345 lines
9.6 KiB
C++
345 lines
9.6 KiB
C++
#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/Types>
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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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/// 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( const float angle,
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const float x,
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const float y,
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const 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( const 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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// assume Z up, Y north, X east and euler convention
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// as per Open Flight & Performer.
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// applies a positive rotation about Y axis for roll,
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// then applies a positive roation about X for pitch,
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// and finally a negative rotation about the Z axis.
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void Quat::makeRotate( float heading, float pitch, float roll)
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{
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Quat q_roll; q_roll.makeRotate(roll,0.0,1.0,0.0);
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Quat q_pitch; q_pitch.makeRotate(pitch,1.0,0.0,0.0);
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Quat q_heading; q_heading.makeRotate(-heading,0.0,0.0,1.0);
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// note reverse order than would be done using matrices
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// which raises the interesting question whether the definition
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// of Quat*Quat should be changed to fit with the v' = v x M
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// convention of Matrix. Will investigate further later on.
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// Robert Osfield. April 2002.
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*this = q_heading*q_pitch*q_roll;
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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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// 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, Vec3& vec ) 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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/// float coshalfangle = _fv[3];
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/// These are not checked for performance reasons ? (cop out!)
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/// Point for discussion - how do one handle errors in the osg?
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/// if ( abs(sinhalfangle) > 1.0 ) { error };
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/// if ( abs(coshalfangle) > 1.0 ) { error };
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// *angle = atan2( sinhalfangle, coshalfangle ); // see man atan2
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// -pi < angle < pi
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angle = 2 * atan2( sinhalfangle, _fv[3] );
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vec = Vec3(_fv[0], _fv[1], _fv[2]) / sinhalfangle;
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}
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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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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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/// 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( const 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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void Quat::set( const Matrix& m )
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{
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// Source: Gamasutra, Rotating Objects Using Quaternions
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//
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//http://www.gamasutra.com/features/programming/19980703/quaternions_01.htm
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float tr, s;
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float tq[4];
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int i, j, k;
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int nxt[3] = {1, 2, 0};
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tr = m(0,0) + m(1,1) + m(2,2);
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// check the diagonal
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if (tr > 0.0)
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{
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s = (float)sqrt (tr + 1.0);
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QW = s / 2.0f;
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s = 0.5f / s;
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QX = (m(1,2) - m(2,1)) * s;
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QY = (m(2,0) - m(0,2)) * s;
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QZ = (m(0,1) - m(1,0)) * s;
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}
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else
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{
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// diagonal is negative
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i = 0;
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if (m(1,1) > m(0,0))
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i = 1;
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if (m(2,2) > m(i,i))
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i = 2;
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j = nxt[i];
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k = nxt[j];
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s = (float)sqrt ((m(i,i) - (m(j,j) + m(k,k))) + 1.0);
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tq[i] = s * 0.5f;
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if (s != 0.0f)
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s = 0.5f / s;
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tq[3] = (m(j,k) - m(k,j)) * s;
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tq[j] = (m(i,j) + m(j,i)) * s;
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tq[k] = (m(i,k) + m(k,i)) * s;
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QX = tq[0];
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QY = tq[1];
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QZ = tq[2];
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QW = tq[3];
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}
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}
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void Quat::get( Matrix& m ) const
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{
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// Source: Gamasutra, Rotating Objects Using Quaternions
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//
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//http://www.gamasutra.com/features/programming/19980703/quaternions_01.htm
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double wx, wy, wz, xx, yy, yz, xy, xz, zz, x2, y2, z2;
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// calculate coefficients
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x2 = QX + QX;
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y2 = QY + QY;
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z2 = QZ + QZ;
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xx = QX * x2;
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xy = QX * y2;
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xz = QX * z2;
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yy = QY * y2;
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yz = QY * z2;
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zz = QZ * z2;
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wx = QW * x2;
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wy = QW * y2;
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wz = QW * z2;
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// Note. Gamasutra gets the matrix assignments inverted, resulting
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// in left-handed rotations, which is contrary to OpenGL and OSG's
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// methodology. The matrix assignment has been altered in the next
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// few lines of code to do the right thing.
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// Don Burns - Oct 13, 2001
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m(0,0) = 1.0f - (yy + zz);
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m(1,0) = xy - wz;
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m(2,0) = xz + wy;
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m(3,0) = 0.0f;
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m(0,1) = xy + wz;
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m(1,1) = 1.0f - (xx + zz);
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m(2,1) = yz - wx;
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m(3,1) = 0.0f;
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m(0,2) = xz - wy;
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m(1,2) = yz + wx;
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m(2,2) = 1.0f - (xx + yy);
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m(3,2) = 0.0f;
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m(0,3) = 0;
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m(1,3) = 0;
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m(2,3) = 0;
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m(3,3) = 1;
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}
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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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