266 lines
7.4 KiB
C++
266 lines
7.4 KiB
C++
/* -*-c++-*- OpenSceneGraph - Copyright (C) 1998-2003 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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#include <stdio.h>
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#include <osg/Quat>
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#include <osg/Vec4>
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#include <osg/Vec3>
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#include <osg/Matrixf>
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#include <osg/Matrixd>
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#include <math.h>
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/// Good introductions to Quaternions at:
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/// http://www.gamasutra.com/features/programming/19980703/quaternions_01.htm
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/// http://mathworld.wolfram.com/Quaternion.html
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using namespace osg;
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void Quat::set(const Matrixf& matrix)
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{
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matrix.get(*this);
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}
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void Quat::set(const Matrixd& matrix)
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{
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matrix.get(*this);
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}
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void Quat::get(Matrixf& matrix) const
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{
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matrix.set(*this);
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}
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void Quat::get(Matrixd& matrix) const
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{
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matrix.set(*this);
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}
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/// Set the elements of the Quat to represent a rotation of angle
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/// (radians) around the axis (x,y,z)
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void Quat::makeRotate( float angle,
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float x,
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float y,
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float z )
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{
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float inversenorm = 1.0/sqrt( x*x + y*y + z*z );
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float coshalfangle = cos( 0.5*angle );
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float sinhalfangle = sin( 0.5*angle );
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_fv[0] = x * sinhalfangle * inversenorm;
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_fv[1] = y * sinhalfangle * inversenorm;
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_fv[2] = z * sinhalfangle * inversenorm;
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_fv[3] = coshalfangle;
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}
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void Quat::makeRotate( float angle, const Vec3& vec )
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{
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makeRotate( angle, vec[0], vec[1], vec[2] );
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}
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void Quat::makeRotate ( float angle1, const Vec3& axis1,
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float angle2, const Vec3& axis2,
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float angle3, const Vec3& axis3)
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{
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Quat q1; q1.makeRotate(angle1,axis1);
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Quat q2; q2.makeRotate(angle2,axis2);
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Quat q3; q3.makeRotate(angle3,axis3);
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*this = q1*q2*q3;
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}
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// Make a rotation Quat which will rotate vec1 to vec2
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// Generally take adot 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 Quat::makeRotate( const Vec3& from, const Vec3& to )
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{
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const float epsilon = 0.00001f;
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float length1 = from.length();
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float length2 = to.length();
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// dot product vec1*vec2
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float cosangle = from*to/(length1*length2);
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if ( fabs(cosangle - 1) < epsilon )
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{
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// cosangle is close to 1, so the vectors are close to being coincident
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// Need to generate an angle of zero with any vector we like
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// We'll choose (1,0,0)
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makeRotate( 0.0, 1.0, 0.0, 0.0 );
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}
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else
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if ( fabs(cosangle + 1.0) < epsilon )
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{
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// vectors are close to being opposite, so will need to find a
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// vector orthongonal to from to rotate about.
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osg::Vec3 tmp;
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if (fabs(from.x())<fabs(from.y()))
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if (fabs(from.x())<fabs(from.z())) tmp.set(1.0,0.0,0.0); // use x axis.
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else tmp.set(0.0,0.0,1.0);
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else if (fabs(from.y())<fabs(from.z())) tmp.set(0.0,1.0,0.0);
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else tmp.set(0.0,0.0,1.0);
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// find orthogonal axis.
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Vec3 axis(from^tmp);
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axis.normalize();
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_fv[0] = axis[0]; // sin of half angle of PI is 1.0.
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_fv[1] = axis[1]; // sin of half angle of PI is 1.0.
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_fv[2] = axis[2]; // sin of half angle of PI is 1.0.
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_fv[3] = 0; // cos of half angle of PI is zero.
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}
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else
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{
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// This is the usual situation - take a cross-product of vec1 and vec2
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// and that is the axis around which to rotate.
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Vec3 axis(from^to);
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float angle = acos( cosangle );
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makeRotate( angle, axis );
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}
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}
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void Quat::getRotate( float& angle, Vec3& vec ) const
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{
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getRotate(angle,vec[0],vec[1],vec[2]);
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}
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// Get the angle of rotation and axis of this Quat object.
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// Won't give very meaningful results if the Quat is not associated
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// with a rotation!
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void Quat::getRotate( float& angle, float& x, float& y, float& z ) const
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{
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float sinhalfangle = sqrt( _fv[0]*_fv[0] + _fv[1]*_fv[1] + _fv[2]*_fv[2] );
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angle = 2 * atan2( sinhalfangle, _fv[3] );
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if(sinhalfangle)
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{
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x = _fv[0] / sinhalfangle;
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y = _fv[1] / sinhalfangle;
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z = _fv[2] / sinhalfangle;
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}
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else
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{
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x = 0.0f;
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y = 0.0f;
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z = 1.0f;
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}
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}
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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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/// Reference: Shoemake at SIGGRAPH 89
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/// See also
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/// http://www.gamasutra.com/features/programming/19980703/quaternions_01.htm
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void Quat::slerp( float t, const Quat& from, const Quat& to )
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{
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const double epsilon = 0.00001;
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double omega, cosomega, sinomega, scale_from, scale_to ;
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osg::Quat quatTo(to);
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// this is a dot product
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cosomega = from.asVec4() * to.asVec4();
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if ( cosomega <0.0 )
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{
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cosomega = -cosomega;
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quatTo.set(-to._fv);
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}
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if( (1.0 - cosomega) > epsilon )
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{
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omega= acos(cosomega) ; // 0 <= omega <= Pi (see man acos)
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sinomega = sin(omega) ; // this sinomega should always be +ve so
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// could try sinomega=sqrt(1-cosomega*cosomega) to avoid a sin()?
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scale_from = sin((1.0-t)*omega)/sinomega ;
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scale_to = sin(t*omega)/sinomega ;
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}
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else
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{
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/* --------------------------------------------------
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The ends of the vectors are very close
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we can use simple linear interpolation - no need
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to worry about the "spherical" interpolation
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-------------------------------------------------- */
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scale_from = 1.0 - t ;
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scale_to = t ;
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}
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// use Vec4 arithmetic
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_fv = (from._fv*scale_from) + (quatTo._fv*scale_to);
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// so that we get a Vec4
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}
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#define QX _fv[0]
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#define QY _fv[1]
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#define QZ _fv[2]
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#define QW _fv[3]
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#ifdef OSG_USE_UNIT_TESTS
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void test_Quat_Eueler(float heading,float pitch,float roll)
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{
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osg::Quat q;
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q.makeRotate(heading,pitch,roll);
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osg::Matrix q_m;
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q.get(q_m);
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osg::Vec3 xAxis(1,0,0);
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osg::Vec3 yAxis(0,1,0);
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osg::Vec3 zAxis(0,0,1);
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cout << "heading = "<<heading<<" pitch = "<<pitch<<" roll = "<<roll<<endl;
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cout <<"q_m = "<<q_m;
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cout <<"xAxis*q_m = "<<xAxis*q_m << endl;
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cout <<"yAxis*q_m = "<<yAxis*q_m << endl;
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cout <<"zAxis*q_m = "<<zAxis*q_m << endl;
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osg::Matrix r_m = osg::Matrix::rotate(roll,0.0,1.0,0.0)*
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osg::Matrix::rotate(pitch,1.0,0.0,0.0)*
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osg::Matrix::rotate(-heading,0.0,0.0,1.0);
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cout << "r_m = "<<r_m;
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cout <<"xAxis*r_m = "<<xAxis*r_m << endl;
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cout <<"yAxis*r_m = "<<yAxis*r_m << endl;
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cout <<"zAxis*r_m = "<<zAxis*r_m << endl;
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cout << endl<<"*****************************************" << endl<< endl;
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}
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void test_Quat()
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{
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test_Quat_Eueler(osg::DegreesToRadians(20),0,0);
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test_Quat_Eueler(0,osg::DegreesToRadians(20),0);
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test_Quat_Eueler(0,0,osg::DegreesToRadians(20));
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test_Quat_Eueler(osg::DegreesToRadians(20),osg::DegreesToRadians(20),osg::DegreesToRadians(20));
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return 0;
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}
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#endif
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