NazaraEngine/include/Nazara/Math/Quaternion.inl

// Copyright (C) 2012 Rémi Bèges - Jérôme Leclercq
// This file is part of the "Nazara Engine - Mathematics module"
// For conditions of distribution and use, see copyright notice in Config.hpp

#include <Nazara/Core/StringStream.hpp>
#include <Nazara/Math/Basic.hpp>
#include <Nazara/Math/Config.hpp>
#include <Nazara/Math/EulerAngles.hpp>
#include <Nazara/Math/Vector3.hpp>
#include <limits>
#include <Nazara/Core/Debug.hpp>

#define F(a) static_cast<T>(a)

template<typename T>
NzQuaternion<T>::NzQuaternion()
{
}

template<typename T>
NzQuaternion<T>::NzQuaternion(T W, T X, T Y, T Z)
{
	Set(W, X, Y, Z);
}

template<typename T>
NzQuaternion<T>::NzQuaternion(T quat[4])
{
	Set(quat);
}

template<typename T>
NzQuaternion<T>::NzQuaternion(T angle, const NzVector3<T>& axis)
{
	Set(angle, axis);
}

template<typename T>
NzQuaternion<T>::NzQuaternion(const NzEulerAngles<T>& angles)
{
	Set(angles);
}
/*
template<typename T>
NzQuaternion<T>::NzQuaternion(const NzMatrix3<T>& mat)
{
	Set(mat);
}
*/
template<typename T>
template<typename U>
NzQuaternion<T>::NzQuaternion(const NzQuaternion<U>& quat)
{
	Set(quat);
}

template<typename T>
T NzQuaternion<T>::DotProduct(const NzQuaternion& quat) const
{
	return w*quat.w + x*quat.x + y*quat.y + z*quat.z;
}

template<typename T>
NzQuaternion<T> NzQuaternion<T>::GetConjugate() const
{
	return NzQuaternion(w, -x, -y, -z);
}

template<typename T>
NzQuaternion<T> NzQuaternion<T>::GetNormalized() const
{
	NzQuaternion<T> quat(*this);
	quat.Normalize();

	return quat;
}

template<typename T>
void NzQuaternion<T>::MakeIdentity()
{
	Set(1.0, 0.0, 0.0, 0.0);
}

template<typename T>
void NzQuaternion<T>::MakeZero()
{
	Set(0.0, 0.0, 0.0, 0.0);
}

template<typename T>
T NzQuaternion<T>::Magnitude() const
{
	return std::sqrt(SquaredMagnitude());
}

template<typename T>
T NzQuaternion<T>::Normalize()
{
	T squaredMagnitude = SquaredMagnitude();

	if (squaredMagnitude-F(1.0) > std::numeric_limits<T>::epsilon())
	{
		T magnitude = std::sqrt(squaredMagnitude);

		w /= magnitude;
		x /= magnitude;
		y /= magnitude;
		z /= magnitude;

		return magnitude;
	}
	else
		return F(1.0); // Le quaternion est déjà normalisé
}

template<typename T>
void NzQuaternion<T>::Set(T W, T X, T Y, T Z)
{
	w = W;
	x = X;
	y = Y;
	z = Z;
}

template<typename T>
void NzQuaternion<T>::Set(T quat[4])
{
	w = quat[0];
	x = quat[1];
	y = quat[2];
	z = quat[3];
}

template<typename T>
void NzQuaternion<T>::Set(T angle, const NzVector3<T>& normalizedAxis)
{
	#if !NAZARA_MATH_ANGLE_RADIAN
	angle = NzDegreeToRadian(angle);
	#endif

	angle /= 2;

	auto sinAngle = std::sin(angle);

	w = std::cos(angle);
	x = normalizedAxis.x * sinAngle;
	y = normalizedAxis.y * sinAngle;
	z = normalizedAxis.z * sinAngle;
}

template<typename T>
void NzQuaternion<T>::Set(const NzEulerAngles<T>& angles)
{
	Set(angles.ToQuaternion());
}

template<typename T>
template<typename U>
void NzQuaternion<T>::Set(const NzQuaternion<U>& quat)
{
	w = static_cast<T>(quat.w);
	x = static_cast<T>(quat.x);
	y = static_cast<T>(quat.y);
	z = static_cast<T>(quat.z);
}

template<typename T>
void NzQuaternion<T>::Set(const NzQuaternion& quat)
{
	w = quat.w;
	x = quat.x;
	y = quat.y;
	z = quat.z;
}

template<typename T>
T NzQuaternion<T>::SquaredMagnitude() const
{
	return w*w + x*x + y*y + z*z;
}

template<typename T>
NzEulerAngles<T> NzQuaternion<T>::ToEulerAngles() const
{
	T test = x*y + z*w;
	if (test > F(0.499))
		// singularity at north pole
		return NzEulerAngles<T>(NzDegrees(F(90.0)), NzRadians(F(2.0) * std::atan2(x, w)), F(0.0));

	if (test < F(-0.499))
		return NzEulerAngles<T>(NzDegrees(F(-90.0)), NzRadians(F(-2.0) * std::atan2(x, w)), F(0.0));

	T xx = x*x;
	T yy = y*y;
	T zz = z*z;

	return NzEulerAngles<T>(NzRadians(std::atan2(F(2.0)*x*w - F(2.0)*y*z, F(1.0) - F(2.0)*xx - F(2.0)*zz)),
							NzRadians(std::atan2(F(2.0)*y*w - F(2.0)*x*z, F(1.0) - F(2.0)*yy - F(2.0)*zz)),
							NzRadians(std::asin(F(2.0)*test)));
}

template<typename T>
NzString NzQuaternion<T>::ToString() const
{
	NzStringStream ss;

	return ss << "Quaternion(" << w << " | " << x << ", " << y << ", " << z << ')';
}

template<typename T>
NzQuaternion<T>::operator NzString() const
{
	return ToString();
}

template<typename T>
NzQuaternion<T>& NzQuaternion<T>::operator=(const NzQuaternion& quat)
{
	Set(quat);

	return *this;
}

template<typename T>
NzQuaternion<T> NzQuaternion<T>::operator+(const NzQuaternion& quat) const
{
	return NzQuaternion(w + quat.w,
	                    x + quat.x,
	                    y + quat.y,
	                    z + quat.z);
}

template<typename T>
NzQuaternion<T> NzQuaternion<T>::operator*(const NzQuaternion& quat) const
{
	return NzQuaternion(w*quat.w - x*quat.x - y*quat.y - z*quat.z,
	                    w*quat.x + x*quat.w + y*quat.z - z*quat.y,
	                    w*quat.y + y*quat.w + z*quat.x - x*quat.z,
	                    w*quat.z + z*quat.w + x*quat.y - y*quat.x);
}

template<typename T>
NzVector3<T> NzQuaternion<T>::operator*(const NzVector3<T>& vec) const
{
	NzVector3<T> normal(vec);
	normal.Normalize();

	NzQuaternion qvec(0.0, normal.x, normal.y, normal.z);
	NzQuaternion result(operator*(qvec * GetConjugate()));

	return NzVector3<T>(result.x, result.y, result.z);

}

template<typename T>
NzQuaternion<T> NzQuaternion<T>::operator*(T scale) const
{
	return NzQuaternion(w * scale,
						x * scale,
						y * scale,
						z * scale);
}

template<typename T>
NzQuaternion<T> NzQuaternion<T>::operator/(const NzQuaternion& quat) const
{
	return GetConjugate(quat) * (*this);
}

template<typename T>
NzQuaternion<T>& NzQuaternion<T>::operator+=(const NzQuaternion& quat)
{
	return operator=(operator+(quat));
}

template<typename T>
NzQuaternion<T>& NzQuaternion<T>::operator*=(const NzQuaternion& quat)
{
	return operator=(operator*(quat));
}

template<typename T>
NzQuaternion<T>& NzQuaternion<T>::operator*=(T scale)
{
	return operator=(operator*(scale));
}

template<typename T>
NzQuaternion<T>& NzQuaternion<T>::operator/=(const NzQuaternion& quat)
{
	return operator=(operator/(quat));
}

template<typename T>
bool NzQuaternion<T>::operator==(const NzQuaternion& quat) const
{
	return NzNumberEquals(w, quat.w) &&
		   NzNumberEquals(x, quat.x) &&
		   NzNumberEquals(y, quat.y) &&
		   NzNumberEquals(z, quat.z);
}

template<typename T>
bool NzQuaternion<T>::operator!=(const NzQuaternion& quat) const
{
	return !operator==(quat);
}

template<typename T>
bool NzQuaternion<T>::operator<(const NzQuaternion& quat) const
{
	 return w < quat.w && x < quat.x && y < quat.y && z < quat.z;
}

template<typename T>
bool NzQuaternion<T>::operator<=(const NzQuaternion& quat) const
{
	return operator<(quat) || operator==(quat);
}

template<typename T>
bool NzQuaternion<T>::operator>(const NzQuaternion& quat) const
{
	return !operator<=(quat);
}

template<typename T>
bool NzQuaternion<T>::operator>=(const NzQuaternion& quat) const
{
	return !operator<(quat);
}

template<typename T>
NzQuaternion<T> NzQuaternion<T>::Identity()
{
	NzQuaternion quaternion;
	quaternion.MakeIdentity();

	return quaternion;
}

template<typename T>
NzQuaternion<T> NzQuaternion<T>::Slerp(const NzQuaternion& quatA, const NzQuaternion& quatB, T interp)
{
	if (interp <= F(0.0))
		return quatA;

	if (interp >= F(1.0))
		return quatB;

	NzQuaternion q;

	T cosOmega = quatA.DotProduct(quatB);
	if (cosOmega < F(0.0))
	{
		// On inverse tout
		q.Set(-quatB.w, -quatB.x, -quatB.y, -quatB.z);
		cosOmega = -cosOmega;
	}
	else
		q.Set(quatB);

	T k0, k1;
	if (cosOmega > F(0.9999))
	{
		// Interpolation linéaire pour éviter une division par zéro
        k0 = F(1.0) - interp;
        k1 = interp;
    }
    else
    {
        T sinOmega = std::sqrt(F(1.0) - cosOmega*cosOmega);
        T omega = std::atan2(sinOmega, cosOmega);

		// Pour éviter deux divisions
		sinOmega = F(1.0)/sinOmega;

        k0 = std::sin((F(1.0) - interp) * omega) * sinOmega;
        k1 = std::sin(interp*omega) * sinOmega;
    }

    NzQuaternion result(k0 * quatA.w, k0 * quatA.x, k0 * quatA.y, k0 * quatA.z);
    return result += q*k1;
}

template<typename T>
NzQuaternion<T> NzQuaternion<T>::Zero()
{
	NzQuaternion quaternion;
	quaternion.MakeZero();

	return quaternion;
}

template<typename T>
std::ostream& operator<<(std::ostream& out, const NzQuaternion<T>& quat)
{
	return out << quat.ToString();
}

#undef F

#include <Nazara/Core/DebugOff.hpp>