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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 \ No newline at end of file
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