Hi all,
it's been known for a while [1] that there are inconsistencies with the
way OSG handles Quat * Vec3. In short: Quat * Vec3 is written in code as
a post-multiply, but the result of the operation is as if a pre-multiply
was performed. The attached test app also shows the problem (more on it
later).
[1]
http://thread.gmane.org/gmane.comp.graphics.openscenegraph.user/21003
and
http://thread.gmane.org/gmane.comp.graphics.openscenegraph.user/33099
What doesn't work?
There are many examples that can be constructed of where a mathematical
expression usings quats and vectors would not provide the expected
results. See also [1]. The easiest one I could come up with is this:
((q1 * q2) * v) != (q1 * (q2 * v))
Why are there not more complaints?
I suppose most people do all the quat multiplications before they
multiply with the vector. Since OSG does not have a pre-multiply for
quat, the only option is then to post-multiply the resulting quat with
the vector.
What can be done?
As a first step I think we can add the pre-multiply to OSG. The attached
header does this. (To fix the post-multiply can be done later.)
What will break?
I think and hope nothing, since there was no pre-multiply that people
could have used. (Fixing the post-multiply would break current code.)
Why now?
The itch finally got annoying enough.
What about the post-multiply?
I think we should in some way let developers know that the post-multiply
they currently use will change in future and that they should switch
their multiply to the pre-version (which will behave the same as current
code). I think a compiler warning or error would help more than only
documentation. Something like a deprecated warning. I need help with
this though, I do not know how to generate a warning in a cross-platform
manner. Later we can then fix the post-multiply quat code.
Test app details:
The test app considers two rotations and a vector. It shows that for
Matrix and Vec3 interactions everything is consistent, e.g.
((m1 * m2) * v) == (m1 * (m2 * v))
and
(v * (m1 * m2)) == ((v * m1) * m2)
It then shows that Quat post-multiply does not behave as Matrix
post-multiply does and actually behaves more like Matrix pre-multiply
does. It also shows the inconsistency of various expressions.
We also know (from the osgunittest example) that
m1(q1) * m2(q2) == q1 * q2
so the internal quat * quat is consistent with the matrix multiply
order. It is only the quat * vec that is not.
Finally it shows that with the added pre-multiply (enable by making the
#if 0 a 1), the quat pre-mult behaves the same as the matrix pre-mult.
Comments welcome.
regards
jp
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/* -*-c++-*- OpenSceneGraph - Copyright (C) 1998-2006 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.
*/
#ifndef OSG_QUAT
#define OSG_QUAT 1
#include <osg/Export>
#include <osg/Vec3f>
#include <osg/Vec4f>
#include <osg/Vec3d>
#include <osg/Vec4d>
namespace osg {
class Matrixf;
class Matrixd;
/** A quaternion class. It can be used to represent an orientation in 3D
space.*/
class OSG_EXPORT Quat
{
public:
typedef double value_type;
value_type _v[4]; // a four-vector
inline Quat() { _v[0]=0.0; _v[1]=0.0; _v[2]=0.0; _v[3]=1.0; }
inline Quat( value_type x, value_type y, value_type z, value_type w )
{
_v[0]=x;
_v[1]=y;
_v[2]=z;
_v[3]=w;
}
inline Quat( const Vec4f& v )
{
_v[0]=v.x();
_v[1]=v.y();
_v[2]=v.z();
_v[3]=v.w();
}
inline Quat( const Vec4d& v )
{
_v[0]=v.x();
_v[1]=v.y();
_v[2]=v.z();
_v[3]=v.w();
}
inline Quat( value_type angle, const Vec3f& axis)
{
makeRotate(angle,axis);
}
inline Quat( value_type angle, const Vec3d& axis)
{
makeRotate(angle,axis);
}
inline Quat( value_type angle1, const Vec3f& axis1,
value_type angle2, const Vec3f& axis2,
value_type angle3, const Vec3f& axis3)
{
makeRotate(angle1,axis1,angle2,axis2,angle3,axis3);
}
inline Quat( value_type angle1, const Vec3d& axis1,
value_type angle2, const Vec3d& axis2,
value_type angle3, const Vec3d& axis3)
{
makeRotate(angle1,axis1,angle2,axis2,angle3,axis3);
}
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; }
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]; }
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]; }
inline bool operator < (const Quat& v) const
{
if (_v[0]<v._v[0]) return true;
else if (_v[0]>v._v[0]) return false;
else if (_v[1]<v._v[1]) return true;
else if (_v[1]>v._v[1]) return false;
else if (_v[2]<v._v[2]) return true;
else if (_v[2]>v._v[2]) return false;
else return (_v[3]<v._v[3]);
}
/* ----------------------------------
Methods to access data members
---------------------------------- */
inline Vec4d asVec4() const
{
return Vec4d(_v[0], _v[1], _v[2], _v[3]);
}
inline Vec3d asVec3() const
{
return Vec3d(_v[0], _v[1], _v[2]);
}
inline void set(value_type x, value_type y, value_type z, value_type w)
{
_v[0]=x;
_v[1]=y;
_v[2]=z;
_v[3]=w;
}
inline void set(const osg::Vec4f& v)
{
_v[0]=v.x();
_v[1]=v.y();
_v[2]=v.z();
_v[3]=v.w();
}
inline void set(const osg::Vec4d& v)
{
_v[0]=v.x();
_v[1]=v.y();
_v[2]=v.z();
_v[3]=v.w();
}
void set(const Matrixf& matrix);
void set(const Matrixd& matrix);
void get(Matrixf& matrix) const;
void get(Matrixd& matrix) const;
inline value_type & operator [] (int i) { return _v[i]; }
inline value_type operator [] (int i) const { return _v[i]; }
inline value_type & x() { return _v[0]; }
inline value_type & y() { return _v[1]; }
inline value_type & z() { return _v[2]; }
inline value_type & w() { return _v[3]; }
inline value_type x() const { return _v[0]; }
inline value_type y() const { return _v[1]; }
inline value_type z() const { return _v[2]; }
inline value_type w() const { return _v[3]; }
/** return true if the Quat represents a zero rotation, and therefore
can be ignored in computations.*/
bool zeroRotation() const { return _v[0]==0.0 && _v[1]==0.0 &&
_v[2]==0.0 && _v[3]==1.0; }
/* -------------------------------------------------------------
BASIC ARITHMETIC METHODS
Implemented in terms of Vec4s. Some Vec4 operators, e.g.
operator* are not appropriate for quaternions (as
mathematical objects) so they are implemented differently.
Also define methods for conjugate and the multiplicative inverse.
------------------------------------------------------------- */
/// Multiply by scalar
inline const Quat operator * (value_type rhs) const
{
return Quat(_v[0]*rhs, _v[1]*rhs, _v[2]*rhs, _v[3]*rhs);
}
/// Unary multiply by scalar
inline Quat& operator *= (value_type rhs)
{
_v[0]*=rhs;
_v[1]*=rhs;
_v[2]*=rhs;
_v[3]*=rhs;
return *this; // enable nesting
}
/// Binary multiply
inline const Quat operator*(const Quat& rhs) const
{
return Quat( rhs._v[3]*_v[0] + rhs._v[0]*_v[3] + rhs._v[1]*_v[2] -
rhs._v[2]*_v[1],
rhs._v[3]*_v[1] - rhs._v[0]*_v[2] + rhs._v[1]*_v[3] +
rhs._v[2]*_v[0],
rhs._v[3]*_v[2] + rhs._v[0]*_v[1] - rhs._v[1]*_v[0] +
rhs._v[2]*_v[3],
rhs._v[3]*_v[3] - rhs._v[0]*_v[0] - rhs._v[1]*_v[1] -
rhs._v[2]*_v[2] );
}
/// Unary multiply
inline Quat& operator*=(const Quat& rhs)
{
value_type x = rhs._v[3]*_v[0] + rhs._v[0]*_v[3] + rhs._v[1]*_v[2]
- rhs._v[2]*_v[1];
value_type y = rhs._v[3]*_v[1] - rhs._v[0]*_v[2] + rhs._v[1]*_v[3]
+ rhs._v[2]*_v[0];
value_type z = rhs._v[3]*_v[2] + rhs._v[0]*_v[1] - rhs._v[1]*_v[0]
+ rhs._v[2]*_v[3];
_v[3] = rhs._v[3]*_v[3] - rhs._v[0]*_v[0] - rhs._v[1]*_v[1] -
rhs._v[2]*_v[2];
_v[2] = z;
_v[1] = y;
_v[0] = x;
return (*this); // enable nesting
}
/// Divide by scalar
inline Quat operator / (value_type rhs) const
{
value_type div = 1.0/rhs;
return Quat(_v[0]*div, _v[1]*div, _v[2]*div, _v[3]*div);
}
/// Unary divide by scalar
inline Quat& operator /= (value_type rhs)
{
value_type div = 1.0/rhs;
_v[0]*=div;
_v[1]*=div;
_v[2]*=div;
_v[3]*=div;
return *this;
}
/// Binary divide
inline const Quat operator/(const Quat& denom) const
{
return ( (*this) * denom.inverse() );
}
/// Unary divide
inline Quat& operator/=(const Quat& denom)
{
(*this) = (*this) * denom.inverse();
return (*this); // enable nesting
}
/// Binary addition
inline const Quat operator + (const Quat& rhs) const
{
return Quat(_v[0]+rhs._v[0], _v[1]+rhs._v[1],
_v[2]+rhs._v[2], _v[3]+rhs._v[3]);
}
/// Unary addition
inline Quat& operator += (const Quat& rhs)
{
_v[0] += rhs._v[0];
_v[1] += rhs._v[1];
_v[2] += rhs._v[2];
_v[3] += rhs._v[3];
return *this; // enable nesting
}
/// Binary subtraction
inline const Quat operator - (const Quat& rhs) const
{
return Quat(_v[0]-rhs._v[0], _v[1]-rhs._v[1],
_v[2]-rhs._v[2], _v[3]-rhs._v[3] );
}
/// Unary subtraction
inline Quat& operator -= (const Quat& rhs)
{
_v[0]-=rhs._v[0];
_v[1]-=rhs._v[1];
_v[2]-=rhs._v[2];
_v[3]-=rhs._v[3];
return *this; // enable nesting
}
/** Negation operator - returns the negative of the quaternion.
Basically just calls operator - () on the Vec4 */
inline const Quat operator - () const
{
return Quat (-_v[0], -_v[1], -_v[2], -_v[3]);
}
/// Length of the quaternion = sqrt( vec . vec )
value_type length() const
{
return sqrt( _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] + _v[3]*_v[3]);
}
/// Length of the quaternion = vec . vec
value_type length2() const
{
return _v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2] + _v[3]*_v[3];
}
/// Conjugate
inline Quat conj () const
{
return Quat( -_v[0], -_v[1], -_v[2], _v[3] );
}
/// Multiplicative inverse method: q^(-1) = q^*/(q.q^*)
inline const Quat inverse () const
{
return conj() / length2();
}
/* --------------------------------------------------------
METHODS RELATED TO ROTATIONS
Set a quaternion which will perform a rotation of an
angle around the axis given by the vector (x,y,z).
Should be written to also accept an angle and a Vec3?
Define Spherical Linear interpolation method also
Not inlined - see the Quat.cpp file for implementation
-------------------------------------------------------- */
void makeRotate( value_type angle,
value_type x, value_type y, value_type z );
void makeRotate ( value_type angle, const Vec3f& vec );
void makeRotate ( value_type angle, const Vec3d& vec );
void makeRotate ( value_type angle1, const Vec3f& axis1,
value_type angle2, const Vec3f& axis2,
value_type angle3, const Vec3f& axis3);
void makeRotate ( value_type angle1, const Vec3d& axis1,
value_type angle2, const Vec3d& axis2,
value_type angle3, const Vec3d& axis3);
/** Make a rotation Quat which will rotate vec1 to vec2.
Generally take a dot 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 when the vectors
are co-incident or opposite in direction.*/
void makeRotate( const Vec3f& vec1, const Vec3f& vec2 );
/** Make a rotation Quat which will rotate vec1 to vec2.
Generally take a dot 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 makeRotate( const Vec3d& vec1, const Vec3d& vec2 );
void makeRotate_original( const Vec3d& vec1, const Vec3d& vec2 );
/** Return the angle and vector components represented by the
quaternion.*/
void getRotate ( value_type & angle, value_type & x, value_type & y,
value_type & z ) const;
/** Return the angle and vector represented by the quaternion.*/
void getRotate ( value_type & angle, Vec3f& vec ) const;
/** Return the angle and vector represented by the quaternion.*/
void getRotate ( value_type & angle, Vec3d& vec ) const;
/** Spherical Linear Interpolation.
As t goes from 0 to 1, the Quat object goes from "from" to "to". */
void slerp ( value_type t, const Quat& from, const Quat& to);
/** Rotate a vector by this quaternion.*/
Vec3f operator* (const Vec3f& v) const
{
// nVidia SDK implementation
Vec3f uv, uuv;
Vec3f qvec(_v[0], _v[1], _v[2]);
uv = qvec ^ v;
uuv = qvec ^ uv;
uv *= ( 2.0f * _v[3] );
uuv *= 2.0f;
return v + uv + uuv;
}
/** Rotate a vector by this quaternion.*/
Vec3d operator* (const Vec3d& v) const
{
// nVidia SDK implementation
Vec3d uv, uuv;
Vec3d qvec(_v[0], _v[1], _v[2]);
uv = qvec ^ v;
uuv = qvec ^ uv;
uv *= ( 2.0f * _v[3] );
uuv *= 2.0f;
return v + uv + uuv;
}
protected:
}; // end of class prototype
/** Rotate a vector by this quaternion. Pre-multiply. */
inline Vec3f operator* (const Vec3f& v, const Quat& q)
{
// nVidia SDK implementation
Vec3f uv, uuv;
Vec3f qvec(q._v[0], q._v[1], q._v[2]);
uv = qvec ^ v;
uuv = qvec ^ uv;
uv *= ( 2.0f * q._v[3] );
uuv *= 2.0f;
return v + uv + uuv;
}
/** Rotate a vector by this quaternion. Pre-multiply. */
inline Vec3d operator* (const Vec3d& v, const Quat& q)
{
// nVidia SDK implementation
Vec3d uv, uuv;
Vec3d qvec(q._v[0], q._v[1], q._v[2]);
uv = qvec ^ v;
uuv = qvec ^ uv;
uv *= ( 2.0f * q._v[3] );
uuv *= 2.0f;
return v + uv + uuv;
}
} // end of namespace
#endif
#include <osg/Quat>
#include <osg/Matrixd>
#include <osg/io_utils>
#include <iostream>
#include <math.h>
int main(void)
{
double pitch = osg::DegreesToRadians(45.0);
double roll = osg::DegreesToRadians(45.0);
osg::Vec3d forward_vec(1,0,0);
osg::Quat pitch_quat(pitch, osg::Vec3d(0,1,0));
osg::Quat roll_quat(roll, osg::Vec3d(1,0,0));
osg::Matrixd pitch_mat(pitch_quat);
osg::Matrixd roll_mat(roll_quat);
std::cout << "\nMatrix post-multiply\n";
{
osg::Vec3d fw_pitch = pitch_mat * forward_vec;
std::cout << "Forward vector after pitch:\n" << fw_pitch << "\n";
osg::Vec3d fw_pitch_roll;
fw_pitch_roll = roll_mat * fw_pitch;
std::cout << "Forward vector after roll:\n" << fw_pitch_roll << "\n";
std::cout << "Brackets should not make a difference:\n";
fw_pitch_roll = roll_mat * pitch_mat * forward_vec;
std::cout << fw_pitch_roll << "\n";
fw_pitch_roll = (roll_mat * pitch_mat) * forward_vec;
std::cout << fw_pitch_roll << "\n";
fw_pitch_roll = roll_mat * (pitch_mat * forward_vec);
std::cout << fw_pitch_roll << "\n";
}
std::cout << "\nQuaternion post-multiply\n";
{
osg::Vec3d fw_pitch = pitch_quat * forward_vec;
std::cout << "Forward vector after pitch:\n" << fw_pitch << "\n";
osg::Vec3d fw_pitch_roll;
fw_pitch_roll = roll_quat * fw_pitch;
std::cout << "Forward vector after roll:\n" << fw_pitch_roll << "\n";
std::cout << "Brackets should not make a difference:\n";
fw_pitch_roll = roll_quat * pitch_quat * forward_vec;
std::cout << fw_pitch_roll << "\n";
fw_pitch_roll = (roll_quat * pitch_quat) * forward_vec;
std::cout << fw_pitch_roll << "\n";
fw_pitch_roll = roll_quat * (pitch_quat * forward_vec);
std::cout << fw_pitch_roll << "\n";
}
std::cout << "\nMatrix pre-multiply\n";
{
osg::Vec3d fw_pitch = forward_vec * pitch_mat;
std::cout << "Forward vector after pitch:\n" << fw_pitch << "\n";
osg::Vec3d fw_pitch_roll;
fw_pitch_roll = fw_pitch * roll_mat;
std::cout << "Forward vector after roll:\n" << fw_pitch_roll << "\n";
std::cout << "Brackets should not make a difference:\n";
fw_pitch_roll = forward_vec * pitch_mat * roll_mat;
std::cout << fw_pitch_roll << "\n";
fw_pitch_roll = (forward_vec * pitch_mat) * roll_mat;
std::cout << fw_pitch_roll << "\n";
fw_pitch_roll = forward_vec * (pitch_mat * roll_mat);
std::cout << fw_pitch_roll << "\n";
}
// The following can only compile if the pre-multiply functions are added for
// OSG's Quat.
#if 0
std::cout << "\nQuaternion pre-multiply\n";
{
osg::Vec3d fw_pitch = forward_vec * pitch_quat;
std::cout << "Forward vector after pitch:\n" << fw_pitch << "\n";
osg::Vec3d fw_pitch_roll;
fw_pitch_roll = fw_pitch * roll_quat;
std::cout << "Forward vector after roll:\n" << fw_pitch_roll << "\n";
std::cout << "Brackets should not make a difference:\n";
fw_pitch_roll = forward_vec * pitch_quat * roll_quat;
std::cout << fw_pitch_roll << "\n";
fw_pitch_roll = (forward_vec * pitch_quat) * roll_quat;
std::cout << fw_pitch_roll << "\n";
fw_pitch_roll = forward_vec * (pitch_quat * roll_quat);
std::cout << fw_pitch_roll << "\n";
}
#endif
}
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