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OpenSceneGraph/src/osg/Quat.cpp

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/* -*-c++-*- OpenSceneGraph - Copyright (C) 1998-2003 Robert Osfield
*
* This library is open source and may be redistributed and/or modified under
* the terms of the OpenSceneGraph Public License (OSGPL) version 0.0 or
* (at your option) any later version. The full license is in LICENSE file
* included with this distribution, and on the openscenegraph.org website.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* OpenSceneGraph Public License for more details.
*/
#include <stdio.h>
#include <osg/Quat>
#include <osg/Matrixf>
#include <osg/Matrixd>
#include <osg/Notify>
#include <math.h>
/// Good introductions to Quaternions at:
/// http://www.gamasutra.com/features/programming/19980703/quaternions_01.htm
/// http://mathworld.wolfram.com/Quaternion.html
using namespace osg;
void Quat::set(const Matrixf& matrix)
{
matrix.get(*this);
}
void Quat::set(const Matrixd& matrix)
{
matrix.get(*this);
}
void Quat::get(Matrixf& matrix) const
{
matrix.set(*this);
}
void Quat::get(Matrixd& matrix) const
{
matrix.set(*this);
}
/// Set the elements of the Quat to represent a rotation of angle
/// (radians) around the axis (x,y,z)
void Quat::makeRotate( value_type angle, value_type x, value_type y, value_type z )
{
const value_type epsilon = 0.0000001;
value_type length = sqrt( x*x + y*y + z*z );
if (length < epsilon)
{
// ~zero length axis, so reset rotation to zero.
*this = Quat();
return;
}
value_type inversenorm = 1.0/length;
value_type coshalfangle = cos( 0.5*angle );
value_type sinhalfangle = sin( 0.5*angle );
_v[0] = x * sinhalfangle * inversenorm;
_v[1] = y * sinhalfangle * inversenorm;
_v[2] = z * sinhalfangle * inversenorm;
_v[3] = coshalfangle;
}
void Quat::makeRotate( value_type angle, const Vec3f& vec )
{
makeRotate( angle, vec[0], vec[1], vec[2] );
}
void Quat::makeRotate( value_type angle, const Vec3d& vec )
{
makeRotate( angle, vec[0], vec[1], vec[2] );
}
void Quat::makeRotate ( value_type angle1, const Vec3f& axis1,
value_type angle2, const Vec3f& axis2,
value_type angle3, const Vec3f& axis3)
{
makeRotate(angle1,Vec3d(axis1),
angle2,Vec3d(axis2),
angle3,Vec3d(axis3));
}
void Quat::makeRotate ( value_type angle1, const Vec3d& axis1,
value_type angle2, const Vec3d& axis2,
value_type angle3, const Vec3d& axis3)
{
Quat q1; q1.makeRotate(angle1,axis1);
Quat q2; q2.makeRotate(angle2,axis2);
Quat q3; q3.makeRotate(angle3,axis3);
*this = q1*q2*q3;
}
void Quat::makeRotate( const Vec3f& from, const Vec3f& to )
{
makeRotate( Vec3d(from), Vec3d(to) );
}
// Make a rotation Quat which will rotate vec1 to vec2
// Generally take adot product to get the angle between these
// and then use a cross product to get the rotation axis
// Watch out for the two special cases of when the vectors
// are co-incident or opposite in direction.
void Quat::makeRotate( const Vec3d& from, const Vec3d& to )
{
const value_type epsilon = 0.0000001;
value_type length1 = from.length();
value_type length2 = to.length();
// dot product vec1*vec2
value_type cosangle = from*to/(length1*length2);
if ( fabs(cosangle - 1) < epsilon )
{
osg::notify(osg::INFO)<<"*** Quat::makeRotate(from,to) with near co-linear vectors, epsilon= "<<fabs(cosangle-1)<<std::endl;
// cosangle is close to 1, so the vectors are close to being coincident
// Need to generate an angle of zero with any vector we like
// We'll choose (1,0,0)
makeRotate( 0.0, 0.0, 0.0, 1.0 );
}
else
if ( fabs(cosangle + 1.0) < epsilon )
{
// vectors are close to being opposite, so will need to find a
// vector orthongonal to from to rotate about.
Vec3d tmp;
if (fabs(from.x())<fabs(from.y()))
if (fabs(from.x())<fabs(from.z())) tmp.set(1.0,0.0,0.0); // use x axis.
else tmp.set(0.0,0.0,1.0);
else if (fabs(from.y())<fabs(from.z())) tmp.set(0.0,1.0,0.0);
else tmp.set(0.0,0.0,1.0);
Vec3d fromd(from.x(),from.y(),from.z());
// find orthogonal axis.
Vec3d axis(fromd^tmp);
axis.normalize();
_v[0] = axis[0]; // sin of half angle of PI is 1.0.
_v[1] = axis[1]; // sin of half angle of PI is 1.0.
_v[2] = axis[2]; // sin of half angle of PI is 1.0.
_v[3] = 0; // cos of half angle of PI is zero.
}
else
{
// This is the usual situation - take a cross-product of vec1 and vec2
// and that is the axis around which to rotate.
Vec3d axis(from^to);
value_type angle = acos( cosangle );
makeRotate( angle, axis );
}
}
void Quat::getRotate( value_type& angle, Vec3f& vec ) const
{
value_type x,y,z;
getRotate(angle,x,y,z);
vec[0]=x;
vec[1]=y;
vec[2]=z;
}
void Quat::getRotate( value_type& angle, Vec3d& vec ) const
{
value_type x,y,z;
getRotate(angle,x,y,z);
vec[0]=x;
vec[1]=y;
vec[2]=z;
}
// Get the angle of rotation and axis of this Quat object.
// Won't give very meaningful results if the Quat is not associated
// with a rotation!
void Quat::getRotate( value_type& angle, value_type& x, value_type& y, value_type& z ) const
{
value_type sinhalfangle = sqrt( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] );
angle = 2.0 * atan2( sinhalfangle, _v[3] );
if(sinhalfangle)
{
x = _v[0] / sinhalfangle;
y = _v[1] / sinhalfangle;
z = _v[2] / sinhalfangle;
}
else
{
x = 0.0;
y = 0.0;
z = 1.0;
}
}
/// Spherical Linear Interpolation
/// As t goes from 0 to 1, the Quat object goes from "from" to "to"
/// Reference: Shoemake at SIGGRAPH 89
/// See also
/// http://www.gamasutra.com/features/programming/19980703/quaternions_01.htm
void Quat::slerp( value_type t, const Quat& from, const Quat& to )
{
const double epsilon = 0.00001;
double omega, cosomega, sinomega, scale_from, scale_to ;
osg::Quat quatTo(to);
// this is a dot product
cosomega = from.asVec4() * to.asVec4();
if ( cosomega <0.0 )
{
cosomega = -cosomega;
quatTo = -to;
}
if( (1.0 - cosomega) > epsilon )
{
omega= acos(cosomega) ; // 0 <= omega <= Pi (see man acos)
sinomega = sin(omega) ; // this sinomega should always be +ve so
// could try sinomega=sqrt(1-cosomega*cosomega) to avoid a sin()?
scale_from = sin((1.0-t)*omega)/sinomega ;
scale_to = sin(t*omega)/sinomega ;
}
else
{
/* --------------------------------------------------
The ends of the vectors are very close
we can use simple linear interpolation - no need
to worry about the "spherical" interpolation
-------------------------------------------------- */
scale_from = 1.0 - t ;
scale_to = t ;
}
*this = (from*scale_from) + (quatTo*scale_to);
// so that we get a Vec4
}
#define QX _v[0]
#define QY _v[1]
#define QZ _v[2]
#define QW _v[3]
#ifdef OSG_USE_UNIT_TESTS
void test_Quat_Eueler(value_type heading,value_type pitch,value_type roll)
{
osg::Quat q;
q.makeRotate(heading,pitch,roll);
osg::Matrix q_m;
q.get(q_m);
osg::Vec3 xAxis(1,0,0);
osg::Vec3 yAxis(0,1,0);
osg::Vec3 zAxis(0,0,1);
cout << "heading = "<<heading<<" pitch = "<<pitch<<" roll = "<<roll<<endl;
cout <<"q_m = "<<q_m;
cout <<"xAxis*q_m = "<<xAxis*q_m << endl;
cout <<"yAxis*q_m = "<<yAxis*q_m << endl;
cout <<"zAxis*q_m = "<<zAxis*q_m << endl;
osg::Matrix r_m = osg::Matrix::rotate(roll,0.0,1.0,0.0)*
osg::Matrix::rotate(pitch,1.0,0.0,0.0)*
osg::Matrix::rotate(-heading,0.0,0.0,1.0);
cout << "r_m = "<<r_m;
cout <<"xAxis*r_m = "<<xAxis*r_m << endl;
cout <<"yAxis*r_m = "<<yAxis*r_m << endl;
cout <<"zAxis*r_m = "<<zAxis*r_m << endl;
cout << endl<<"*****************************************" << endl<< endl;
}
void test_Quat()
{
test_Quat_Eueler(osg::DegreesToRadians(20),0,0);
test_Quat_Eueler(0,osg::DegreesToRadians(20),0);
test_Quat_Eueler(0,0,osg::DegreesToRadians(20));
test_Quat_Eueler(osg::DegreesToRadians(20),osg::DegreesToRadians(20),osg::DegreesToRadians(20));
return 0;
}
#endif
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