/
DualQuaternion.cpp
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/
DualQuaternion.cpp
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/***************************************************************************
* Copyright (c) 2019 Viktor Titov (DeepSOIC) <vv.titov@gmail.com> *
* *
* This file is part of the FreeCAD CAx development system. *
* *
* This library is free software; you can redistribute it and/or *
* modify it under the terms of the GNU Library General Public *
* License as published by the Free Software Foundation; either *
* version 2 of the License, or (at your option) any later version. *
* *
* 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 *
* GNU Library General Public License for more details. *
* *
* You should have received a copy of the GNU Library General Public *
* License along with this library; see the file COPYING.LIB. If not, *
* write to the Free Software Foundation, Inc., 59 Temple Place, *
* Suite 330, Boston, MA 02111-1307, USA *
* *
***************************************************************************/
#include "PreCompiled.h"
#include "DualQuaternion.h"
#include "cassert"
Base::DualQuat Base::operator+(Base::DualQuat a, Base::DualQuat b)
{
return DualQuat(
a.x + b.x,
a.y + b.y,
a.z + b.z,
a.w + b.w
);
}
Base::DualQuat Base::operator-(Base::DualQuat a, Base::DualQuat b)
{
return DualQuat(
a.x - b.x,
a.y - b.y,
a.z - b.z,
a.w - b.w
);
}
Base::DualQuat Base::operator*(Base::DualQuat a, Base::DualQuat b)
{
return DualQuat(
a.w * b.x + a.x * b.w + a.y * b.z - a.z * b.y,
a.w * b.y + a.y * b.w + a.z * b.x - a.x * b.z,
a.w * b.z + a.z * b.w + a.x * b.y - a.y * b.x,
a.w * b.w - a.x * b.x - a.y * b.y - a.z * b.z
);
}
Base::DualQuat Base::operator*(Base::DualQuat a, double b)
{
return DualQuat(
a.x * b,
a.y * b,
a.z * b,
a.w * b
);
}
Base::DualQuat Base::operator*(double a, Base::DualQuat b)
{
return DualQuat(
b.x * a,
b.y * a,
b.z * a,
b.w * a
);
}
Base::DualQuat Base::operator*(Base::DualQuat a, Base::DualNumber b)
{
return DualQuat(
a.x * b,
a.y * b,
a.z * b,
a.w * b
);
}
Base::DualQuat Base::operator*(Base::DualNumber a, Base::DualQuat b)
{
return DualQuat(
b.x * a,
b.y * a,
b.z * a,
b.w * a
);
}
Base::DualQuat::DualQuat(Base::DualQuat re, Base::DualQuat du)
: x(re.x.re, du.x.re),
y(re.y.re, du.y.re),
z(re.z.re, du.z.re),
w(re.w.re, du.w.re)
{
assert(re.dual().length() < 1e-12);
assert(du.dual().length() < 1e-12);
}
double Base::DualQuat::dot(Base::DualQuat a, Base::DualQuat b)
{
return a.x.re * b.x.re +
a.y.re * b.y.re +
a.z.re * b.z.re +
a.w.re * b.w.re ;
}
Base::DualQuat Base::DualQuat::pow(double t, bool shorten) const
{
/* implemented after "Dual-Quaternions: From Classical Mechanics to
* Computer Graphics and Beyond" by Ben Kenwright www.xbdev.net
* bkenwright@xbdev.net
* http://www.xbdev.net/misc_demos/demos/dual_quaternions_beyond/paper.pdf
*
* There are some differences:
*
* * Special handling of no-rotation situation (because normalization
* multiplier becomes infinite in this situation, breaking the algorithm).
*
* * Dual quaternions are implemented as a collection of dual numbers,
* rather than a collection of two quaternions like it is done in suggested
* inplementation in the paper.
*
* * acos replaced with atan2 for improved angle accuracy for small angles
*
* */
double le = this->vec().length();
if (le < 1e-12) {
//special case of no rotation. Interpolate position
return DualQuat(this->real(), this->dual()*t);
}
double normmult = 1.0/le;
DualQuat self = *this;
if (shorten){
if (dot(self, identity()) < -1e-12){ //using negative tolerance instead of zero, for stability in situations the choice is ambiguous (180-degree rotations)
self = -self;
}
}
//to screw coordinates
double theta = self.theta();
double pitch = -2.0 * self.w.du * normmult;
DualQuat l = self.real().vec() * normmult; //abusing DualQuat to store vectors. Very handy in this case.
DualQuat m = (self.dual().vec() - pitch/2*cos(theta/2)*l)*normmult;
//interpolate
theta *= t;
pitch *= t;
//back to quaternion
return DualQuat(
l * sin(theta/2) + DualQuat(0,0,0,cos(theta/2)),
m * sin(theta/2) + pitch / 2 * cos(theta/2) * l + DualQuat(0,0,0,-pitch/2*sin(theta/2))
);
}