Quaternion.cpp

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//
// This file is part of the Marble Virtual Globe.
//
// This program is free software licensed under the GNU LGPL. You can
// find a copy of this license in LICENSE.txt in the top directory of
// the source code.
//
// Copyright 2006-2007 Torsten Rahn <tackat@kde.org>
// Copyright 2007      Inge Wallin  <ingwa@kde.org>
// Copyright 2011      Bernhard Beschow <bbeschow@cs.tu-berlin.de>
//

#include "Quaternion.h"

#include <cmath>
using namespace std;

#include <QString>
#include <QDebug>


using namespace Marble;

Quaternion::Quaternion()
{
//    like in libeigen we keep the quaternion uninitialized
//    set( 1.0, 0.0, 0.0, 0.0 );
}

Quaternion::Quaternion(qreal w, qreal x, qreal y, qreal z)
{
    v[Q_W] = w;
    v[Q_X] = x;
    v[Q_Y] = y;
    v[Q_Z] = z;
}

Quaternion Quaternion::fromSpherical(qreal lon, qreal lat)
{
    const qreal w = 0.0;
    const qreal x = cos(lat) * sin(lon);
    const qreal y = sin(lat);
    const qreal z = cos(lat) * cos(lon);

    return Quaternion( w, x, y, z );
}

void Quaternion::getSpherical(qreal &lon, qreal &lat) const 
{
    qreal  y = v[Q_Y];
    if ( y > 1.0 )
        y = 1.0;
    else if ( y < -1.0 )
        y = -1.0;

    lat = asin( y );

    if(v[Q_X] * v[Q_X] + v[Q_Z] * v[Q_Z] > 0.00005) 
        lon = atan2(v[Q_X], v[Q_Z]);
    else
        lon = 0.0;
}

void Quaternion::normalize() 
{
    (*this) *= 1.0 / length();
}

qreal Quaternion::length() const
{
    return sqrt(v[Q_W] * v[Q_W] + v[Q_X] * v[Q_X] + v[Q_Y] * v[Q_Y] + v[Q_Z] * v[Q_Z]);
}

Quaternion& Quaternion::operator*=(qreal mult)
{
    (*this) = (*this) * mult;

    return *this;
}

Quaternion Quaternion::inverse() const
{
    Quaternion  inverse( v[Q_W], -v[Q_X], -v[Q_Y], -v[Q_Z] );
    inverse.normalize();

    return inverse;
}

Quaternion Quaternion::log() const
{
    double const qlen = length();
    double const vlen = sqrt(v[Q_X]*v[Q_X] + v[Q_Y]*v[Q_Y] + v[Q_Z]*v[Q_Z]);
    double const a = acos(v[Q_W]/qlen) / vlen;
    return Quaternion(std::log(qlen), v[Q_X] * a, v[Q_Y] * a, v[Q_Z] * a);
}

Quaternion Quaternion::exp() const
{
    double const vlen = sqrt(v[Q_X]*v[Q_X] + v[Q_Y]*v[Q_Y] + v[Q_Z]*v[Q_Z]);
    double const s = std::exp(v[Q_W]);
    double const a = s * sin(vlen) / vlen;
    return Quaternion(s * cos(vlen), v[Q_X] * a, v[Q_Y] * a, v[Q_Z] * a);
}

Quaternion Quaternion::fromEuler(qreal pitch, qreal yaw, qreal roll)
{
    const qreal cPhi = cos(0.5 * pitch); // also: "heading"
    const qreal cThe = cos(0.5 * yaw);   // also: "attitude"
    const qreal cPsi = cos(0.5 * roll);  // also: "bank"

    const qreal sPhi = sin(0.5 * pitch);
    const qreal sThe = sin(0.5 * yaw);
    const qreal sPsi = sin(0.5 * roll);

    const qreal w = cPhi * cThe * cPsi + sPhi * sThe * sPsi;
    const qreal x = sPhi * cThe * cPsi - cPhi * sThe * sPsi;
    const qreal y = cPhi * sThe * cPsi + sPhi * cThe * sPsi;
    const qreal z = cPhi * cThe * sPsi - sPhi * sThe * cPsi;

    return Quaternion( w, x, y, z );
}

qreal Quaternion::pitch() const // "heading", phi
{
    return atan2(         2.0*(v[Q_X]*v[Q_W]-v[Q_Y]*v[Q_Z]),
                  ( 1.0 - 2.0*(v[Q_X]*v[Q_X]+v[Q_Z]*v[Q_Z]) ) );
}

qreal Quaternion::yaw() const // "attitude", theta
{
    return atan2(         2.0*(v[Q_Y]*v[Q_W]-v[Q_X]*v[Q_Z]),
                  ( 1.0 - 2.0*(v[Q_Y]*v[Q_Y]+v[Q_Z]*v[Q_Z]) ) );
}

qreal Quaternion::roll() const // "bank", psi 
{
    return asin(2.0*(v[Q_X]*v[Q_Y]+v[Q_Z]*v[Q_W]));
}

#ifndef QT_NO_DEBUG_STREAM
QDebug operator<<(QDebug debug, const Quaternion &q)
{
    QString quatdisplay = QString("Quaternion: w= %1, x= %2, y= %3, z= %4, |q|= %5" )
        .arg(q.v[Q_W]).arg(q.v[Q_X]).arg(q.v[Q_Y]).arg(q.v[Q_Z]).arg(q.length());

    debug << quatdisplay;

    return debug;
}
#endif

Quaternion& Quaternion::operator*=(const Quaternion &q)
{
    (*this) = (*this) * q;

    return *this;
}

bool Quaternion::operator==(const Quaternion &q) const
{

    return ( v[Q_W] == q.v[Q_W]
         && v[Q_X] == q.v[Q_X]
         && v[Q_Y] == q.v[Q_Y]
         && v[Q_Z] == q.v[Q_Z] );
}

Quaternion Quaternion::operator*(const Quaternion &q) const
{
    const qreal w = v[Q_W] * q.v[Q_W] - v[Q_X] * q.v[Q_X] - v[Q_Y] * q.v[Q_Y] - v[Q_Z] * q.v[Q_Z];
    const qreal x = v[Q_W] * q.v[Q_X] + v[Q_X] * q.v[Q_W] + v[Q_Y] * q.v[Q_Z] - v[Q_Z] * q.v[Q_Y];
    const qreal y = v[Q_W] * q.v[Q_Y] - v[Q_X] * q.v[Q_Z] + v[Q_Y] * q.v[Q_W] + v[Q_Z] * q.v[Q_X];
    const qreal z = v[Q_W] * q.v[Q_Z] + v[Q_X] * q.v[Q_Y] - v[Q_Y] * q.v[Q_X] + v[Q_Z] * q.v[Q_W];

    return Quaternion( w, x, y, z );
}

Quaternion Quaternion::operator+(const Quaternion &q) const
{
    return Quaternion(v[Q_W] + q.v[Q_W],
                      v[Q_X] + q.v[Q_X],
                      v[Q_Y] + q.v[Q_Y],
                      v[Q_Z] + q.v[Q_Z]);
}

Quaternion Quaternion::operator*(qreal factor) const
{
    return Quaternion( v[Q_W] * factor, v[Q_X] * factor, v[Q_Y] * factor, v[Q_Z] * factor );
}

void Quaternion::rotateAroundAxis(const Quaternion &q)
{
    const qreal w = + v[Q_X] * q.v[Q_X] + v[Q_Y] * q.v[Q_Y] + v[Q_Z] * q.v[Q_Z];
    const qreal x = + v[Q_X] * q.v[Q_W] - v[Q_Y] * q.v[Q_Z] + v[Q_Z] * q.v[Q_Y];
    const qreal y = + v[Q_X] * q.v[Q_Z] + v[Q_Y] * q.v[Q_W] - v[Q_Z] * q.v[Q_X];
    const qreal z = - v[Q_X] * q.v[Q_Y] + v[Q_Y] * q.v[Q_X] + v[Q_Z] * q.v[Q_W];

    (*this) = q * Quaternion( w, x, y, z );
}

Quaternion Quaternion::slerp(const Quaternion &q1, const Quaternion &q2, qreal t)
{
    qreal  p1;
    qreal  p2;

    // Let alpha be the angle between the two quaternions.
    qreal  cosAlpha = ( q1.v[Q_X] * q2.v[Q_X]
                         + q1.v[Q_Y] * q2.v[Q_Y]
                         + q1.v[Q_Z] * q2.v[Q_Z]
                         + q1.v[Q_W] * q2.v[Q_W] );
    qreal  alpha    = acos( cosAlpha );
    qreal  sinAlpha = sin( alpha );

    if ( sinAlpha > 0.0 ) {
        p1 = sin( ( 1.0 - t ) * alpha ) / sinAlpha;
        p2 = sin( t           * alpha ) / sinAlpha;
    } else {
        // both Quaternions are equal
        p1 = 1.0;
        p2 = 0.0;
    }

    const qreal w = p1 * q1.v[Q_W] + p2 * q2.v[Q_W];
    const qreal x = p1 * q1.v[Q_X] + p2 * q2.v[Q_X];
    const qreal y = p1 * q1.v[Q_Y] + p2 * q2.v[Q_Y];
    const qreal z = p1 * q1.v[Q_Z] + p2 * q2.v[Q_Z];

    return Quaternion( w, x, y, z );
}

Quaternion Quaternion::nlerp(const Quaternion &q1, const Quaternion &q2, qreal t)
{
    const qreal p1 = 1.0 - t;

    const qreal w = p1 * q1.v[Q_W] + t * q2.v[Q_W];
    const qreal x = p1 * q1.v[Q_X] + t * q2.v[Q_X];
    const qreal y = p1 * q1.v[Q_Y] + t * q2.v[Q_Y];
    const qreal z = p1 * q1.v[Q_Z] + t * q2.v[Q_Z];

    Quaternion result( w, x, y, z );
    result.normalize();

    return result;
}

void Quaternion::toMatrix(matrix &m) const
{

    const qreal xy = v[Q_X] * v[Q_Y], xz = v[Q_X] * v[Q_Z];
    const qreal yy = v[Q_Y] * v[Q_Y], yw = v[Q_Y] * v[Q_W];
    const qreal zw = v[Q_Z] * v[Q_W], zz = v[Q_Z] * v[Q_Z];

    m[0][0] = 1.0 - 2.0 * (yy + zz);
    m[0][1] = 2.0 * (xy + zw);
    m[0][2] = 2.0 * (xz - yw);
    m[0][3] = 0.0;

    const qreal xx = v[Q_X] * v[Q_X];
    const qreal xw = v[Q_X] * v[Q_W];
    const qreal yz = v[Q_Y] * v[Q_Z];

    m[1][0] = 2.0 * (xy - zw);
    m[1][1] = 1.0 - 2.0 * (xx + zz);
    m[1][2] = 2.0 * (yz + xw);
    m[1][3] = 0.0;

    m[2][0] = 2.0 * (xz + yw);
    m[2][1] = 2.0 * (yz - xw);
    m[2][2] = 1.0 - 2.0 * (xx + yy);
    m[2][3] = 0.0;
}

void Quaternion::rotateAroundAxis(const matrix &m)
{
    const qreal x =  m[0][0] * v[Q_X] + m[1][0] * v[Q_Y] + m[2][0] * v[Q_Z];
    const qreal y =  m[0][1] * v[Q_X] + m[1][1] * v[Q_Y] + m[2][1] * v[Q_Z];
    const qreal z =  m[0][2] * v[Q_X] + m[1][2] * v[Q_Y] + m[2][2] * v[Q_Z];

    v[Q_W] = 1.0;
    v[Q_X] = x;
    v[Q_Y] = y;
    v[Q_Z] = z;
}