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// Inertial Measurement Unit Maths Library
//
// Copyright 2013-2021 Sam Cowen <[email protected]>
// Bug fixes and cleanups by Gé Vissers ([email protected])
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
#ifndef IMUMATH_QUATERNION_HPP
#define IMUMATH_QUATERNION_HPP
#include <math.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include "matrix.h"
namespace imu {
class Quaternion {
public:
Quaternion() : _w(1.0), _x(0.0), _y(0.0), _z(0.0) {}
Quaternion(double w, double x, double y, double z)
: _w(w), _x(x), _y(y), _z(z) {}
Quaternion(double w, Vector<3> vec)
: _w(w), _x(vec.x()), _y(vec.y()), _z(vec.z()) {}
double &w() { return _w; }
double &x() { return _x; }
double &y() { return _y; }
double &z() { return _z; }
double w() const { return _w; }
double x() const { return _x; }
double y() const { return _y; }
double z() const { return _z; }
double magnitude() const {
return sqrt(_w * _w + _x * _x + _y * _y + _z * _z);
}
void normalize() {
double mag = magnitude();
*this = this->scale(1 / mag);
}
Quaternion conjugate() const { return Quaternion(_w, -_x, -_y, -_z); }
void fromAxisAngle(const Vector<3> &axis, double theta) {
_w = cos(theta / 2);
// only need to calculate sine of half theta once
double sht = sin(theta / 2);
_x = axis.x() * sht;
_y = axis.y() * sht;
_z = axis.z() * sht;
}
void fromMatrix(const Matrix<3> &m) {
double tr = m.trace();
double S;
if (tr > 0) {
S = sqrt(tr + 1.0) * 2;
_w = 0.25 * S;
_x = (m(2, 1) - m(1, 2)) / S;
_y = (m(0, 2) - m(2, 0)) / S;
_z = (m(1, 0) - m(0, 1)) / S;
} else if (m(0, 0) > m(1, 1) && m(0, 0) > m(2, 2)) {
S = sqrt(1.0 + m(0, 0) - m(1, 1) - m(2, 2)) * 2;
_w = (m(2, 1) - m(1, 2)) / S;
_x = 0.25 * S;
_y = (m(0, 1) + m(1, 0)) / S;
_z = (m(0, 2) + m(2, 0)) / S;
} else if (m(1, 1) > m(2, 2)) {
S = sqrt(1.0 + m(1, 1) - m(0, 0) - m(2, 2)) * 2;
_w = (m(0, 2) - m(2, 0)) / S;
_x = (m(0, 1) + m(1, 0)) / S;
_y = 0.25 * S;
_z = (m(1, 2) + m(2, 1)) / S;
} else {
S = sqrt(1.0 + m(2, 2) - m(0, 0) - m(1, 1)) * 2;
_w = (m(1, 0) - m(0, 1)) / S;
_x = (m(0, 2) + m(2, 0)) / S;
_y = (m(1, 2) + m(2, 1)) / S;
_z = 0.25 * S;
}
}
void toAxisAngle(Vector<3> &axis, double &angle) const {
double sqw = sqrt(1 - _w * _w);
if (sqw == 0) // it's a singularity and divide by zero, avoid
return;
angle = 2 * acos(_w);
axis.x() = _x / sqw;
axis.y() = _y / sqw;
axis.z() = _z / sqw;
}
Matrix<3> toMatrix() const {
Matrix<3> ret;
ret.cell(0, 0) = 1 - 2 * _y * _y - 2 * _z * _z;
ret.cell(0, 1) = 2 * _x * _y - 2 * _w * _z;
ret.cell(0, 2) = 2 * _x * _z + 2 * _w * _y;
ret.cell(1, 0) = 2 * _x * _y + 2 * _w * _z;
ret.cell(1, 1) = 1 - 2 * _x * _x - 2 * _z * _z;
ret.cell(1, 2) = 2 * _y * _z - 2 * _w * _x;
ret.cell(2, 0) = 2 * _x * _z - 2 * _w * _y;
ret.cell(2, 1) = 2 * _y * _z + 2 * _w * _x;
ret.cell(2, 2) = 1 - 2 * _x * _x - 2 * _y * _y;
return ret;
}
// Returns euler angles that represent the quaternion. Angles are
// returned in rotation order and right-handed about the specified
// axes:
//
// v[0] is applied 1st about z (ie, roll)
// v[1] is applied 2nd about y (ie, pitch)
// v[2] is applied 3rd about x (ie, yaw)
//
// Note that this means result.x() is not a rotation about x;
// similarly for result.z().
//
Vector<3> toEuler() const {
Vector<3> ret;
double sqw = _w * _w;
double sqx = _x * _x;
double sqy = _y * _y;
double sqz = _z * _z;
ret.x() = atan2(2.0 * (_x * _y + _z * _w), (sqx - sqy - sqz + sqw));
ret.y() = asin(-2.0 * (_x * _z - _y * _w) / (sqx + sqy + sqz + sqw));
ret.z() = atan2(2.0 * (_y * _z + _x * _w), (-sqx - sqy + sqz + sqw));
return ret;
}
Vector<3> toAngularVelocity(double dt) const {
Vector<3> ret;
Quaternion one(1.0, 0.0, 0.0, 0.0);
Quaternion delta = one - *this;
Quaternion r = (delta / dt);
r = r * 2;
r = r * one;
ret.x() = r.x();
ret.y() = r.y();
ret.z() = r.z();
return ret;
}
Vector<3> rotateVector(const Vector<2> &v) const {
return rotateVector(Vector<3>(v.x(), v.y()));
}
Vector<3> rotateVector(const Vector<3> &v) const {
Vector<3> qv(_x, _y, _z);
Vector<3> t = qv.cross(v) * 2.0;
return v + t * _w + qv.cross(t);
}
Quaternion operator*(const Quaternion &q) const {
return Quaternion(_w * q._w - _x * q._x - _y * q._y - _z * q._z,
_w * q._x + _x * q._w + _y * q._z - _z * q._y,
_w * q._y - _x * q._z + _y * q._w + _z * q._x,
_w * q._z + _x * q._y - _y * q._x + _z * q._w);
}
Quaternion operator+(const Quaternion &q) const {
return Quaternion(_w + q._w, _x + q._x, _y + q._y, _z + q._z);
}
Quaternion operator-(const Quaternion &q) const {
return Quaternion(_w - q._w, _x - q._x, _y - q._y, _z - q._z);
}
Quaternion operator/(double scalar) const {
return Quaternion(_w / scalar, _x / scalar, _y / scalar, _z / scalar);
}
Quaternion operator*(double scalar) const { return scale(scalar); }
Quaternion scale(double scalar) const {
return Quaternion(_w * scalar, _x * scalar, _y * scalar, _z * scalar);
}
private:
double _w, _x, _y, _z;
};
} // namespace imu
#endif
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