429 lines
9.0 KiB
C++
429 lines
9.0 KiB
C++
// Copyright (C) 2012 Rémi Bèges - Jérôme Leclercq
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// This file is part of the "Nazara Engine - Mathematics module"
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// For conditions of distribution and use, see copyright notice in Config.hpp
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#include <Nazara/Core/StringStream.hpp>
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#include <Nazara/Math/Basic.hpp>
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#include <Nazara/Math/Config.hpp>
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#include <Nazara/Math/EulerAngles.hpp>
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#include <Nazara/Math/Vector3.hpp>
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#include <limits>
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#include <Nazara/Core/Debug.hpp>
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#define F(a) static_cast<T>(a)
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template<typename T>
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NzQuaternion<T>::NzQuaternion()
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{
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}
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template<typename T>
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NzQuaternion<T>::NzQuaternion(T W, T X, T Y, T Z)
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{
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Set(W, X, Y, Z);
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}
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template<typename T>
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NzQuaternion<T>::NzQuaternion(T quat[4])
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{
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Set(quat);
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}
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template<typename T>
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NzQuaternion<T>::NzQuaternion(T angle, const NzVector3<T>& axis)
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{
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Set(angle, axis);
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}
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template<typename T>
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NzQuaternion<T>::NzQuaternion(const NzEulerAngles<T>& angles)
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{
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Set(angles);
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}
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/*
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template<typename T>
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NzQuaternion<T>::NzQuaternion(const NzMatrix3<T>& mat)
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{
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Set(mat);
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}
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*/
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template<typename T>
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template<typename U>
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NzQuaternion<T>::NzQuaternion(const NzQuaternion<U>& quat)
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{
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Set(quat);
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}
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template<typename T>
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T NzQuaternion<T>::DotProduct(const NzQuaternion& quat) const
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{
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return w*quat.w + x*quat.x + y*quat.y + z*quat.z;
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}
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template<typename T>
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NzQuaternion<T> NzQuaternion<T>::GetConjugate() const
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{
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return NzQuaternion(w, -x, -y, -z);
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}
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template<typename T>
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NzQuaternion<T> NzQuaternion<T>::GetInverse() const
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{
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NzQuaternion<T> quat(*this);
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quat.Inverse();
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return quat;
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}
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template<typename T>
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NzQuaternion<T> NzQuaternion<T>::GetNormal() const
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{
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NzQuaternion<T> quat(*this);
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quat.Normalize();
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return quat;
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}
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template<typename T>
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void NzQuaternion<T>::Inverse()
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{
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T norm = SquaredMagnitude();
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if (norm > F(0.0))
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{
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T invNorm = F(1.0) / norm;
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w *= invNorm;
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x *= -invNorm;
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y *= -invNorm;
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z *= -invNorm;
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}
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}
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template<typename T>
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void NzQuaternion<T>::MakeIdentity()
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{
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Set(F(1.0), F(0.0), F(0.0), F(0.0));
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}
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template<typename T>
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void NzQuaternion<T>::MakeZero()
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{
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Set(F(0.0), F(0.0), F(0.0), F(0.0));
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}
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template<typename T>
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T NzQuaternion<T>::Magnitude() const
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{
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return std::sqrt(SquaredMagnitude());
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}
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template<typename T>
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T NzQuaternion<T>::Normalize()
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{
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T squaredMagnitude = SquaredMagnitude();
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// Inutile de vérifier si la magnitude au carrée est négative (Elle ne peut pas l'être)
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if (!NzNumberEquals(squaredMagnitude, F(1.0)))
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{
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T norm = std::sqrt(squaredMagnitude);
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T invNorm = F(1.0) / norm;
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w *= invNorm;
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x *= invNorm;
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y *= invNorm;
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z *= invNorm;
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return norm;
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}
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else
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return F(1.0); // Le quaternion est déjà normalisé
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}
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template<typename T>
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void NzQuaternion<T>::Set(T W, T X, T Y, T Z)
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{
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w = W;
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x = X;
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y = Y;
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z = Z;
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}
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template<typename T>
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void NzQuaternion<T>::Set(T quat[4])
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{
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w = quat[0];
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x = quat[1];
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y = quat[2];
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z = quat[3];
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}
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template<typename T>
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void NzQuaternion<T>::Set(T angle, const NzVector3<T>& axis)
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{
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angle /= F(2.0);
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#if !NAZARA_MATH_ANGLE_RADIAN
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angle = NzDegreeToRadian(angle);
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#endif
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NzVector3<T> normalizedAxis = axis.GetNormal();
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T sinAngle = std::sin(angle);
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w = std::cos(angle);
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x = normalizedAxis.x * sinAngle;
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y = normalizedAxis.y * sinAngle;
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z = normalizedAxis.z * sinAngle;
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Normalize();
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}
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template<typename T>
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void NzQuaternion<T>::Set(const NzEulerAngles<T>& angles)
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{
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Set(angles.ToQuaternion());
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}
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template<typename T>
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template<typename U>
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void NzQuaternion<T>::Set(const NzQuaternion<U>& quat)
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{
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w = static_cast<T>(quat.w);
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x = static_cast<T>(quat.x);
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y = static_cast<T>(quat.y);
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z = static_cast<T>(quat.z);
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}
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template<typename T>
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void NzQuaternion<T>::Set(const NzQuaternion& quat)
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{
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w = quat.w;
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x = quat.x;
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y = quat.y;
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z = quat.z;
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}
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template<typename T>
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T NzQuaternion<T>::SquaredMagnitude() const
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{
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return w*w + x*x + y*y + z*z;
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}
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template<typename T>
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NzEulerAngles<T> NzQuaternion<T>::ToEulerAngles() const
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{
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T test = x*y + z*w;
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if (test > F(0.499))
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// singularity at north pole
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return NzEulerAngles<T>(NzDegrees(F(90.0)), NzRadians(F(2.0) * std::atan2(x, w)), F(0.0));
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if (test < F(-0.499))
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return NzEulerAngles<T>(NzDegrees(F(-90.0)), NzRadians(F(-2.0) * std::atan2(x, w)), F(0.0));
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return NzEulerAngles<T>(NzRadians(std::atan2(F(2.0)*x*w - F(2.0)*y*z, F(1.0) - F(2.0)*x* - F(2.0)*z*z)),
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NzRadians(std::atan2(F(2.0)*y*w - F(2.0)*x*z, F(1.0) - F(2.0)*y*y - F(2.0)*z*z)),
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NzRadians(std::asin(F(2.0)*test)));
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}
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template<typename T>
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NzString NzQuaternion<T>::ToString() const
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{
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NzStringStream ss;
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return ss << "Quaternion(" << w << " | " << x << ", " << y << ", " << z << ')';
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}
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template<typename T>
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NzQuaternion<T>::operator NzString() const
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{
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return ToString();
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}
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template<typename T>
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NzQuaternion<T>& NzQuaternion<T>::operator=(const NzQuaternion& quat)
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{
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Set(quat);
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return *this;
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}
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template<typename T>
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NzQuaternion<T> NzQuaternion<T>::operator+(const NzQuaternion& quat) const
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{
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return NzQuaternion(w + quat.w,
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x + quat.x,
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y + quat.y,
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z + quat.z);
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}
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template<typename T>
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NzQuaternion<T> NzQuaternion<T>::operator*(const NzQuaternion& quat) const
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{
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return NzQuaternion(w*quat.w - x*quat.x - y*quat.y - z*quat.z,
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w*quat.x + x*quat.w + y*quat.z - z*quat.y,
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w*quat.y + y*quat.w + z*quat.x - x*quat.z,
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w*quat.z + z*quat.w + x*quat.y - y*quat.x);
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}
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template<typename T>
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NzVector3<T> NzQuaternion<T>::operator*(const NzVector3<T>& vec) const
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{
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NzVector3f quatVec(x, y, z);
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NzVector3f uv = quatVec.CrossProduct(vec);
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NzVector3f uuv = quatVec.CrossProduct(uv);
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uv *= F(2.0) * w;
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uuv *= F(2.0);
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return vec + uv + uuv;
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}
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template<typename T>
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NzQuaternion<T> NzQuaternion<T>::operator*(T scale) const
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{
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return NzQuaternion(w * scale,
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x * scale,
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y * scale,
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z * scale);
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}
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template<typename T>
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NzQuaternion<T> NzQuaternion<T>::operator/(const NzQuaternion& quat) const
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{
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return GetConjugate(quat) * (*this);
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}
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template<typename T>
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NzQuaternion<T>& NzQuaternion<T>::operator+=(const NzQuaternion& quat)
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{
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return operator=(operator+(quat));
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}
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template<typename T>
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NzQuaternion<T>& NzQuaternion<T>::operator*=(const NzQuaternion& quat)
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{
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return operator=(operator*(quat));
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}
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template<typename T>
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NzQuaternion<T>& NzQuaternion<T>::operator*=(T scale)
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{
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return operator=(operator*(scale));
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}
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template<typename T>
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NzQuaternion<T>& NzQuaternion<T>::operator/=(const NzQuaternion& quat)
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{
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return operator=(operator/(quat));
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}
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template<typename T>
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bool NzQuaternion<T>::operator==(const NzQuaternion& quat) const
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{
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return NzNumberEquals(w, quat.w) &&
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NzNumberEquals(x, quat.x) &&
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NzNumberEquals(y, quat.y) &&
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NzNumberEquals(z, quat.z);
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}
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template<typename T>
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bool NzQuaternion<T>::operator!=(const NzQuaternion& quat) const
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{
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return !operator==(quat);
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}
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template<typename T>
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bool NzQuaternion<T>::operator<(const NzQuaternion& quat) const
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{
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return w < quat.w && x < quat.x && y < quat.y && z < quat.z;
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}
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template<typename T>
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bool NzQuaternion<T>::operator<=(const NzQuaternion& quat) const
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{
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return operator<(quat) || operator==(quat);
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}
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template<typename T>
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bool NzQuaternion<T>::operator>(const NzQuaternion& quat) const
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{
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return !operator<=(quat);
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}
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template<typename T>
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bool NzQuaternion<T>::operator>=(const NzQuaternion& quat) const
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{
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return !operator<(quat);
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}
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template<typename T>
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NzQuaternion<T> NzQuaternion<T>::Identity()
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{
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NzQuaternion quaternion;
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quaternion.MakeIdentity();
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return quaternion;
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}
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template<typename T>
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NzQuaternion<T> NzQuaternion<T>::Slerp(const NzQuaternion& quatA, const NzQuaternion& quatB, T interp)
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{
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if (interp <= F(0.0))
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return quatA;
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if (interp >= F(1.0))
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return quatB;
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NzQuaternion q;
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T cosOmega = quatA.DotProduct(quatB);
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if (cosOmega < F(0.0))
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{
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// On inverse tout
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q.Set(-quatB.w, -quatB.x, -quatB.y, -quatB.z);
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cosOmega = -cosOmega;
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}
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else
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q.Set(quatB);
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T k0, k1;
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if (cosOmega > F(0.9999))
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{
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// Interpolation linéaire pour éviter une division par zéro
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k0 = F(1.0) - interp;
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k1 = interp;
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}
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else
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{
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T sinOmega = std::sqrt(F(1.0) - cosOmega*cosOmega);
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T omega = std::atan2(sinOmega, cosOmega);
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// Pour éviter deux divisions
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sinOmega = F(1.0)/sinOmega;
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k0 = std::sin((F(1.0) - interp) * omega) * sinOmega;
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k1 = std::sin(interp*omega) * sinOmega;
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}
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NzQuaternion result(k0 * quatA.w, k0 * quatA.x, k0 * quatA.y, k0 * quatA.z);
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return result += q*k1;
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}
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template<typename T>
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NzQuaternion<T> NzQuaternion<T>::Zero()
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{
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NzQuaternion quaternion;
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quaternion.MakeZero();
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return quaternion;
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}
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template<typename T>
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std::ostream& operator<<(std::ostream& out, const NzQuaternion<T>& quat)
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{
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return out << quat.ToString();
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}
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#undef F
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#include <Nazara/Core/DebugOff.hpp>
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