370 lines
7.6 KiB
C++
370 lines
7.6 KiB
C++
// Copyright (C) 2012 Rémi Bèges
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// Jérôme Leclercq
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// This file is part of the "Nazara Engine".
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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 <Nazara/Core/Debug.hpp>
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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& vec) const
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{
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return w*vec.w + x*vec.x + y*vec.y + z.vec.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>::GetNormalized() 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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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 squaredLength = SquaredMagnitude();
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if (std::fabs(squaredLength) > 0.00001 && std::fabs(squaredLength - 1.0) > 0.00001)
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{
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T length = std::sqrt(squaredLength);
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w /= length;
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x /= length;
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y /= length;
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z /= length;
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return length;
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}
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else
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return 1.0; // Le quaternion est déjà normalisé
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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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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>& normalizedAxis)
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{
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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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angle /= 2;
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auto 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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}
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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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void NzQuaternion<T>::SetIdentity()
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{
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Set(1.0, 0.0, 0.0, 0.0);
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}
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template<typename T>
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void NzQuaternion<T>::SetZero()
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{
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Set(0.0, 0.0, 0.0, 0.0);
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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 <= 0.0)
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return quatA;
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if (interp >= 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 < 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 > 0.9999)
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{
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// Interpolation linéaire pour éviter une division par zéro
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k0 = 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(1.0f - (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 = 1/sinOmega;
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k0 = std::sin((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;
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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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Normalize();
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T test = x*y + z*w;
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if (test > 0.499)
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// singularity at north pole
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return NzEulerAngles<T>(NzDegrees(90.0), NzRadians(2.0 * std::atan2(x, w)), 0.0);
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if (test < -0.499)
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return NzEulerAngles<T>(NzDegrees(-90.0), NzRadians(-2.0 * std::atan2(x, w)), 0.0);
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T xx = x*x;
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T yy = y*y;
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T zz = z*z;
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return NzEulerAngles<T>(NzRadians(std::atan2(2.0*x*w - 2.0*y*z, 1.0 - 2.0*xx - 2.0*zz)),
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NzRadians(std::atan2(2.0*y*w - 2.0*x*z, 1.f - 2.0*yy - 2.0*zz)),
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NzRadians(std::asin(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> 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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NzVector3<T> normal(vec);
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normal.Normalize();
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NzQuaternion qvec(0.0, normal.x, normal.y, normal.z);
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NzQuaternion result = operator*(qvec * GetConjugate());
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return NzVector3<T>(result.x, result.y, result.z);
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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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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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#include <Nazara/Core/DebugOff.hpp>
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