965 lines
21 KiB
C++
965 lines
21 KiB
C++
///////////////////////////////////////////////////////////////////////////
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//
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// Copyright (c) 2002-2012, Industrial Light & Magic, a division of Lucas
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// Digital Ltd. LLC
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//
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// All rights reserved.
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above
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// copyright notice, this list of conditions and the following disclaimer
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// in the documentation and/or other materials provided with the
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// distribution.
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// * Neither the name of Industrial Light & Magic nor the names of
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// its contributors may be used to endorse or promote products derived
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// from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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///////////////////////////////////////////////////////////////////////////
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#ifndef INCLUDED_IMATHQUAT_H
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#define INCLUDED_IMATHQUAT_H
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//----------------------------------------------------------------------
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//
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// template class Quat<T>
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//
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// "Quaternions came from Hamilton ... and have been an unmixed
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// evil to those who have touched them in any way. Vector is a
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// useless survival ... and has never been of the slightest use
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// to any creature."
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//
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// - Lord Kelvin
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//
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// This class implements the quaternion numerical type -- you
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// will probably want to use this class to represent orientations
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// in R3 and to convert between various euler angle reps. You
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// should probably use Imath::Euler<> for that.
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//
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//----------------------------------------------------------------------
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#include "ImathExc.h"
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#include "ImathMatrix.h"
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#include "ImathNamespace.h"
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#include <iostream>
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#include <algorithm>
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IMATH_INTERNAL_NAMESPACE_HEADER_ENTER
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#if (defined _WIN32 || defined _WIN64) && defined _MSC_VER
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// Disable MS VC++ warnings about conversion from double to float
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#pragma warning(disable:4244)
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#endif
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template <class T>
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class Quat
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{
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public:
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T r; // real part
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Vec3<T> v; // imaginary vector
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//-----------------------------------------------------
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// Constructors - default constructor is identity quat
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//-----------------------------------------------------
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Quat ();
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template <class S>
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Quat (const Quat<S> &q);
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Quat (T s, T i, T j, T k);
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Quat (T s, Vec3<T> d);
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static Quat<T> identity ();
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//-------------------------------------------------
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// Basic Algebra - Operators and Methods
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// The operator return values are *NOT* normalized
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//
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// operator^ and euclideanInnnerProduct() both
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// implement the 4D dot product
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//
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// operator/ uses the inverse() quaternion
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//
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// operator~ is conjugate -- if (S+V) is quat then
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// the conjugate (S+V)* == (S-V)
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//
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// some operators (*,/,*=,/=) treat the quat as
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// a 4D vector when one of the operands is scalar
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//-------------------------------------------------
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const Quat<T> & operator = (const Quat<T> &q);
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const Quat<T> & operator *= (const Quat<T> &q);
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const Quat<T> & operator *= (T t);
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const Quat<T> & operator /= (const Quat<T> &q);
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const Quat<T> & operator /= (T t);
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const Quat<T> & operator += (const Quat<T> &q);
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const Quat<T> & operator -= (const Quat<T> &q);
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T & operator [] (int index); // as 4D vector
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T operator [] (int index) const;
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template <class S> bool operator == (const Quat<S> &q) const;
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template <class S> bool operator != (const Quat<S> &q) const;
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Quat<T> & invert (); // this -> 1 / this
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Quat<T> inverse () const;
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Quat<T> & normalize (); // returns this
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Quat<T> normalized () const;
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T length () const; // in R4
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Vec3<T> rotateVector(const Vec3<T> &original) const;
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T euclideanInnerProduct(const Quat<T> &q) const;
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//-----------------------
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// Rotation conversion
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//-----------------------
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Quat<T> & setAxisAngle (const Vec3<T> &axis, T radians);
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Quat<T> & setRotation (const Vec3<T> &fromDirection,
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const Vec3<T> &toDirection);
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T angle () const;
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Vec3<T> axis () const;
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Matrix33<T> toMatrix33 () const;
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Matrix44<T> toMatrix44 () const;
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Quat<T> log () const;
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Quat<T> exp () const;
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private:
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void setRotationInternal (const Vec3<T> &f0,
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const Vec3<T> &t0,
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Quat<T> &q);
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};
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template<class T>
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Quat<T> slerp (const Quat<T> &q1, const Quat<T> &q2, T t);
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template<class T>
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Quat<T> slerpShortestArc
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(const Quat<T> &q1, const Quat<T> &q2, T t);
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template<class T>
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Quat<T> squad (const Quat<T> &q1, const Quat<T> &q2,
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const Quat<T> &qa, const Quat<T> &qb, T t);
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template<class T>
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void intermediate (const Quat<T> &q0, const Quat<T> &q1,
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const Quat<T> &q2, const Quat<T> &q3,
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Quat<T> &qa, Quat<T> &qb);
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template<class T>
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Matrix33<T> operator * (const Matrix33<T> &M, const Quat<T> &q);
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template<class T>
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Matrix33<T> operator * (const Quat<T> &q, const Matrix33<T> &M);
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template<class T>
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std::ostream & operator << (std::ostream &o, const Quat<T> &q);
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template<class T>
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Quat<T> operator * (const Quat<T> &q1, const Quat<T> &q2);
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template<class T>
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Quat<T> operator / (const Quat<T> &q1, const Quat<T> &q2);
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template<class T>
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Quat<T> operator / (const Quat<T> &q, T t);
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template<class T>
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Quat<T> operator * (const Quat<T> &q, T t);
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template<class T>
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Quat<T> operator * (T t, const Quat<T> &q);
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template<class T>
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Quat<T> operator + (const Quat<T> &q1, const Quat<T> &q2);
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template<class T>
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Quat<T> operator - (const Quat<T> &q1, const Quat<T> &q2);
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template<class T>
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Quat<T> operator ~ (const Quat<T> &q);
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template<class T>
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Quat<T> operator - (const Quat<T> &q);
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template<class T>
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Vec3<T> operator * (const Vec3<T> &v, const Quat<T> &q);
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//--------------------
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// Convenient typedefs
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//--------------------
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typedef Quat<float> Quatf;
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typedef Quat<double> Quatd;
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//---------------
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// Implementation
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//---------------
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template<class T>
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inline
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Quat<T>::Quat (): r (1), v (0, 0, 0)
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{
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// empty
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}
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template<class T>
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template <class S>
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inline
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Quat<T>::Quat (const Quat<S> &q): r (q.r), v (q.v)
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{
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// empty
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}
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template<class T>
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inline
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Quat<T>::Quat (T s, T i, T j, T k): r (s), v (i, j, k)
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{
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// empty
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}
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template<class T>
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inline
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Quat<T>::Quat (T s, Vec3<T> d): r (s), v (d)
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{
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// empty
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}
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template<class T>
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inline Quat<T>
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Quat<T>::identity ()
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{
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return Quat<T>();
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}
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template<class T>
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inline const Quat<T> &
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Quat<T>::operator = (const Quat<T> &q)
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{
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r = q.r;
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v = q.v;
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return *this;
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}
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template<class T>
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inline const Quat<T> &
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Quat<T>::operator *= (const Quat<T> &q)
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{
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T rtmp = r * q.r - (v ^ q.v);
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v = r * q.v + v * q.r + v % q.v;
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r = rtmp;
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return *this;
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}
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template<class T>
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inline const Quat<T> &
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Quat<T>::operator *= (T t)
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{
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r *= t;
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v *= t;
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return *this;
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}
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template<class T>
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inline const Quat<T> &
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Quat<T>::operator /= (const Quat<T> &q)
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{
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*this = *this * q.inverse();
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return *this;
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}
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template<class T>
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inline const Quat<T> &
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Quat<T>::operator /= (T t)
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{
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r /= t;
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v /= t;
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return *this;
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}
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template<class T>
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inline const Quat<T> &
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Quat<T>::operator += (const Quat<T> &q)
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{
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r += q.r;
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v += q.v;
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return *this;
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}
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template<class T>
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inline const Quat<T> &
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Quat<T>::operator -= (const Quat<T> &q)
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{
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r -= q.r;
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v -= q.v;
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return *this;
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}
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template<class T>
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inline T &
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Quat<T>::operator [] (int index)
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{
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return index ? v[index - 1] : r;
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}
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template<class T>
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inline T
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Quat<T>::operator [] (int index) const
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{
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return index ? v[index - 1] : r;
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}
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template <class T>
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template <class S>
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inline bool
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Quat<T>::operator == (const Quat<S> &q) const
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{
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return r == q.r && v == q.v;
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}
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template <class T>
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template <class S>
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inline bool
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Quat<T>::operator != (const Quat<S> &q) const
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{
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return r != q.r || v != q.v;
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}
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template<class T>
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inline T
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operator ^ (const Quat<T>& q1 ,const Quat<T>& q2)
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{
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return q1.r * q2.r + (q1.v ^ q2.v);
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}
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template <class T>
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inline T
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Quat<T>::length () const
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{
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return Math<T>::sqrt (r * r + (v ^ v));
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}
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template <class T>
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inline Quat<T> &
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Quat<T>::normalize ()
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{
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if (T l = length())
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{
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r /= l;
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v /= l;
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}
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else
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{
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r = 1;
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v = Vec3<T> (0);
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}
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return *this;
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}
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template <class T>
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inline Quat<T>
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Quat<T>::normalized () const
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{
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if (T l = length())
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return Quat (r / l, v / l);
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return Quat();
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}
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template<class T>
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inline Quat<T>
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Quat<T>::inverse () const
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{
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//
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// 1 Q*
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// - = ---- where Q* is conjugate (operator~)
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// Q Q* Q and (Q* Q) == Q ^ Q (4D dot)
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//
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T qdot = *this ^ *this;
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return Quat (r / qdot, -v / qdot);
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}
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template<class T>
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inline Quat<T> &
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Quat<T>::invert ()
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{
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T qdot = (*this) ^ (*this);
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r /= qdot;
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v = -v / qdot;
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return *this;
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}
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template<class T>
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inline Vec3<T>
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Quat<T>::rotateVector(const Vec3<T>& original) const
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{
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//
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// Given a vector p and a quaternion q (aka this),
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// calculate p' = qpq*
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//
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// Assumes unit quaternions (because non-unit
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// quaternions cannot be used to rotate vectors
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// anyway).
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//
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Quat<T> vec (0, original); // temporarily promote grade of original
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Quat<T> inv (*this);
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inv.v *= -1; // unit multiplicative inverse
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Quat<T> result = *this * vec * inv;
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return result.v;
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}
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template<class T>
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inline T
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Quat<T>::euclideanInnerProduct (const Quat<T> &q) const
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{
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return r * q.r + v.x * q.v.x + v.y * q.v.y + v.z * q.v.z;
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}
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template<class T>
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T
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angle4D (const Quat<T> &q1, const Quat<T> &q2)
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{
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//
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// Compute the angle between two quaternions,
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// interpreting the quaternions as 4D vectors.
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//
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Quat<T> d = q1 - q2;
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T lengthD = Math<T>::sqrt (d ^ d);
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Quat<T> s = q1 + q2;
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T lengthS = Math<T>::sqrt (s ^ s);
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return 2 * Math<T>::atan2 (lengthD, lengthS);
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}
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template<class T>
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Quat<T>
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slerp (const Quat<T> &q1, const Quat<T> &q2, T t)
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{
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//
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// Spherical linear interpolation.
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// Assumes q1 and q2 are normalized and that q1 != -q2.
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//
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// This method does *not* interpolate along the shortest
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// arc between q1 and q2. If you desire interpolation
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// along the shortest arc, and q1^q2 is negative, then
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// consider calling slerpShortestArc(), below, or flipping
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// the second quaternion explicitly.
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//
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// The implementation of squad() depends on a slerp()
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// that interpolates as is, without the automatic
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// flipping.
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//
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// Don Hatch explains the method we use here on his
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// web page, The Right Way to Calculate Stuff, at
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// http://www.plunk.org/~hatch/rightway.php
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//
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T a = angle4D (q1, q2);
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T s = 1 - t;
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Quat<T> q = sinx_over_x (s * a) / sinx_over_x (a) * s * q1 +
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sinx_over_x (t * a) / sinx_over_x (a) * t * q2;
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return q.normalized();
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}
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template<class T>
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Quat<T>
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slerpShortestArc (const Quat<T> &q1, const Quat<T> &q2, T t)
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{
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//
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// Spherical linear interpolation along the shortest
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// arc from q1 to either q2 or -q2, whichever is closer.
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// Assumes q1 and q2 are unit quaternions.
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//
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if ((q1 ^ q2) >= 0)
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return slerp (q1, q2, t);
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else
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return slerp (q1, -q2, t);
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}
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template<class T>
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Quat<T>
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spline (const Quat<T> &q0, const Quat<T> &q1,
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const Quat<T> &q2, const Quat<T> &q3,
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T t)
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{
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//
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// Spherical Cubic Spline Interpolation -
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// from Advanced Animation and Rendering
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// Techniques by Watt and Watt, Page 366:
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// A spherical curve is constructed using three
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// spherical linear interpolations of a quadrangle
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// of unit quaternions: q1, qa, qb, q2.
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// Given a set of quaternion keys: q0, q1, q2, q3,
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// this routine does the interpolation between
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// q1 and q2 by constructing two intermediate
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// quaternions: qa and qb. The qa and qb are
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// computed by the intermediate function to
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// guarantee the continuity of tangents across
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// adjacent cubic segments. The qa represents in-tangent
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// for q1 and the qb represents the out-tangent for q2.
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//
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// The q1 q2 is the cubic segment being interpolated.
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// The q0 is from the previous adjacent segment and q3 is
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// from the next adjacent segment. The q0 and q3 are used
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// in computing qa and qb.
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//
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|
|
Quat<T> qa = intermediate (q0, q1, q2);
|
|
Quat<T> qb = intermediate (q1, q2, q3);
|
|
Quat<T> result = squad (q1, qa, qb, q2, t);
|
|
|
|
return result;
|
|
}
|
|
|
|
|
|
template<class T>
|
|
Quat<T>
|
|
squad (const Quat<T> &q1, const Quat<T> &qa,
|
|
const Quat<T> &qb, const Quat<T> &q2,
|
|
T t)
|
|
{
|
|
//
|
|
// Spherical Quadrangle Interpolation -
|
|
// from Advanced Animation and Rendering
|
|
// Techniques by Watt and Watt, Page 366:
|
|
// It constructs a spherical cubic interpolation as
|
|
// a series of three spherical linear interpolations
|
|
// of a quadrangle of unit quaternions.
|
|
//
|
|
|
|
Quat<T> r1 = slerp (q1, q2, t);
|
|
Quat<T> r2 = slerp (qa, qb, t);
|
|
Quat<T> result = slerp (r1, r2, 2 * t * (1 - t));
|
|
|
|
return result;
|
|
}
|
|
|
|
|
|
template<class T>
|
|
Quat<T>
|
|
intermediate (const Quat<T> &q0, const Quat<T> &q1, const Quat<T> &q2)
|
|
{
|
|
//
|
|
// From advanced Animation and Rendering
|
|
// Techniques by Watt and Watt, Page 366:
|
|
// computing the inner quadrangle
|
|
// points (qa and qb) to guarantee tangent
|
|
// continuity.
|
|
//
|
|
|
|
Quat<T> q1inv = q1.inverse();
|
|
Quat<T> c1 = q1inv * q2;
|
|
Quat<T> c2 = q1inv * q0;
|
|
Quat<T> c3 = (T) (-0.25) * (c2.log() + c1.log());
|
|
Quat<T> qa = q1 * c3.exp();
|
|
qa.normalize();
|
|
return qa;
|
|
}
|
|
|
|
|
|
template <class T>
|
|
inline Quat<T>
|
|
Quat<T>::log () const
|
|
{
|
|
//
|
|
// For unit quaternion, from Advanced Animation and
|
|
// Rendering Techniques by Watt and Watt, Page 366:
|
|
//
|
|
|
|
T theta = Math<T>::acos (std::min (r, (T) 1.0));
|
|
|
|
if (theta == 0)
|
|
return Quat<T> (0, v);
|
|
|
|
T sintheta = Math<T>::sin (theta);
|
|
|
|
T k;
|
|
if (abs (sintheta) < 1 && abs (theta) >= limits<T>::max() * abs (sintheta))
|
|
k = 1;
|
|
else
|
|
k = theta / sintheta;
|
|
|
|
return Quat<T> ((T) 0, v.x * k, v.y * k, v.z * k);
|
|
}
|
|
|
|
|
|
template <class T>
|
|
inline Quat<T>
|
|
Quat<T>::exp () const
|
|
{
|
|
//
|
|
// For pure quaternion (zero scalar part):
|
|
// from Advanced Animation and Rendering
|
|
// Techniques by Watt and Watt, Page 366:
|
|
//
|
|
|
|
T theta = v.length();
|
|
T sintheta = Math<T>::sin (theta);
|
|
|
|
T k;
|
|
if (abs (theta) < 1 && abs (sintheta) >= limits<T>::max() * abs (theta))
|
|
k = 1;
|
|
else
|
|
k = sintheta / theta;
|
|
|
|
T costheta = Math<T>::cos (theta);
|
|
|
|
return Quat<T> (costheta, v.x * k, v.y * k, v.z * k);
|
|
}
|
|
|
|
|
|
template <class T>
|
|
inline T
|
|
Quat<T>::angle () const
|
|
{
|
|
return 2 * Math<T>::atan2 (v.length(), r);
|
|
}
|
|
|
|
|
|
template <class T>
|
|
inline Vec3<T>
|
|
Quat<T>::axis () const
|
|
{
|
|
return v.normalized();
|
|
}
|
|
|
|
|
|
template <class T>
|
|
inline Quat<T> &
|
|
Quat<T>::setAxisAngle (const Vec3<T> &axis, T radians)
|
|
{
|
|
r = Math<T>::cos (radians / 2);
|
|
v = axis.normalized() * Math<T>::sin (radians / 2);
|
|
return *this;
|
|
}
|
|
|
|
|
|
template <class T>
|
|
Quat<T> &
|
|
Quat<T>::setRotation (const Vec3<T> &from, const Vec3<T> &to)
|
|
{
|
|
//
|
|
// Create a quaternion that rotates vector from into vector to,
|
|
// such that the rotation is around an axis that is the cross
|
|
// product of from and to.
|
|
//
|
|
// This function calls function setRotationInternal(), which is
|
|
// numerically accurate only for rotation angles that are not much
|
|
// greater than pi/2. In order to achieve good accuracy for angles
|
|
// greater than pi/2, we split large angles in half, and rotate in
|
|
// two steps.
|
|
//
|
|
|
|
//
|
|
// Normalize from and to, yielding f0 and t0.
|
|
//
|
|
|
|
Vec3<T> f0 = from.normalized();
|
|
Vec3<T> t0 = to.normalized();
|
|
|
|
if ((f0 ^ t0) >= 0)
|
|
{
|
|
//
|
|
// The rotation angle is less than or equal to pi/2.
|
|
//
|
|
|
|
setRotationInternal (f0, t0, *this);
|
|
}
|
|
else
|
|
{
|
|
//
|
|
// The angle is greater than pi/2. After computing h0,
|
|
// which is halfway between f0 and t0, we rotate first
|
|
// from f0 to h0, then from h0 to t0.
|
|
//
|
|
|
|
Vec3<T> h0 = (f0 + t0).normalized();
|
|
|
|
if ((h0 ^ h0) != 0)
|
|
{
|
|
setRotationInternal (f0, h0, *this);
|
|
|
|
Quat<T> q;
|
|
setRotationInternal (h0, t0, q);
|
|
|
|
*this *= q;
|
|
}
|
|
else
|
|
{
|
|
//
|
|
// f0 and t0 point in exactly opposite directions.
|
|
// Pick an arbitrary axis that is orthogonal to f0,
|
|
// and rotate by pi.
|
|
//
|
|
|
|
r = T (0);
|
|
|
|
Vec3<T> f02 = f0 * f0;
|
|
|
|
if (f02.x <= f02.y && f02.x <= f02.z)
|
|
v = (f0 % Vec3<T> (1, 0, 0)).normalized();
|
|
else if (f02.y <= f02.z)
|
|
v = (f0 % Vec3<T> (0, 1, 0)).normalized();
|
|
else
|
|
v = (f0 % Vec3<T> (0, 0, 1)).normalized();
|
|
}
|
|
}
|
|
|
|
return *this;
|
|
}
|
|
|
|
|
|
template <class T>
|
|
void
|
|
Quat<T>::setRotationInternal (const Vec3<T> &f0, const Vec3<T> &t0, Quat<T> &q)
|
|
{
|
|
//
|
|
// The following is equivalent to setAxisAngle(n,2*phi),
|
|
// where the rotation axis, n, is orthogonal to the f0 and
|
|
// t0 vectors, and 2*phi is the angle between f0 and t0.
|
|
//
|
|
// This function is called by setRotation(), above; it assumes
|
|
// that f0 and t0 are normalized and that the angle between
|
|
// them is not much greater than pi/2. This function becomes
|
|
// numerically inaccurate if f0 and t0 point into nearly
|
|
// opposite directions.
|
|
//
|
|
|
|
//
|
|
// Find a normalized vector, h0, that is halfway between f0 and t0.
|
|
// The angle between f0 and h0 is phi.
|
|
//
|
|
|
|
Vec3<T> h0 = (f0 + t0).normalized();
|
|
|
|
//
|
|
// Store the rotation axis and rotation angle.
|
|
//
|
|
|
|
q.r = f0 ^ h0; // f0 ^ h0 == cos (phi)
|
|
q.v = f0 % h0; // (f0 % h0).length() == sin (phi)
|
|
}
|
|
|
|
|
|
template<class T>
|
|
Matrix33<T>
|
|
Quat<T>::toMatrix33() const
|
|
{
|
|
return Matrix33<T> (1 - 2 * (v.y * v.y + v.z * v.z),
|
|
2 * (v.x * v.y + v.z * r),
|
|
2 * (v.z * v.x - v.y * r),
|
|
|
|
2 * (v.x * v.y - v.z * r),
|
|
1 - 2 * (v.z * v.z + v.x * v.x),
|
|
2 * (v.y * v.z + v.x * r),
|
|
|
|
2 * (v.z * v.x + v.y * r),
|
|
2 * (v.y * v.z - v.x * r),
|
|
1 - 2 * (v.y * v.y + v.x * v.x));
|
|
}
|
|
|
|
template<class T>
|
|
Matrix44<T>
|
|
Quat<T>::toMatrix44() const
|
|
{
|
|
return Matrix44<T> (1 - 2 * (v.y * v.y + v.z * v.z),
|
|
2 * (v.x * v.y + v.z * r),
|
|
2 * (v.z * v.x - v.y * r),
|
|
0,
|
|
2 * (v.x * v.y - v.z * r),
|
|
1 - 2 * (v.z * v.z + v.x * v.x),
|
|
2 * (v.y * v.z + v.x * r),
|
|
0,
|
|
2 * (v.z * v.x + v.y * r),
|
|
2 * (v.y * v.z - v.x * r),
|
|
1 - 2 * (v.y * v.y + v.x * v.x),
|
|
0,
|
|
0,
|
|
0,
|
|
0,
|
|
1);
|
|
}
|
|
|
|
|
|
template<class T>
|
|
inline Matrix33<T>
|
|
operator * (const Matrix33<T> &M, const Quat<T> &q)
|
|
{
|
|
return M * q.toMatrix33();
|
|
}
|
|
|
|
|
|
template<class T>
|
|
inline Matrix33<T>
|
|
operator * (const Quat<T> &q, const Matrix33<T> &M)
|
|
{
|
|
return q.toMatrix33() * M;
|
|
}
|
|
|
|
|
|
template<class T>
|
|
std::ostream &
|
|
operator << (std::ostream &o, const Quat<T> &q)
|
|
{
|
|
return o << "(" << q.r
|
|
<< " " << q.v.x
|
|
<< " " << q.v.y
|
|
<< " " << q.v.z
|
|
<< ")";
|
|
}
|
|
|
|
|
|
template<class T>
|
|
inline Quat<T>
|
|
operator * (const Quat<T> &q1, const Quat<T> &q2)
|
|
{
|
|
return Quat<T> (q1.r * q2.r - (q1.v ^ q2.v),
|
|
q1.r * q2.v + q1.v * q2.r + q1.v % q2.v);
|
|
}
|
|
|
|
|
|
template<class T>
|
|
inline Quat<T>
|
|
operator / (const Quat<T> &q1, const Quat<T> &q2)
|
|
{
|
|
return q1 * q2.inverse();
|
|
}
|
|
|
|
|
|
template<class T>
|
|
inline Quat<T>
|
|
operator / (const Quat<T> &q, T t)
|
|
{
|
|
return Quat<T> (q.r / t, q.v / t);
|
|
}
|
|
|
|
|
|
template<class T>
|
|
inline Quat<T>
|
|
operator * (const Quat<T> &q, T t)
|
|
{
|
|
return Quat<T> (q.r * t, q.v * t);
|
|
}
|
|
|
|
|
|
template<class T>
|
|
inline Quat<T>
|
|
operator * (T t, const Quat<T> &q)
|
|
{
|
|
return Quat<T> (q.r * t, q.v * t);
|
|
}
|
|
|
|
|
|
template<class T>
|
|
inline Quat<T>
|
|
operator + (const Quat<T> &q1, const Quat<T> &q2)
|
|
{
|
|
return Quat<T> (q1.r + q2.r, q1.v + q2.v);
|
|
}
|
|
|
|
|
|
template<class T>
|
|
inline Quat<T>
|
|
operator - (const Quat<T> &q1, const Quat<T> &q2)
|
|
{
|
|
return Quat<T> (q1.r - q2.r, q1.v - q2.v);
|
|
}
|
|
|
|
|
|
template<class T>
|
|
inline Quat<T>
|
|
operator ~ (const Quat<T> &q)
|
|
{
|
|
return Quat<T> (q.r, -q.v);
|
|
}
|
|
|
|
|
|
template<class T>
|
|
inline Quat<T>
|
|
operator - (const Quat<T> &q)
|
|
{
|
|
return Quat<T> (-q.r, -q.v);
|
|
}
|
|
|
|
|
|
template<class T>
|
|
inline Vec3<T>
|
|
operator * (const Vec3<T> &v, const Quat<T> &q)
|
|
{
|
|
Vec3<T> a = q.v % v;
|
|
Vec3<T> b = q.v % a;
|
|
return v + T (2) * (q.r * a + b);
|
|
}
|
|
|
|
#if (defined _WIN32 || defined _WIN64) && defined _MSC_VER
|
|
#pragma warning(default:4244)
|
|
#endif
|
|
|
|
IMATH_INTERNAL_NAMESPACE_HEADER_EXIT
|
|
|
|
#endif // INCLUDED_IMATHQUAT_H
|