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/****************************************************************************
*
* Copyright (c) 2013-2015 PX4 Development Team. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
* 3. Neither the name PX4 nor the names of its contributors may be
* used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
* OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
* AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
****************************************************************************/
/**
* @file Quaternion.hpp
*
* Quaternion class
*
* @author Anton Babushkin <anton.babushkin@me.com>
* @author Pavel Kirienko <pavel.kirienko@gmail.com>
* @author Lorenz Meier <lorenz@px4.io>
*/
#ifndef QUATERNION_HPP
#define QUATERNION_HPP
#include <math.h>
#include "Vector.hpp"
#include "Matrix.hpp"
namespace math
{
class __EXPORT Quaternion : public Vector<4>
{
public:
/**
* trivial ctor
*/
Quaternion() : Vector<4>() {}
/**
* copy ctor
*/
Quaternion(const Quaternion &q) : Vector<4>(q) {}
/**
* casting from vector
*/
Quaternion(const Vector<4> &v) : Vector<4>(v) {}
/**
* setting ctor
*/
Quaternion(const float d[4]) : Vector<4>(d) {}
/**
* setting ctor
*/
Quaternion(const float a0, const float b0, const float c0, const float d0): Vector<4>(a0, b0, c0, d0) {}
using Vector<4>::operator *;
/**
* multiplication
*/
const Quaternion operator *(const Quaternion &q) const {
return Quaternion(
data[0] * q.data[0] - data[1] * q.data[1] - data[2] * q.data[2] - data[3] * q.data[3],
data[0] * q.data[1] + data[1] * q.data[0] + data[2] * q.data[3] - data[3] * q.data[2],
data[0] * q.data[2] - data[1] * q.data[3] + data[2] * q.data[0] + data[3] * q.data[1],
data[0] * q.data[3] + data[1] * q.data[2] - data[2] * q.data[1] + data[3] * q.data[0]);
}
/**
* derivative
*/
const Quaternion derivative(const Vector<3> &w) {
float dataQ[] = {
data[0], -data[1], -data[2], -data[3],
data[1], data[0], -data[3], data[2],
data[2], data[3], data[0], -data[1],
data[3], -data[2], data[1], data[0]
};
Matrix<4, 4> Q(dataQ);
Vector<4> v(0.0f, w.data[0], w.data[1], w.data[2]);
return Q * v * 0.5f;
}
/**
* imaginary part of quaternion
*/
Vector<3> imag(void) {
return Vector<3>(&data[1]);
}
/**
* set quaternion to rotation defined by euler angles
*/
void from_euler(float roll, float pitch, float yaw) {
double cosPhi_2 = cos(double(roll) / 2.0);
double sinPhi_2 = sin(double(roll) / 2.0);
double cosTheta_2 = cos(double(pitch) / 2.0);
double sinTheta_2 = sin(double(pitch) / 2.0);
double cosPsi_2 = cos(double(yaw) / 2.0);
double sinPsi_2 = sin(double(yaw) / 2.0);
/* operations executed in double to avoid loss of precision through
* consecutive multiplications. Result stored as float.
*/
data[0] = static_cast<float>(cosPhi_2 * cosTheta_2 * cosPsi_2 + sinPhi_2 * sinTheta_2 * sinPsi_2);
data[1] = static_cast<float>(sinPhi_2 * cosTheta_2 * cosPsi_2 - cosPhi_2 * sinTheta_2 * sinPsi_2);
data[2] = static_cast<float>(cosPhi_2 * sinTheta_2 * cosPsi_2 + sinPhi_2 * cosTheta_2 * sinPsi_2);
data[3] = static_cast<float>(cosPhi_2 * cosTheta_2 * sinPsi_2 - sinPhi_2 * sinTheta_2 * cosPsi_2);
}
void from_dcm(const Matrix<3, 3> &dcm) {
float tr = dcm.data[0][0] + dcm.data[1][1] + dcm.data[2][2];
if (tr > 0.0f) {
float s = sqrtf(tr + 1.0f);
data[0] = s * 0.5f;
s = 0.5f / s;
data[1] = (dcm.data[2][1] - dcm.data[1][2]) * s;
data[2] = (dcm.data[0][2] - dcm.data[2][0]) * s;
data[3] = (dcm.data[1][0] - dcm.data[0][1]) * s;
} else {
/* Find maximum diagonal element in dcm
* store index in dcm_i */
int dcm_i = 0;
for (int i = 1; i < 3; i++) {
if (dcm.data[i][i] > dcm.data[dcm_i][dcm_i]) {
dcm_i = i;
}
}
int dcm_j = (dcm_i + 1) % 3;
int dcm_k = (dcm_i + 2) % 3;
float s = sqrtf((dcm.data[dcm_i][dcm_i] - dcm.data[dcm_j][dcm_j] -
dcm.data[dcm_k][dcm_k]) + 1.0f);
data[dcm_i + 1] = s * 0.5f;
s = 0.5f / s;
data[dcm_j + 1] = (dcm.data[dcm_i][dcm_j] + dcm.data[dcm_j][dcm_i]) * s;
data[dcm_k + 1] = (dcm.data[dcm_k][dcm_i] + dcm.data[dcm_i][dcm_k]) * s;
data[0] = (dcm.data[dcm_k][dcm_j] - dcm.data[dcm_j][dcm_k]) * s;
}
}
/**
* create rotation matrix for the quaternion
*/
Matrix<3, 3> to_dcm(void) const {
Matrix<3, 3> R;
float aSq = data[0] * data[0];
float bSq = data[1] * data[1];
float cSq = data[2] * data[2];
float dSq = data[3] * data[3];
R.data[0][0] = aSq + bSq - cSq - dSq;
R.data[0][1] = 2.0f * (data[1] * data[2] - data[0] * data[3]);
R.data[0][2] = 2.0f * (data[0] * data[2] + data[1] * data[3]);
R.data[1][0] = 2.0f * (data[1] * data[2] + data[0] * data[3]);
R.data[1][1] = aSq - bSq + cSq - dSq;
R.data[1][2] = 2.0f * (data[2] * data[3] - data[0] * data[1]);
R.data[2][0] = 2.0f * (data[1] * data[3] - data[0] * data[2]);
R.data[2][1] = 2.0f * (data[0] * data[1] + data[2] * data[3]);
R.data[2][2] = aSq - bSq - cSq + dSq;
return R;
}
};
}
#endif // QUATERNION_HPP
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