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393 lines
13 KiB
393 lines
13 KiB
/* -*-c++-*- OpenSceneGraph - Copyright (C) 1998-2006 Robert Osfield |
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* |
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* This library is open source and may be redistributed and/or modified under |
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* the terms of the OpenSceneGraph Public License (OSGPL) version 0.0 or |
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* (at your option) any later version. The full license is in LICENSE file |
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* included with this distribution, and on the openscenegraph.org website. |
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* |
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* This library is distributed in the hope that it will be useful, |
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* but WITHOUT ANY WARRANTY; without even the implied warranty of |
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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* OpenSceneGraph Public License for more details. |
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*/ |
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#ifndef OSG_QUAT |
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#define OSG_QUAT 1 |
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#include <osg/Export> |
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#include <osg/Vec3f> |
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#include <osg/Vec4f> |
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#include <osg/Vec3d> |
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#include <osg/Vec4d> |
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namespace osg { |
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class Matrixf; |
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class Matrixd; |
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/** A quaternion class. It can be used to represent an orientation in 3D space.*/ |
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class OSG_EXPORT Quat |
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{ |
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public: |
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typedef double value_type; |
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value_type _v[4]; // a four-vector |
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inline Quat() { _v[0]=0.0; _v[1]=0.0; _v[2]=0.0; _v[3]=1.0; } |
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inline Quat( value_type x, value_type y, value_type z, value_type w ) |
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{ |
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_v[0]=x; |
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_v[1]=y; |
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_v[2]=z; |
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_v[3]=w; |
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} |
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inline Quat( const Vec4f& v ) |
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{ |
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_v[0]=v.x(); |
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_v[1]=v.y(); |
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_v[2]=v.z(); |
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_v[3]=v.w(); |
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} |
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inline Quat( const Vec4d& v ) |
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{ |
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_v[0]=v.x(); |
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_v[1]=v.y(); |
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_v[2]=v.z(); |
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_v[3]=v.w(); |
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} |
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inline Quat( value_type angle, const Vec3f& axis) |
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{ |
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makeRotate(angle,axis); |
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} |
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inline Quat( value_type angle, const Vec3d& axis) |
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{ |
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makeRotate(angle,axis); |
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} |
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inline Quat( value_type angle1, const Vec3f& axis1, |
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value_type angle2, const Vec3f& axis2, |
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value_type angle3, const Vec3f& axis3) |
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{ |
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makeRotate(angle1,axis1,angle2,axis2,angle3,axis3); |
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} |
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inline Quat( value_type angle1, const Vec3d& axis1, |
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value_type angle2, const Vec3d& axis2, |
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value_type angle3, const Vec3d& axis3) |
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{ |
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makeRotate(angle1,axis1,angle2,axis2,angle3,axis3); |
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} |
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inline Quat& operator = (const Quat& v) { _v[0]=v._v[0]; _v[1]=v._v[1]; _v[2]=v._v[2]; _v[3]=v._v[3]; return *this; } |
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inline bool operator == (const Quat& v) const { return _v[0]==v._v[0] && _v[1]==v._v[1] && _v[2]==v._v[2] && _v[3]==v._v[3]; } |
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inline bool operator != (const Quat& v) const { return _v[0]!=v._v[0] || _v[1]!=v._v[1] || _v[2]!=v._v[2] || _v[3]!=v._v[3]; } |
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inline bool operator < (const Quat& v) const |
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{ |
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if (_v[0]<v._v[0]) return true; |
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else if (_v[0]>v._v[0]) return false; |
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else if (_v[1]<v._v[1]) return true; |
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else if (_v[1]>v._v[1]) return false; |
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else if (_v[2]<v._v[2]) return true; |
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else if (_v[2]>v._v[2]) return false; |
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else return (_v[3]<v._v[3]); |
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} |
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/* ---------------------------------- |
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Methods to access data members |
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---------------------------------- */ |
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inline Vec4d asVec4() const |
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{ |
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return Vec4d(_v[0], _v[1], _v[2], _v[3]); |
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} |
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inline Vec3d asVec3() const |
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{ |
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return Vec3d(_v[0], _v[1], _v[2]); |
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} |
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inline void set(value_type x, value_type y, value_type z, value_type w) |
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{ |
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_v[0]=x; |
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_v[1]=y; |
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_v[2]=z; |
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_v[3]=w; |
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} |
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inline void set(const osg::Vec4f& v) |
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{ |
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_v[0]=v.x(); |
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_v[1]=v.y(); |
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_v[2]=v.z(); |
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_v[3]=v.w(); |
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} |
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inline void set(const osg::Vec4d& v) |
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{ |
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_v[0]=v.x(); |
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_v[1]=v.y(); |
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_v[2]=v.z(); |
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_v[3]=v.w(); |
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} |
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void set(const Matrixf& matrix); |
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void set(const Matrixd& matrix); |
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void get(Matrixf& matrix) const; |
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void get(Matrixd& matrix) const; |
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inline value_type & operator [] (int i) { return _v[i]; } |
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inline value_type operator [] (int i) const { return _v[i]; } |
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inline value_type & x() { return _v[0]; } |
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inline value_type & y() { return _v[1]; } |
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inline value_type & z() { return _v[2]; } |
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inline value_type & w() { return _v[3]; } |
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inline value_type x() const { return _v[0]; } |
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inline value_type y() const { return _v[1]; } |
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inline value_type z() const { return _v[2]; } |
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inline value_type w() const { return _v[3]; } |
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/** return true if the Quat represents a zero rotation, and therefore can be ignored in computations.*/ |
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bool zeroRotation() const { return _v[0]==0.0 && _v[1]==0.0 && _v[2]==0.0 && _v[3]==1.0; } |
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/* ------------------------------------------------------------- |
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BASIC ARITHMETIC METHODS |
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Implemented in terms of Vec4s. Some Vec4 operators, e.g. |
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operator* are not appropriate for quaternions (as |
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mathematical objects) so they are implemented differently. |
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Also define methods for conjugate and the multiplicative inverse. |
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------------------------------------------------------------- */ |
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/// Multiply by scalar |
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inline const Quat operator * (value_type rhs) const |
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{ |
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return Quat(_v[0]*rhs, _v[1]*rhs, _v[2]*rhs, _v[3]*rhs); |
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} |
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/// Unary multiply by scalar |
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inline Quat& operator *= (value_type rhs) |
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{ |
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_v[0]*=rhs; |
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_v[1]*=rhs; |
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_v[2]*=rhs; |
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_v[3]*=rhs; |
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return *this; // enable nesting |
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} |
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/// Binary multiply |
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inline const Quat operator*(const Quat& rhs) const |
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{ |
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return Quat( rhs._v[3]*_v[0] + rhs._v[0]*_v[3] + rhs._v[1]*_v[2] - rhs._v[2]*_v[1], |
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rhs._v[3]*_v[1] - rhs._v[0]*_v[2] + rhs._v[1]*_v[3] + rhs._v[2]*_v[0], |
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rhs._v[3]*_v[2] + rhs._v[0]*_v[1] - rhs._v[1]*_v[0] + rhs._v[2]*_v[3], |
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rhs._v[3]*_v[3] - rhs._v[0]*_v[0] - rhs._v[1]*_v[1] - rhs._v[2]*_v[2] ); |
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} |
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/// Unary multiply |
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inline Quat& operator*=(const Quat& rhs) |
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{ |
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value_type x = rhs._v[3]*_v[0] + rhs._v[0]*_v[3] + rhs._v[1]*_v[2] - rhs._v[2]*_v[1]; |
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value_type y = rhs._v[3]*_v[1] - rhs._v[0]*_v[2] + rhs._v[1]*_v[3] + rhs._v[2]*_v[0]; |
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value_type z = rhs._v[3]*_v[2] + rhs._v[0]*_v[1] - rhs._v[1]*_v[0] + rhs._v[2]*_v[3]; |
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_v[3] = rhs._v[3]*_v[3] - rhs._v[0]*_v[0] - rhs._v[1]*_v[1] - rhs._v[2]*_v[2]; |
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_v[2] = z; |
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_v[1] = y; |
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_v[0] = x; |
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return (*this); // enable nesting |
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} |
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/// Divide by scalar |
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inline Quat operator / (value_type rhs) const |
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{ |
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value_type div = 1.0/rhs; |
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return Quat(_v[0]*div, _v[1]*div, _v[2]*div, _v[3]*div); |
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} |
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/// Unary divide by scalar |
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inline Quat& operator /= (value_type rhs) |
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{ |
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value_type div = 1.0/rhs; |
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_v[0]*=div; |
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_v[1]*=div; |
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_v[2]*=div; |
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_v[3]*=div; |
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return *this; |
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} |
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/// Binary divide |
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inline const Quat operator/(const Quat& denom) const |
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{ |
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return ( (*this) * denom.inverse() ); |
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} |
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/// Unary divide |
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inline Quat& operator/=(const Quat& denom) |
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{ |
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(*this) = (*this) * denom.inverse(); |
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return (*this); // enable nesting |
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} |
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/// Binary addition |
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inline const Quat operator + (const Quat& rhs) const |
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{ |
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return Quat(_v[0]+rhs._v[0], _v[1]+rhs._v[1], |
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_v[2]+rhs._v[2], _v[3]+rhs._v[3]); |
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} |
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/// Unary addition |
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inline Quat& operator += (const Quat& rhs) |
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{ |
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_v[0] += rhs._v[0]; |
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_v[1] += rhs._v[1]; |
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_v[2] += rhs._v[2]; |
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_v[3] += rhs._v[3]; |
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return *this; // enable nesting |
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} |
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/// Binary subtraction |
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inline const Quat operator - (const Quat& rhs) const |
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{ |
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return Quat(_v[0]-rhs._v[0], _v[1]-rhs._v[1], |
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_v[2]-rhs._v[2], _v[3]-rhs._v[3] ); |
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} |
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/// Unary subtraction |
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inline Quat& operator -= (const Quat& rhs) |
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{ |
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_v[0]-=rhs._v[0]; |
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_v[1]-=rhs._v[1]; |
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_v[2]-=rhs._v[2]; |
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_v[3]-=rhs._v[3]; |
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return *this; // enable nesting |
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} |
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/** Negation operator - returns the negative of the quaternion. |
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Basically just calls operator - () on the Vec4 */ |
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inline const Quat operator - () const |
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{ |
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return Quat (-_v[0], -_v[1], -_v[2], -_v[3]); |
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} |
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/// Length of the quaternion = sqrt( vec . vec ) |
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value_type length() const |
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{ |
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return sqrt( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] + _v[3]*_v[3]); |
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} |
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/// Length of the quaternion = vec . vec |
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value_type length2() const |
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{ |
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return _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] + _v[3]*_v[3]; |
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} |
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/// Conjugate |
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inline Quat conj () const |
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{ |
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return Quat( -_v[0], -_v[1], -_v[2], _v[3] ); |
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} |
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/// Multiplicative inverse method: q^(-1) = q^*/(q.q^*) |
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inline const Quat inverse () const |
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{ |
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return conj() / length2(); |
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} |
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/* -------------------------------------------------------- |
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METHODS RELATED TO ROTATIONS |
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Set a quaternion which will perform a rotation of an |
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angle around the axis given by the vector (x,y,z). |
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Should be written to also accept an angle and a Vec3? |
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Define Spherical Linear interpolation method also |
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Not inlined - see the Quat.cpp file for implementation |
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-------------------------------------------------------- */ |
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void makeRotate( value_type angle, |
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value_type x, value_type y, value_type z ); |
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void makeRotate ( value_type angle, const Vec3f& vec ); |
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void makeRotate ( value_type angle, const Vec3d& vec ); |
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void makeRotate ( value_type angle1, const Vec3f& axis1, |
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value_type angle2, const Vec3f& axis2, |
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value_type angle3, const Vec3f& axis3); |
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void makeRotate ( value_type angle1, const Vec3d& axis1, |
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value_type angle2, const Vec3d& axis2, |
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value_type angle3, const Vec3d& axis3); |
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/** Make a rotation Quat which will rotate vec1 to vec2. |
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Generally take a dot product to get the angle between these |
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and then use a cross product to get the rotation axis |
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Watch out for the two special cases when the vectors |
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are co-incident or opposite in direction.*/ |
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void makeRotate( const Vec3f& vec1, const Vec3f& vec2 ); |
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/** Make a rotation Quat which will rotate vec1 to vec2. |
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Generally take a dot product to get the angle between these |
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and then use a cross product to get the rotation axis |
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Watch out for the two special cases of when the vectors |
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are co-incident or opposite in direction.*/ |
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void makeRotate( const Vec3d& vec1, const Vec3d& vec2 ); |
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void makeRotate_original( const Vec3d& vec1, const Vec3d& vec2 ); |
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/** Return the angle and vector components represented by the quaternion.*/ |
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void getRotate ( value_type & angle, value_type & x, value_type & y, value_type & z ) const; |
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/** Return the angle and vector represented by the quaternion.*/ |
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void getRotate ( value_type & angle, Vec3f& vec ) const; |
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/** Return the angle and vector represented by the quaternion.*/ |
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void getRotate ( value_type & angle, Vec3d& vec ) const; |
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/** Spherical Linear Interpolation. |
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As t goes from 0 to 1, the Quat object goes from "from" to "to". */ |
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void slerp ( value_type t, const Quat& from, const Quat& to); |
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/** Rotate a vector by this quaternion.*/ |
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Vec3f operator* (const Vec3f& v) const |
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{ |
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// nVidia SDK implementation |
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Vec3f uv, uuv; |
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Vec3f qvec(_v[0], _v[1], _v[2]); |
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uv = qvec ^ v; |
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uuv = qvec ^ uv; |
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uv *= ( 2.0f * _v[3] ); |
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uuv *= 2.0f; |
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return v + uv + uuv; |
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} |
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/** Rotate a vector by this quaternion.*/ |
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Vec3d operator* (const Vec3d& v) const |
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{ |
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// nVidia SDK implementation |
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Vec3d uv, uuv; |
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Vec3d qvec(_v[0], _v[1], _v[2]); |
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uv = qvec ^ v; |
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uuv = qvec ^ uv; |
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uv *= ( 2.0f * _v[3] ); |
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uuv *= 2.0f; |
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return v + uv + uuv; |
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} |
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protected: |
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}; // end of class prototype |
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} // end of namespace |
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#endif
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