)0.5 * pi);
Dest.k[0] = Sq1 * k[0] + Sq2 * Temp[1];
Dest.k[1] = Sq1 * k[1] + Sq2 * Temp[0];
Dest.k[2] = Sq1 * k[2] + Sq2 * Temp[3];
Dest.k[3] = Sq1 * k[3] + Sq2 * Temp[2];
}
}*/
// perators
T& operator [] (int i) { return k[i]; }
// quaternion multiply
quaternion_base operator *(const quaternion_base& other) const
{
// (w1 dot w2 - v1 dot v2, w1 dot v2 + w2 dot v1 + v1 cross v2)
quaternion_base r;
r.k[0] = k[3] * other.k[0] + k[0] * other.k[3] + k[1] * other.k[2] - k[2] * other.k[1];
r.k[1] = k[3] * other.k[1] + k[1] * other.k[3] + k[2] * other.k[0] - k[0] * other.k[2];
r.k[2] = k[3] * other.k[2] + k[2] * other.k[3] + k[0] * other.k[1] - k[1] * other.k[0];
r.k[3] = k[3] * other.k[3] - k[0] * other.k[0] - k[1] * other.k[1] - k[2] * other.k[2];
return normalize(r);
}
/*
bool operator == (const quaternion_base<T>& t) const { return ((k[0] == t.k[0]) && (k[1] == t.k[1]) && (k[2] == t.k[2]) && (k[3] == t.k[3])); }
bool operator != (const quaternion_base<T>& t) const { return ((k[0] != t.k[0]) || (k[1] != t.k[1]) || (k[2] != t.k[2]) || (k[3] != t.k[3])); }
void operator = (const quaternion_base<T>& other) { k[0] = other.k[0]; k[1] = other.k[1]; k[2] = other.k[2]; k[3] = other.k[3]; }
*/
/*void operator *= (const TQuaternion<T>& t) { TQuaternion Temp = Multiply(t); *this = Temp; }
TQuaternion operator * (const TQuaternion<T>& t) const { return Multiply(t); }
*/
};
template<typename T>
inline quaternion_base<T> normalize(const quaternion_base<T> &v)
{
T factor = 1.0f/v.magnitude();
return quaternion_base<T>(v.k[0]*factor, v.k[1]*factor,v. k[2]*factor,v. k[3]*factor);
}
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