ardupilot/libraries/AP_Math/quaternion.cpp

/*
 * quaternion.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"
#include <AP_InternalError/AP_InternalError.h>

// return the rotation matrix equivalent for this quaternion
void Quaternion::rotation_matrix(Matrix3f &m) const
{
    const float q3q3 = q3 * q3;
    const float q3q4 = q3 * q4;
    const float q2q2 = q2 * q2;
    const float q2q3 = q2 * q3;
    const float q2q4 = q2 * q4;
    const float q1q2 = q1 * q2;
    const float q1q3 = q1 * q3;
    const float q1q4 = q1 * q4;
    const float q4q4 = q4 * q4;

    m.a.x = 1.0f-2.0f*(q3q3 + q4q4);
    m.a.y = 2.0f*(q2q3 - q1q4);
    m.a.z = 2.0f*(q2q4 + q1q3);
    m.b.x = 2.0f*(q2q3 + q1q4);
    m.b.y = 1.0f-2.0f*(q2q2 + q4q4);
    m.b.z = 2.0f*(q3q4 - q1q2);
    m.c.x = 2.0f*(q2q4 - q1q3);
    m.c.y = 2.0f*(q3q4 + q1q2);
    m.c.z = 1.0f-2.0f*(q2q2 + q3q3);
}

// return the rotation matrix equivalent for this quaternion after normalization
void Quaternion::rotation_matrix_norm(Matrix3f &m) const
{
    const float q1q1 = q1 * q1;
    const float q1q2 = q1 * q2;
    const float q1q3 = q1 * q3;
    const float q1q4 = q1 * q4;
    const float q2q2 = q2 * q2;
    const float q2q3 = q2 * q3;
    const float q2q4 = q2 * q4;
    const float q3q3 = q3 * q3;
    const float q3q4 = q3 * q4;
    const float q4q4 = q4 * q4;
    const float invs = 1.0f / (q1q1 + q2q2 + q3q3 + q4q4);

    m.a.x = ( q2q2 - q3q3 - q4q4 + q1q1)*invs;
    m.a.y = 2.0f*(q2q3 - q1q4)*invs;
    m.a.z = 2.0f*(q2q4 + q1q3)*invs;
    m.b.x = 2.0f*(q2q3 + q1q4)*invs;
    m.b.y = (-q2q2 + q3q3 - q4q4 + q1q1)*invs;
    m.b.z = 2.0f*(q3q4 - q1q2)*invs;
    m.c.x = 2.0f*(q2q4 - q1q3)*invs;
    m.c.y = 2.0f*(q3q4 + q1q2)*invs;
    m.c.z = (-q2q2 - q3q3 + q4q4 + q1q1)*invs;
}

// return the rotation matrix equivalent for this quaternion
// Thanks to Martin John Baker
// http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm
void Quaternion::from_rotation_matrix(const Matrix3f &m)
{
    const float &m00 = m.a.x;
    const float &m11 = m.b.y;
    const float &m22 = m.c.z;
    const float &m10 = m.b.x;
    const float &m01 = m.a.y;
    const float &m20 = m.c.x;
    const float &m02 = m.a.z;
    const float &m21 = m.c.y;
    const float &m12 = m.b.z;
    float &qw = q1;
    float &qx = q2;
    float &qy = q3;
    float &qz = q4;

    const float tr = m00 + m11 + m22;

    if (tr > 0) {
        const float S = sqrtf(tr+1) * 2;
        qw = 0.25f * S;
        qx = (m21 - m12) / S;
        qy = (m02 - m20) / S;
        qz = (m10 - m01) / S;
    } else if ((m00 > m11) && (m00 > m22)) {
        const float S = sqrtf(1.0f + m00 - m11 - m22) * 2.0f;
        qw = (m21 - m12) / S;
        qx = 0.25f * S;
        qy = (m01 + m10) / S;
        qz = (m02 + m20) / S;
    } else if (m11 > m22) {
        const float S = sqrtf(1.0f + m11 - m00 - m22) * 2.0f;
        qw = (m02 - m20) / S;
        qx = (m01 + m10) / S;
        qy = 0.25f * S;
        qz = (m12 + m21) / S;
    } else {
        const float S = sqrtf(1.0f + m22 - m00 - m11) * 2.0f;
        qw = (m10 - m01) / S;
        qx = (m02 + m20) / S;
        qy = (m12 + m21) / S;
        qz = 0.25f * S;
    }
}

// create a quaternion from a given rotation
void Quaternion::from_rotation(enum Rotation rotation)
{
    // the constants below can be calculated using the following formula:
    //     Matrix3f m_from_rot;
    //     m_from_rot.from_rotation(rotation);
    //     Quaternion q_from_m;
    //     from_rotation_matrix(m_from_rot);

    switch (rotation) {
    case ROTATION_NONE:
        q1 = 1;
        q2 = q3 = q4 = 0;
        return;

    case ROTATION_YAW_45:
        q1 = 0.92387956f;
        q2 = q3 = 0;
        q4 = 0.38268343f;
        return;

    case ROTATION_YAW_90:
        q1 = HALF_SQRT_2;
        q2 = q3 = 0;
        q4 = HALF_SQRT_2;
        return;

    case ROTATION_YAW_135:
        q1 = 0.38268343f;
        q2 = q3 = 0;
        q4 = 0.92387956f;
        return;

    case ROTATION_YAW_180:
        q1 = q2 = q3 = 0;
        q4=1;
        return;

    case ROTATION_YAW_225:
        q1 = -0.38268343f;
        q2 = q3 = 0;
        q4 = 0.92387956f;
        return;

    case ROTATION_YAW_270:
        q1 = HALF_SQRT_2;
        q2 = q3 = 0;
        q4 = -HALF_SQRT_2;
        return;

    case ROTATION_YAW_315:
        q1 = 0.92387956f;
        q2 = q3 = 0;
        q4 = -0.38268343f;
        return;

    case ROTATION_ROLL_180:
        q1 = q3 = q4 = 0;
        q2 = 1;
        return;

    case ROTATION_ROLL_180_YAW_45:
        q1 = q4 = 0;
        q2 = 0.92387956f;
        q3 = 0.38268343f;
        return;

    case ROTATION_ROLL_180_YAW_90:
        q1 = q4 = 0;
        q2 = q3 = HALF_SQRT_2;
        return;

    case ROTATION_ROLL_180_YAW_135:
        q1 = q4 = 0;
        q2 = 0.38268343f;
        q3 = 0.92387956f;
        return;

    case ROTATION_PITCH_180:
        q1 = q2 = q4 = 0;
        q3 = 1;
        return;

    case ROTATION_ROLL_180_YAW_225:
        q1 = q4 = 0;
        q2 = -0.38268343f;
        q3 = 0.92387956f;
        return;

    case ROTATION_ROLL_180_YAW_270:
        q1 = q4 = 0;
        q2 = -HALF_SQRT_2;
        q3 = HALF_SQRT_2;
        return;

    case ROTATION_ROLL_180_YAW_315:
        q1 = q4 = 0;
        q2 = 0.92387956f;
        q3 = -0.38268343f;
        return;

    case ROTATION_ROLL_90:
        q1 = q2 = HALF_SQRT_2;
        q3 = q4 = 0;
        return;

    case ROTATION_ROLL_90_YAW_45:
        q1 = 0.65328151f;
        q2 = 0.65328145f;
        q3 = q4 = 0.27059802f;
        return;

    case ROTATION_ROLL_90_YAW_90:
        q1 = q2 = q3 = q4 = 0.5f;
        return;

    case ROTATION_ROLL_90_YAW_135:
        q1 = q2 = 0.27059802f;
        q3 = 0.65328145f;
        q4 = 0.65328151f;
        return;

    case ROTATION_ROLL_270:
        q1 = HALF_SQRT_2;
        q2 = -HALF_SQRT_2;
        q3 = q4 = 0;
        return;

    case ROTATION_ROLL_270_YAW_45:
        q1 = 0.65328151f;
        q2 = -0.65328145f;
        q3 = -0.27059802f;
        q4 = 0.27059802f;
        return;

    case ROTATION_ROLL_270_YAW_90:
        q1 = q4 = 0.5f;
        q2 = q3 = -0.5f;
        return;

    case ROTATION_ROLL_270_YAW_135:
        q1 = 0.27059802f;
        q2 = -0.27059802f;
        q3 = -0.65328145f;
        q4 = 0.65328151f;
        return;

    case ROTATION_PITCH_90:
        q1 = q3 = HALF_SQRT_2;
        q2 = q4 = 0;
        return;

    case ROTATION_PITCH_270:
        q1 = HALF_SQRT_2;
        q2 = q4 = 0;
        q3 = -HALF_SQRT_2;
        return;

    case ROTATION_PITCH_180_YAW_90:
        q1 = q4 = 0;
        q2 = -HALF_SQRT_2;
        q3 = HALF_SQRT_2;
        return;

    case ROTATION_PITCH_180_YAW_270:
        q1 = q4 = 0;
        q2 = q3 = HALF_SQRT_2;
        return;

    case ROTATION_ROLL_90_PITCH_90:
        q1 = q2 = q3 = -0.5f;
        q4 = 0.5f;
        return;

    case ROTATION_ROLL_180_PITCH_90:
        q1 = q3 = 0;
        q2 = -HALF_SQRT_2;
        q4 = HALF_SQRT_2;
        return;

    case ROTATION_ROLL_270_PITCH_90:
        q1 = q3 = q4 = 0.5f;
        q2 = -0.5f;
        return;

    case ROTATION_ROLL_90_PITCH_180:
        q1 = q2 = 0;
        q3 = -HALF_SQRT_2;
        q4 = HALF_SQRT_2;
        return;

    case ROTATION_ROLL_270_PITCH_180:
        q1 = q2 = 0;
        q3 = q4 = HALF_SQRT_2;
        return;

    case ROTATION_ROLL_90_PITCH_270:
        q1 = q2 = q4 = 0.5f;
        q3 = -0.5;
        return;

    case ROTATION_ROLL_180_PITCH_270:
        q1 = q3 = 0;
        q2 = q4 = HALF_SQRT_2;
        return;

    case ROTATION_ROLL_270_PITCH_270:
        q1 = -0.5f;
        q2 = q3 = q4 = 0.5f;
        return;

    case ROTATION_ROLL_90_PITCH_180_YAW_90:
        q1 = q3 = -0.5f;
        q2 = q4 = 0.5f;
        return;

    case ROTATION_ROLL_90_YAW_270:
        q1 = q2 = -0.5f;
        q3 = q4 = 0.5f;
        return;

    case ROTATION_ROLL_90_PITCH_68_YAW_293:
        q1 = 0.26774535f;
        q2 = 0.70698798f;
        q3 = 0.01295743f;
        q4 = -0.65445596f;
        return;

    case ROTATION_PITCH_315:
        q1 = 0.92387956f;
        q2 = q4 = 0;
        q3 = -0.38268343f;
        return;

    case ROTATION_ROLL_90_PITCH_315:
        q1 = 0.65328151f;
        q2 = 0.65328145f;
        q3 = -0.27059802f;
        q4 = 0.27059802f;
        return;

    case ROTATION_PITCH_7:
        q1 = 0.99813479f;
        q2 = q4 = 0;
        q3 = 0.06104854f;
        return;

    case ROTATION_CUSTOM:
        // Error; custom rotations not supported
        INTERNAL_ERROR(AP_InternalError::error_t::flow_of_control);
        return;

    case ROTATION_MAX:
        break;
    }
    // rotation invalid
    INTERNAL_ERROR(AP_InternalError::error_t::bad_rotation);
}

// rotate this quaternion by the given rotation
void Quaternion::rotate(enum Rotation rotation)
{
    // create quaternion from rotation matrix
    Quaternion q_from_rot;
    q_from_rot.from_rotation(rotation);

    // rotate this quaternion
    *this *= q_from_rot;
}

// convert a vector from earth to body frame
void Quaternion::earth_to_body(Vector3f &v) const
{
    Matrix3f m;
    rotation_matrix(m);
    v = m * v;
}

// create a quaternion from Euler angles
void Quaternion::from_euler(float roll, float pitch, float yaw)
{
    const float cr2 = cosf(roll*0.5f);
    const float cp2 = cosf(pitch*0.5f);
    const float cy2 = cosf(yaw*0.5f);
    const float sr2 = sinf(roll*0.5f);
    const float sp2 = sinf(pitch*0.5f);
    const float sy2 = sinf(yaw*0.5f);

    q1 = cr2*cp2*cy2 + sr2*sp2*sy2;
    q2 = sr2*cp2*cy2 - cr2*sp2*sy2;
    q3 = cr2*sp2*cy2 + sr2*cp2*sy2;
    q4 = cr2*cp2*sy2 - sr2*sp2*cy2;
}

// create a quaternion from Euler angles applied in yaw, roll, pitch order
// instead of the normal yaw, pitch, roll order
void Quaternion::from_vector312(float roll, float pitch, float yaw)
{
    Matrix3f m;
    m.from_euler312(roll, pitch, yaw);

    from_rotation_matrix(m);
}

// create a quaternion from its axis-angle representation
void Quaternion::from_axis_angle(Vector3f v)
{
    const float theta = v.length();
    if (is_zero(theta)) {
        q1 = 1.0f;
        q2=q3=q4=0.0f;
        return;
    }
    v /= theta;
    from_axis_angle(v,theta);
}

// create a quaternion from its axis-angle representation
// the axis vector must be length 1, theta is in radians
void Quaternion::from_axis_angle(const Vector3f &axis, float theta)
{
    // axis must be a unit vector as there is no check for length
    if (is_zero(theta)) {
        q1 = 1.0f;
        q2=q3=q4=0.0f;
        return;
    }
    const float st2 = sinf(theta/2.0f);

    q1 = cosf(theta/2.0f);
    q2 = axis.x * st2;
    q3 = axis.y * st2;
    q4 = axis.z * st2;
}

// rotate by the provided axis angle
void Quaternion::rotate(const Vector3f &v)
{
    Quaternion r;
    r.from_axis_angle(v);
    (*this) *= r;
}

// convert this quaternion to a rotation vector where the direction of the vector represents
// the axis of rotation and the length of the vector represents the angle of rotation
void Quaternion::to_axis_angle(Vector3f &v) const
{
    const float l = sqrtf(sq(q2)+sq(q3)+sq(q4));
    v = Vector3f(q2,q3,q4);
    if (!is_zero(l)) {
        v /= l;
        v *= wrap_PI(2.0f * atan2f(l,q1));
    }
}

// create a quaternion from its axis-angle representation
// only use with small angles.  I.e. length of v should less than 0.17 radians (i.e. 10 degrees)
void Quaternion::from_axis_angle_fast(Vector3f v)
{
    const float theta = v.length();
    if (is_zero(theta)) {
        q1 = 1.0f;
        q2=q3=q4=0.0f;
        return;
    }
    v /= theta;
    from_axis_angle_fast(v,theta);
}

// create a quaternion from its axis-angle representation
// theta should less than 0.17 radians (i.e. 10 degrees)
void Quaternion::from_axis_angle_fast(const Vector3f &axis, float theta)
{
    const float t2 = theta/2.0f;
    const float sqt2 = sq(t2);
    const float st2 = t2-sqt2*t2/6.0f;

    q1 = 1.0f-(sqt2/2.0f)+sq(sqt2)/24.0f;
    q2 = axis.x * st2;
    q3 = axis.y * st2;
    q4 = axis.z * st2;
}

// rotate by the provided axis angle
// only use with small angles.  I.e. length of v should less than 0.17 radians (i.e. 10 degrees)
void Quaternion::rotate_fast(const Vector3f &v)
{
    const float theta = v.length();
    if (is_zero(theta)) {
        return;
    }
    const float t2 = theta/2.0f;
    const float sqt2 = sq(t2);
    float st2 = t2-sqt2*t2/6.0f;
    st2 /= theta;

    //"rotation quaternion"
    const float w2 = 1.0f-(sqt2/2.0f)+sq(sqt2)/24.0f;
    const float x2 = v.x * st2;
    const float y2 = v.y * st2;
    const float z2 = v.z * st2;

    //copy our quaternion
    const float w1 = q1;
    const float x1 = q2;
    const float y1 = q3;
    const float z1 = q4;

    //do the multiply into our quaternion
    q1 = w1*w2 - x1*x2 - y1*y2 - z1*z2;
    q2 = w1*x2 + x1*w2 + y1*z2 - z1*y2;
    q3 = w1*y2 - x1*z2 + y1*w2 + z1*x2;
    q4 = w1*z2 + x1*y2 - y1*x2 + z1*w2;
}

// get euler roll angle
float Quaternion::get_euler_roll() const
{
    return (atan2f(2.0f*(q1*q2 + q3*q4), 1.0f - 2.0f*(q2*q2 + q3*q3)));
}

// get euler pitch angle
float Quaternion::get_euler_pitch() const
{
    return safe_asin(2.0f*(q1*q3 - q4*q2));
}

// get euler yaw angle
float Quaternion::get_euler_yaw() const
{
    return atan2f(2.0f*(q1*q4 + q2*q3), 1.0f - 2.0f*(q3*q3 + q4*q4));
}

// create eulers from a quaternion
void Quaternion::to_euler(float &roll, float &pitch, float &yaw) const
{
    roll = get_euler_roll();
    pitch = get_euler_pitch();
    yaw = get_euler_yaw();
}

// create eulers from a quaternion
Vector3f Quaternion::to_vector312(void) const
{
    Matrix3f m;
    rotation_matrix(m);
    return m.to_euler312();
}

float Quaternion::length(void) const
{
    return sqrtf(sq(q1) + sq(q2) + sq(q3) + sq(q4));
}

// return the reverse rotation of this quaternion
Quaternion Quaternion::inverse(void) const
{
    return Quaternion(q1, -q2, -q3, -q4);
}

// reverse the rotation of this quaternion
void Quaternion::invert()
{
    q2 = -q2;
    q3 = -q3;
    q4 = -q4;
}

void Quaternion::normalize(void)
{
    const float quatMag = length();
    if (!is_zero(quatMag)) {
        const float quatMagInv = 1.0f/quatMag;
        q1 *= quatMagInv;
        q2 *= quatMagInv;
        q3 *= quatMagInv;
        q4 *= quatMagInv;
    }
}

Quaternion Quaternion::operator*(const Quaternion &v) const
{
    Quaternion ret;
    const float &w1 = q1;
    const float &x1 = q2;
    const float &y1 = q3;
    const float &z1 = q4;

    const float w2 = v.q1;
    const float x2 = v.q2;
    const float y2 = v.q3;
    const float z2 = v.q4;

    ret.q1 = w1*w2 - x1*x2 - y1*y2 - z1*z2;
    ret.q2 = w1*x2 + x1*w2 + y1*z2 - z1*y2;
    ret.q3 = w1*y2 - x1*z2 + y1*w2 + z1*x2;
    ret.q4 = w1*z2 + x1*y2 - y1*x2 + z1*w2;

    return ret;
}

Quaternion &Quaternion::operator*=(const Quaternion &v)
{
    const float w1 = q1;
    const float x1 = q2;
    const float y1 = q3;
    const float z1 = q4;

    const float w2 = v.q1;
    const float x2 = v.q2;
    const float y2 = v.q3;
    const float z2 = v.q4;

    q1 = w1*w2 - x1*x2 - y1*y2 - z1*z2;
    q2 = w1*x2 + x1*w2 + y1*z2 - z1*y2;
    q3 = w1*y2 - x1*z2 + y1*w2 + z1*x2;
    q4 = w1*z2 + x1*y2 - y1*x2 + z1*w2;

    return *this;
}

Quaternion Quaternion::operator/(const Quaternion &v) const
{
    Quaternion ret;
    const float &quat0 = q1;
    const float &quat1 = q2;
    const float &quat2 = q3;
    const float &quat3 = q4;

    const float rquat0 = v.q1;
    const float rquat1 = v.q2;
    const float rquat2 = v.q3;
    const float rquat3 = v.q4;

    ret.q1 = (rquat0*quat0 + rquat1*quat1 + rquat2*quat2 + rquat3*quat3);
    ret.q2 = (rquat0*quat1 - rquat1*quat0 - rquat2*quat3 + rquat3*quat2);
    ret.q3 = (rquat0*quat2 + rquat1*quat3 - rquat2*quat0 - rquat3*quat1);
    ret.q4 = (rquat0*quat3 - rquat1*quat2 + rquat2*quat1 - rquat3*quat0);
    return ret;
}

// angular difference in radians between quaternions
Quaternion Quaternion::angular_difference(const Quaternion &v) const
{
    return v.inverse() * *this;
}