/* ----------------------------------------------------------------------------- This source file is part of OGRE (Object-oriented Graphics Rendering Engine) For the latest info, see http://www.ogre3d.org/ Copyright (c) 2000-2014 Torus Knot Software Ltd Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. ----------------------------------------------------------------------------- */ // This file is based on material originally from: // Geometric Tools, LLC // Copyright (c) 1998-2010 // Distributed under the Boost Software License, Version 1.0. // http://www.boost.org/LICENSE_1_0.txt // http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt #ifndef __Quaternion_H__ #define __Quaternion_H__ #include "OgrePrerequisites.h" #include "OgreMath.h" namespace Ogre { /** \addtogroup Core * @{ */ /** \addtogroup Math * @{ */ /** Implementation of a Quaternion, i.e. a rotation around an axis. For more information about Quaternions and the theory behind it, we recommend reading: http://www.ogre3d.org/tikiwiki/Quaternion+and+Rotation+Primer and http://www.cprogramming.com/tutorial/3d/quaternions.html and http://www.gamedev.net/page/resources/_/reference/programming/math-and-physics/quaternions/quaternion-powers-r1095 */ class _OgreExport Quaternion { public: /// Default constructor, initializes to identity rotation (aka 0°) inline Quaternion () : w(1), x(0), y(0), z(0) { } /// Copy constructor inline Quaternion(const Ogre::Quaternion& rhs) : w(rhs.w), x(rhs.x), y(rhs.y), z(rhs.z) {} /// Construct from an explicit list of values inline Quaternion ( Real fW, Real fX, Real fY, Real fZ) : w(fW), x(fX), y(fY), z(fZ) { } /// Construct a quaternion from a rotation matrix inline Quaternion(const Matrix3& rot) { this->FromRotationMatrix(rot); } /// Construct a quaternion from an angle/axis inline Quaternion(const Radian& rfAngle, const Vector3& rkAxis) { this->FromAngleAxis(rfAngle, rkAxis); } /// Construct a quaternion from 3 orthonormal local axes inline Quaternion(const Vector3& xaxis, const Vector3& yaxis, const Vector3& zaxis) { this->FromAxes(xaxis, yaxis, zaxis); } /// Construct a quaternion from 3 orthonormal local axes inline Quaternion(const Vector3* akAxis) { this->FromAxes(akAxis); } /// Construct a quaternion from 4 manual w/x/y/z values inline Quaternion(Real* valptr) { memcpy(&w, valptr, sizeof(Real)*4); } /** Exchange the contents of this quaternion with another. */ inline void swap(Quaternion& other) { std::swap(w, other.w); std::swap(x, other.x); std::swap(y, other.y); std::swap(z, other.z); } /// Array accessor operator inline Real operator [] ( const size_t i ) const { assert( i < 4 ); return *(&w+i); } /// Array accessor operator inline Real& operator [] ( const size_t i ) { assert( i < 4 ); return *(&w+i); } /// Pointer accessor for direct copying inline Real* ptr() { return &w; } /// Pointer accessor for direct copying inline const Real* ptr() const { return &w; } void FromRotationMatrix (const Matrix3& kRot); void ToRotationMatrix (Matrix3& kRot) const; /** Setups the quaternion using the supplied vector, and "roll" around that vector by the specified radians. */ void FromAngleAxis (const Radian& rfAngle, const Vector3& rkAxis); void ToAngleAxis (Radian& rfAngle, Vector3& rkAxis) const; inline void ToAngleAxis (Degree& dAngle, Vector3& rkAxis) const { Radian rAngle; ToAngleAxis ( rAngle, rkAxis ); dAngle = rAngle; } /** Constructs the quaternion using 3 axes, the axes are assumed to be orthonormal @see FromAxes */ void FromAxes (const Vector3* akAxis); void FromAxes (const Vector3& xAxis, const Vector3& yAxis, const Vector3& zAxis); /** Gets the 3 orthonormal axes defining the quaternion. @see FromAxes */ void ToAxes (Vector3* akAxis) const; void ToAxes (Vector3& xAxis, Vector3& yAxis, Vector3& zAxis) const; /** Returns the X orthonormal axis defining the quaternion. Same as doing xAxis = Vector3::UNIT_X * this. Also called the local X-axis */ Vector3 xAxis(void) const; /** Returns the Y orthonormal axis defining the quaternion. Same as doing yAxis = Vector3::UNIT_Y * this. Also called the local Y-axis */ Vector3 yAxis(void) const; /** Returns the Z orthonormal axis defining the quaternion. Same as doing zAxis = Vector3::UNIT_Z * this. Also called the local Z-axis */ Vector3 zAxis(void) const; inline Quaternion& operator= (const Quaternion& rkQ) { w = rkQ.w; x = rkQ.x; y = rkQ.y; z = rkQ.z; return *this; } Quaternion operator+ (const Quaternion& rkQ) const; Quaternion operator- (const Quaternion& rkQ) const; Quaternion operator*(const Quaternion& rkQ) const; Quaternion operator*(Real s) const { return Quaternion(s * w, s * x, s * y, s * z); } friend Quaternion operator*(Real s, const Quaternion& q) { return q * s; } Quaternion operator-() const { return Quaternion(-w, -x, -y, -z); } inline bool operator== (const Quaternion& rhs) const { return (rhs.x == x) && (rhs.y == y) && (rhs.z == z) && (rhs.w == w); } inline bool operator!= (const Quaternion& rhs) const { return !operator==(rhs); } // functions of a quaternion /// Returns the dot product of the quaternion Real Dot(const Quaternion& rkQ) const { return w * rkQ.w + x * rkQ.x + y * rkQ.y + z * rkQ.z; } /// Returns the normal length of this quaternion. Real Norm() const { return Math::Sqrt(w * w + x * x + y * y + z * z); } /// Normalises this quaternion, and returns the previous length Real normalise(void) { Real len = Norm(); *this = 1.0f / len * *this; return len; } Quaternion Inverse () const; /// Apply to non-zero quaternion Quaternion UnitInverse () const; /// Apply to unit-length quaternion Quaternion Exp () const; Quaternion Log () const; /// Rotation of a vector by a quaternion Vector3 operator* (const Vector3& rkVector) const; /** Calculate the local roll element of this quaternion. @param reprojectAxis By default the method returns the 'intuitive' result that is, if you projected the local X of the quaternion onto the XY plane, the angle between it and global X is returned. The co-domain of the returned value is from -180 to 180 degrees. If set to false though, the result is the rotation around Z axis that could be used to implement the quaternion using some non-intuitive order of rotations. This behavior is preserved for backward compatibility, to decompose quaternion into yaw, pitch and roll use q.ToRotationMatrix().ToEulerAnglesYXZ(yaw, pitch, roll) instead. */ Radian getRoll(bool reprojectAxis = true) const; /** Calculate the local pitch element of this quaternion @param reprojectAxis By default the method returns the 'intuitive' result that is, if you projected the local Y of the quaternion onto the YZ plane, the angle between it and global Y is returned. The co-domain of the returned value is from -180 to 180 degrees. If set to false though, the result is the rotation around X axis that could be used to implement the quaternion using some non-intuitive order of rotations. This behavior is preserved for backward compatibility, to decompose quaternion into yaw, pitch and roll use q.ToRotationMatrix().ToEulerAnglesYXZ(yaw, pitch, roll) instead. */ Radian getPitch(bool reprojectAxis = true) const; /** Calculate the local yaw element of this quaternion @param reprojectAxis By default the method returns the 'intuitive' result that is, if you projected the local Z of the quaternion onto the ZX plane, the angle between it and global Z is returned. The co-domain of the returned value is from -180 to 180 degrees. If set to false though, the result is the rotation around Y axis that could be used to implement the quaternion using some non-intuitive order of rotations. This behavior is preserved for backward compatibility, to decompose quaternion into yaw, pitch and roll use q.ToRotationMatrix().ToEulerAnglesYXZ(yaw, pitch, roll) instead. */ Radian getYaw(bool reprojectAxis = true) const; /** Equality with tolerance (tolerance is max angle difference) @remark Both equals() and orientationEquals() measure the exact same thing. One measures the difference by angle, the other by a different, non-linear metric. */ bool equals(const Quaternion& rhs, const Radian& tolerance) const { Real d = Dot(rhs); Radian angle = Math::ACos(2.0f * d*d - 1.0f); return Math::Abs(angle.valueRadians()) <= tolerance.valueRadians(); } /** Compare two quaternions which are assumed to be used as orientations. @remark Both equals() and orientationEquals() measure the exact same thing. One measures the difference by angle, the other by a different, non-linear metric. @return true if the two orientations are the same or very close, relative to the given tolerance. Slerp ( 0.75f, A, B ) != Slerp ( 0.25f, B, A ); therefore be careful if your code relies in the order of the operands. This is specially important in IK animation. */ inline bool orientationEquals( const Quaternion& other, Real tolerance = 1e-3f ) const { Real d = this->Dot(other); return 1 - d*d < tolerance; } /** Performs Spherical linear interpolation between two quaternions, and returns the result. Slerp ( 0.0f, A, B ) = A Slerp ( 1.0f, A, B ) = B @return Interpolated quaternion Slerp has the proprieties of performing the interpolation at constant velocity, and being torque-minimal (unless shortestPath=false). However, it's NOT commutative, which means Slerp ( 0.75f, A, B ) != Slerp ( 0.25f, B, A ); therefore be careful if your code relies in the order of the operands. This is specially important in IK animation. */ static Quaternion Slerp (Real fT, const Quaternion& rkP, const Quaternion& rkQ, bool shortestPath = false); /** @see Slerp. It adds extra "spins" (i.e. rotates several times) specified by parameter 'iExtraSpins' while interpolating before arriving to the final values */ static Quaternion SlerpExtraSpins (Real fT, const Quaternion& rkP, const Quaternion& rkQ, int iExtraSpins); /// Setup for spherical quadratic interpolation static void Intermediate (const Quaternion& rkQ0, const Quaternion& rkQ1, const Quaternion& rkQ2, Quaternion& rka, Quaternion& rkB); /// Spherical quadratic interpolation static Quaternion Squad (Real fT, const Quaternion& rkP, const Quaternion& rkA, const Quaternion& rkB, const Quaternion& rkQ, bool shortestPath = false); /** Performs Normalised linear interpolation between two quaternions, and returns the result. nlerp ( 0.0f, A, B ) = A nlerp ( 1.0f, A, B ) = B Nlerp is faster than Slerp. Nlerp has the proprieties of being commutative (@see Slerp; commutativity is desired in certain places, like IK animation), and being torque-minimal (unless shortestPath=false). However, it's performing the interpolation at non-constant velocity; sometimes this is desired, sometimes it is not. Having a non-constant velocity can produce a more natural rotation feeling without the need of tweaking the weights; however if your scene relies on the timing of the rotation or assumes it will point at a specific angle at a specific weight value, Slerp is a better choice. */ static Quaternion nlerp(Real fT, const Quaternion& rkP, const Quaternion& rkQ, bool shortestPath = false); /// Cutoff for sine near zero static const Real msEpsilon; // special values static const Quaternion ZERO; static const Quaternion IDENTITY; Real w, x, y, z; #ifndef OGRE_FAST_MATH /// Check whether this quaternion contains valid values inline bool isNaN() const { return Math::isNaN(x) || Math::isNaN(y) || Math::isNaN(z) || Math::isNaN(w); } #endif }; /** Function for writing to a stream. Outputs "Quaternion(w, x, y, z)" with w,x,y,z being the member values of the quaternion. */ _OgreExport std::ostream& operator<<(std::ostream& o, const Quaternion& q); /** @} */ /** @} */ } #endif