ardupilot/libraries/AP_Math/matrix3.cpp

/*
 * matrix3.cpp
 * Copyright (C) Andrew Tridgell 2012
 *
 * This file is free software: you can redistribute it and/or modify it
 * under the terms of the GNU General Public License as published by the
 * Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This file 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 General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License along
 * with this program.  If not, see <http://www.gnu.org/licenses/>.
 */

#pragma GCC optimize("O2")

#include "AP_Math.h"

// create a rotation matrix given some euler angles
// this is based on https://github.com/ArduPilot/Datasheets/blob/main/References/EulerAngles.pdf
template <typename T>
void Matrix3<T>::from_euler(T roll, T pitch, T yaw)
{
    const T cp = cosF(pitch);
    const T sp = sinF(pitch);
    const T sr = sinF(roll);
    const T cr = cosF(roll);
    const T sy = sinF(yaw);
    const T cy = cosF(yaw);

    a.x = cp * cy;
    a.y = (sr * sp * cy) - (cr * sy);
    a.z = (cr * sp * cy) + (sr * sy);
    b.x = cp * sy;
    b.y = (sr * sp * sy) + (cr * cy);
    b.z = (cr * sp * sy) - (sr * cy);
    c.x = -sp;
    c.y = sr * cp;
    c.z = cr * cp;
}

// calculate euler angles from a rotation matrix
// this is based on https://github.com/ArduPilot/Datasheets/blob/main/References/EulerAngles.pdf
template <typename T>
void Matrix3<T>::to_euler(T *roll, T *pitch, T *yaw) const
{
    if (pitch != nullptr) {
        *pitch = -safe_asin(c.x);
    }
    if (roll != nullptr) {
        *roll = atan2F(c.y, c.z);
    }
    if (yaw != nullptr) {
        *yaw = atan2F(b.x, a.x);
    }
}

template <typename T>
void Matrix3<T>::from_rotation(enum Rotation rotation)
{
    (*this).a = {1,0,0};
    (*this).b = {0,1,0};
    (*this).c = {0,0,1};

    (*this).a.rotate(rotation);
    (*this).b.rotate(rotation);
    (*this).c.rotate(rotation);
    (*this).transpose();
}

/*
  calculate Euler angles (312 convention) for the matrix.
  See http://www.atacolorado.com/eulersequences.doc
  vector is returned in r, p, y order
*/
template <typename T>
Vector3<T> Matrix3<T>::to_euler312() const
{
    return Vector3<T>(asinF(c.y),
                      atan2F(-c.x, c.z),
                      atan2F(-a.y, b.y));
}

/*
  fill the matrix from Euler angles in radians in 312 convention
*/
template <typename T>
void Matrix3<T>::from_euler312(T roll, T pitch, T yaw)
{
    const T c3 = cosF(pitch);
    const T s3 = sinF(pitch);
    const T s2 = sinF(roll);
    const T c2 = cosF(roll);
    const T s1 = sinF(yaw);
    const T c1 = cosF(yaw);

    a.x = c1 * c3 - s1 * s2 * s3;
    b.y = c1 * c2;
    c.z = c3 * c2;
    a.y = -c2*s1;
    a.z = s3*c1 + c3*s2*s1;
    b.x = c3*s1 + s3*s2*c1;
    b.z = s1*s3 - s2*c1*c3;
    c.x = -s3*c2;
    c.y = s2;
}

// apply an additional rotation from a body frame gyro vector
// to a rotation matrix.
template <typename T>
void Matrix3<T>::rotate(const Vector3<T> &g)
{
    (*this) += Matrix3<T>{
        a.y * g.z - a.z * g.y, a.z * g.x - a.x * g.z, a.x * g.y - a.y * g.x,
        b.y * g.z - b.z * g.y, b.z * g.x - b.x * g.z, b.x * g.y - b.y * g.x,
        c.y * g.z - c.z * g.y, c.z * g.x - c.x * g.z, c.x * g.y - c.y * g.x
    };
}

/*
  re-normalise a rotation matrix
*/
template <typename T>
void Matrix3<T>::normalize(void)
{
    const T error = a * b;
    const Vector3<T> t0 = a - (b * (0.5f * error));
    const Vector3<T> t1 = b - (a * (0.5f * error));
    const Vector3<T> t2 = t0 % t1;
    a = t0 * (1.0f / t0.length());
    b = t1 * (1.0f / t1.length());
    c = t2 * (1.0f / t2.length());
}

// multiplication by a vector
template <typename T>
Vector3<T> Matrix3<T>::operator *(const Vector3<T> &v) const
{
    return Vector3<T>(a.x * v.x + a.y * v.y + a.z * v.z,
                      b.x * v.x + b.y * v.y + b.z * v.z,
                      c.x * v.x + c.y * v.y + c.z * v.z);
}

// multiplication by a vector, extracting only the xy components
template <typename T>
Vector2<T> Matrix3<T>::mulXY(const Vector3<T> &v) const
{
    return Vector2<T>(a.x * v.x + a.y * v.y + a.z * v.z,
                      b.x * v.x + b.y * v.y + b.z * v.z);
}

// multiplication of transpose by a vector
template <typename T>
Vector3<T> Matrix3<T>::mul_transpose(const Vector3<T> &v) const
{
    return Vector3<T>(a.x * v.x + b.x * v.y + c.x * v.z,
                      a.y * v.x + b.y * v.y + c.y * v.z,
                      a.z * v.x + b.z * v.y + c.z * v.z);
}

// multiplication by another Matrix3<T>
template <typename T>
Matrix3<T> Matrix3<T>::operator *(const Matrix3<T> &m) const
{
    Matrix3<T> temp (Vector3<T>(a.x * m.a.x + a.y * m.b.x + a.z * m.c.x,
                                a.x * m.a.y + a.y * m.b.y + a.z * m.c.y,
                                a.x * m.a.z + a.y * m.b.z + a.z * m.c.z),
                     Vector3<T>(b.x * m.a.x + b.y * m.b.x + b.z * m.c.x,
                                b.x * m.a.y + b.y * m.b.y + b.z * m.c.y,
                                b.x * m.a.z + b.y * m.b.z + b.z * m.c.z),
                     Vector3<T>(c.x * m.a.x + c.y * m.b.x + c.z * m.c.x,
                                c.x * m.a.y + c.y * m.b.y + c.z * m.c.y,
                                c.x * m.a.z + c.y * m.b.z + c.z * m.c.z));
    return temp;
}

template <typename T>
Matrix3<T> Matrix3<T>::transposed(void) const
{
    return Matrix3<T>(Vector3<T>(a.x, b.x, c.x),
                      Vector3<T>(a.y, b.y, c.y),
                      Vector3<T>(a.z, b.z, c.z));
}

template <typename T>
T Matrix3<T>::det() const
{
    return a.x * (b.y * c.z - b.z * c.y) +
           a.y * (b.z * c.x - b.x * c.z) +
           a.z * (b.x * c.y - b.y * c.x);
}

template <typename T>
bool Matrix3<T>::inverse(Matrix3<T>& inv) const
{
    const T d = det();

    if (is_zero(d)) {
        return false;
    }

    inv.a.x = (b.y * c.z - c.y * b.z) / d;
    inv.a.y = (a.z * c.y - a.y * c.z) / d;
    inv.a.z = (a.y * b.z - a.z * b.y) / d;
    inv.b.x = (b.z * c.x - b.x * c.z) / d;
    inv.b.y = (a.x * c.z - a.z * c.x) / d;
    inv.b.z = (b.x * a.z - a.x * b.z) / d;
    inv.c.x = (b.x * c.y - c.x * b.y) / d;
    inv.c.y = (c.x * a.y - a.x * c.y) / d;
    inv.c.z = (a.x * b.y - b.x * a.y) / d;

    return true;
}

template <typename T>
bool Matrix3<T>::invert()
{
    Matrix3<T> inv;
    bool success = inverse(inv);
    if (success) {
        *this = inv;
    }
    return success;
}

// create rotation matrix for rotation about the vector v by angle theta
// See: http://www.euclideanspace.com/maths/geometry/rotations/conversions/angleToMatrix/
template <typename T>
void Matrix3<T>::from_axis_angle(const Vector3<T> &v, T theta)
{
    const T C = cosF(theta);
    const T S = sinF(theta);
    const T t = 1.0f - C;
    const Vector3<T> normv = v.normalized();
    const T x = normv.x;
    const T y = normv.y;
    const T z = normv.z;

    a.x = t*x*x + C;
    a.y = t*x*y - z*S;
    a.z = t*x*z + y*S;
    b.x = t*x*y + z*S;
    b.y = t*y*y + C;
    b.z = t*y*z - x*S;
    c.x = t*x*z - y*S;
    c.y = t*y*z + x*S;
    c.z = t*z*z + C;
}


// define for float and double
template class Matrix3<float>;
template class Matrix3<double>;