summaryrefslogtreecommitdiffstats
path: root/src/gui/math3d/qquaternion.cpp
blob: 53e01323d9b3252631fdcf706d2fe869abcde508 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
/****************************************************************************
**
** Copyright (C) 2012 Nokia Corporation and/or its subsidiary(-ies).
** All rights reserved.
** Contact: Nokia Corporation (qt-info@nokia.com)
**
** This file is part of the QtGui module of the Qt Toolkit.
**
** $QT_BEGIN_LICENSE:LGPL$
** GNU Lesser General Public License Usage
** This file may be used under the terms of the GNU Lesser General Public
** License version 2.1 as published by the Free Software Foundation and
** appearing in the file LICENSE.LGPL included in the packaging of this
** file. Please review the following information to ensure the GNU Lesser
** General Public License version 2.1 requirements will be met:
** http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html.
**
** In addition, as a special exception, Nokia gives you certain additional
** rights. These rights are described in the Nokia Qt LGPL Exception
** version 1.1, included in the file LGPL_EXCEPTION.txt in this package.
**
** GNU General Public License Usage
** Alternatively, this file may be used under the terms of the GNU General
** Public License version 3.0 as published by the Free Software Foundation
** and appearing in the file LICENSE.GPL included in the packaging of this
** file. Please review the following information to ensure the GNU General
** Public License version 3.0 requirements will be met:
** http://www.gnu.org/copyleft/gpl.html.
**
** Other Usage
** Alternatively, this file may be used in accordance with the terms and
** conditions contained in a signed written agreement between you and Nokia.
**
**
**
**
**
** $QT_END_LICENSE$
**
****************************************************************************/

#include "qquaternion.h"
#include <QtCore/qmath.h>
#include <QtCore/qvariant.h>
#include <QtCore/qdebug.h>

QT_BEGIN_NAMESPACE

#ifndef QT_NO_QUATERNION

/*!
    \class QQuaternion
    \brief The QQuaternion class represents a quaternion consisting of a vector and scalar.
    \since 4.6
    \ingroup painting-3D

    Quaternions are used to represent rotations in 3D space, and
    consist of a 3D rotation axis specified by the x, y, and z
    coordinates, and a scalar representing the rotation angle.
*/

/*!
    \fn QQuaternion::QQuaternion()

    Constructs an identity quaternion, i.e. with coordinates (1, 0, 0, 0).
*/

/*!
    \fn QQuaternion::QQuaternion(qreal scalar, qreal xpos, qreal ypos, qreal zpos)

    Constructs a quaternion with the vector (\a xpos, \a ypos, \a zpos)
    and \a scalar.
*/

#ifndef QT_NO_VECTOR3D

/*!
    \fn QQuaternion::QQuaternion(qreal scalar, const QVector3D& vector)

    Constructs a quaternion vector from the specified \a vector and
    \a scalar.

    \sa vector(), scalar()
*/

/*!
    \fn QVector3D QQuaternion::vector() const

    Returns the vector component of this quaternion.

    \sa setVector(), scalar()
*/

/*!
    \fn void QQuaternion::setVector(const QVector3D& vector)

    Sets the vector component of this quaternion to \a vector.

    \sa vector(), setScalar()
*/

#endif

/*!
    \fn void QQuaternion::setVector(qreal x, qreal y, qreal z)

    Sets the vector component of this quaternion to (\a x, \a y, \a z).

    \sa vector(), setScalar()
*/

#ifndef QT_NO_VECTOR4D

/*!
    \fn QQuaternion::QQuaternion(const QVector4D& vector)

    Constructs a quaternion from the components of \a vector.
*/

/*!
    \fn QVector4D QQuaternion::toVector4D() const

    Returns this quaternion as a 4D vector.
*/

#endif

/*!
    \fn bool QQuaternion::isNull() const

    Returns true if the x, y, z, and scalar components of this
    quaternion are set to 0.0; otherwise returns false.
*/

/*!
    \fn bool QQuaternion::isIdentity() const

    Returns true if the x, y, and z components of this
    quaternion are set to 0.0, and the scalar component is set
    to 1.0; otherwise returns false.
*/

/*!
    \fn qreal QQuaternion::x() const

    Returns the x coordinate of this quaternion's vector.

    \sa setX(), y(), z(), scalar()
*/

/*!
    \fn qreal QQuaternion::y() const

    Returns the y coordinate of this quaternion's vector.

    \sa setY(), x(), z(), scalar()
*/

/*!
    \fn qreal QQuaternion::z() const

    Returns the z coordinate of this quaternion's vector.

    \sa setZ(), x(), y(), scalar()
*/

/*!
    \fn qreal QQuaternion::scalar() const

    Returns the scalar component of this quaternion.

    \sa setScalar(), x(), y(), z()
*/

/*!
    \fn void QQuaternion::setX(qreal x)

    Sets the x coordinate of this quaternion's vector to the given
    \a x coordinate.

    \sa x(), setY(), setZ(), setScalar()
*/

/*!
    \fn void QQuaternion::setY(qreal y)

    Sets the y coordinate of this quaternion's vector to the given
    \a y coordinate.

    \sa y(), setX(), setZ(), setScalar()
*/

/*!
    \fn void QQuaternion::setZ(qreal z)

    Sets the z coordinate of this quaternion's vector to the given
    \a z coordinate.

    \sa z(), setX(), setY(), setScalar()
*/

/*!
    \fn void QQuaternion::setScalar(qreal scalar)

    Sets the scalar component of this quaternion to \a scalar.

    \sa scalar(), setX(), setY(), setZ()
*/

/*!
    Returns the length of the quaternion.  This is also called the "norm".

    \sa lengthSquared(), normalized()
*/
qreal QQuaternion::length() const
{
    return qSqrt(xp * xp + yp * yp + zp * zp + wp * wp);
}

/*!
    Returns the squared length of the quaternion.

    \sa length()
*/
qreal QQuaternion::lengthSquared() const
{
    return xp * xp + yp * yp + zp * zp + wp * wp;
}

/*!
    Returns the normalized unit form of this quaternion.

    If this quaternion is null, then a null quaternion is returned.
    If the length of the quaternion is very close to 1, then the quaternion
    will be returned as-is.  Otherwise the normalized form of the
    quaternion of length 1 will be returned.

    \sa length(), normalize()
*/
QQuaternion QQuaternion::normalized() const
{
    // Need some extra precision if the length is very small.
    double len = double(xp) * double(xp) +
                 double(yp) * double(yp) +
                 double(zp) * double(zp) +
                 double(wp) * double(wp);
    if (qFuzzyIsNull(len - 1.0f))
        return *this;
    else if (!qFuzzyIsNull(len))
        return *this / qSqrt(len);
    else
        return QQuaternion(0.0f, 0.0f, 0.0f, 0.0f);
}

/*!
    Normalizes the currect quaternion in place.  Nothing happens if this
    is a null quaternion or the length of the quaternion is very close to 1.

    \sa length(), normalized()
*/
void QQuaternion::normalize()
{
    // Need some extra precision if the length is very small.
    double len = double(xp) * double(xp) +
                 double(yp) * double(yp) +
                 double(zp) * double(zp) +
                 double(wp) * double(wp);
    if (qFuzzyIsNull(len - 1.0f) || qFuzzyIsNull(len))
        return;

    len = qSqrt(len);

    xp /= len;
    yp /= len;
    zp /= len;
    wp /= len;
}

/*!
    \fn QQuaternion QQuaternion::conjugate() const

    Returns the conjugate of this quaternion, which is
    (-x, -y, -z, scalar).
*/

/*!
    Rotates \a vector with this quaternion to produce a new vector
    in 3D space.  The following code:

    \code
    QVector3D result = q.rotatedVector(vector);
    \endcode

    is equivalent to the following:

    \code
    QVector3D result = (q * QQuaternion(0, vector) * q.conjugate()).vector();
    \endcode
*/
QVector3D QQuaternion::rotatedVector(const QVector3D& vector) const
{
    return (*this * QQuaternion(0, vector) * conjugate()).vector();
}

/*!
    \fn QQuaternion &QQuaternion::operator+=(const QQuaternion &quaternion)

    Adds the given \a quaternion to this quaternion and returns a reference to
    this quaternion.

    \sa operator-=()
*/

/*!
    \fn QQuaternion &QQuaternion::operator-=(const QQuaternion &quaternion)

    Subtracts the given \a quaternion from this quaternion and returns a
    reference to this quaternion.

    \sa operator+=()
*/

/*!
    \fn QQuaternion &QQuaternion::operator*=(qreal factor)

    Multiplies this quaternion's components by the given \a factor, and
    returns a reference to this quaternion.

    \sa operator/=()
*/

/*!
    \fn QQuaternion &QQuaternion::operator*=(const QQuaternion &quaternion)

    Multiplies this quaternion by \a quaternion and returns a reference
    to this quaternion.
*/

/*!
    \fn QQuaternion &QQuaternion::operator/=(qreal divisor)

    Divides this quaternion's components by the given \a divisor, and
    returns a reference to this quaternion.

    \sa operator*=()
*/

#ifndef QT_NO_VECTOR3D

/*!
    Creates a normalized quaternion that corresponds to rotating through
    \a angle degrees about the specified 3D \a axis.
*/
QQuaternion QQuaternion::fromAxisAndAngle(const QVector3D& axis, qreal angle)
{
    // Algorithm from:
    // http://www.j3d.org/matrix_faq/matrfaq_latest.html#Q56
    // We normalize the result just in case the values are close
    // to zero, as suggested in the above FAQ.
    qreal a = (angle / 2.0f) * M_PI / 180.0f;
    qreal s = qSin(a);
    qreal c = qCos(a);
    QVector3D ax = axis.normalized();
    return QQuaternion(c, ax.x() * s, ax.y() * s, ax.z() * s).normalized();
}

#endif

/*!
    Creates a normalized quaternion that corresponds to rotating through
    \a angle degrees about the 3D axis (\a x, \a y, \a z).
*/
QQuaternion QQuaternion::fromAxisAndAngle
        (qreal x, qreal y, qreal z, qreal angle)
{
    qreal length = qSqrt(x * x + y * y + z * z);
    if (!qFuzzyIsNull(length - 1.0f) && !qFuzzyIsNull(length)) {
        x /= length;
        y /= length;
        z /= length;
    }
    qreal a = (angle / 2.0f) * M_PI / 180.0f;
    qreal s = qSin(a);
    qreal c = qCos(a);
    return QQuaternion(c, x * s, y * s, z * s).normalized();
}

/*!
    \fn bool operator==(const QQuaternion &q1, const QQuaternion &q2)
    \relates QQuaternion

    Returns true if \a q1 is equal to \a q2; otherwise returns false.
    This operator uses an exact floating-point comparison.
*/

/*!
    \fn bool operator!=(const QQuaternion &q1, const QQuaternion &q2)
    \relates QQuaternion

    Returns true if \a q1 is not equal to \a q2; otherwise returns false.
    This operator uses an exact floating-point comparison.
*/

/*!
    \fn const QQuaternion operator+(const QQuaternion &q1, const QQuaternion &q2)
    \relates QQuaternion

    Returns a QQuaternion object that is the sum of the given quaternions,
    \a q1 and \a q2; each component is added separately.

    \sa QQuaternion::operator+=()
*/

/*!
    \fn const QQuaternion operator-(const QQuaternion &q1, const QQuaternion &q2)
    \relates QQuaternion

    Returns a QQuaternion object that is formed by subtracting
    \a q2 from \a q1; each component is subtracted separately.

    \sa QQuaternion::operator-=()
*/

/*!
    \fn const QQuaternion operator*(qreal factor, const QQuaternion &quaternion)
    \relates QQuaternion

    Returns a copy of the given \a quaternion,  multiplied by the
    given \a factor.

    \sa QQuaternion::operator*=()
*/

/*!
    \fn const QQuaternion operator*(const QQuaternion &quaternion, qreal factor)
    \relates QQuaternion

    Returns a copy of the given \a quaternion,  multiplied by the
    given \a factor.

    \sa QQuaternion::operator*=()
*/

/*!
    \fn const QQuaternion operator*(const QQuaternion &q1, const QQuaternion& q2)
    \relates QQuaternion

    Multiplies \a q1 and \a q2 using quaternion multiplication.
    The result corresponds to applying both of the rotations specified
    by \a q1 and \a q2.

    \sa QQuaternion::operator*=()
*/

/*!
    \fn const QQuaternion operator-(const QQuaternion &quaternion)
    \relates QQuaternion
    \overload

    Returns a QQuaternion object that is formed by changing the sign of
    all three components of the given \a quaternion.

    Equivalent to \c {QQuaternion(0,0,0,0) - quaternion}.
*/

/*!
    \fn const QQuaternion operator/(const QQuaternion &quaternion, qreal divisor)
    \relates QQuaternion

    Returns the QQuaternion object formed by dividing all components of
    the given \a quaternion by the given \a divisor.

    \sa QQuaternion::operator/=()
*/

/*!
    \fn bool qFuzzyCompare(const QQuaternion& q1, const QQuaternion& q2)
    \relates QQuaternion

    Returns true if \a q1 and \a q2 are equal, allowing for a small
    fuzziness factor for floating-point comparisons; false otherwise.
*/

/*!
    Interpolates along the shortest spherical path between the
    rotational positions \a q1 and \a q2.  The value \a t should
    be between 0 and 1, indicating the spherical distance to travel
    between \a q1 and \a q2.

    If \a t is less than or equal to 0, then \a q1 will be returned.
    If \a t is greater than or equal to 1, then \a q2 will be returned.

    \sa nlerp()
*/
QQuaternion QQuaternion::slerp
    (const QQuaternion& q1, const QQuaternion& q2, qreal t)
{
    // Handle the easy cases first.
    if (t <= 0.0f)
        return q1;
    else if (t >= 1.0f)
        return q2;

    // Determine the angle between the two quaternions.
    QQuaternion q2b;
    qreal dot;
    dot = q1.xp * q2.xp + q1.yp * q2.yp + q1.zp * q2.zp + q1.wp * q2.wp;
    if (dot >= 0.0f) {
        q2b = q2;
    } else {
        q2b = -q2;
        dot = -dot;
    }

    // Get the scale factors.  If they are too small,
    // then revert to simple linear interpolation.
    qreal factor1 = 1.0f - t;
    qreal factor2 = t;
    if ((1.0f - dot) > 0.0000001) {
        qreal angle = qreal(qAcos(dot));
        qreal sinOfAngle = qreal(qSin(angle));
        if (sinOfAngle > 0.0000001) {
            factor1 = qreal(qSin((1.0f - t) * angle)) / sinOfAngle;
            factor2 = qreal(qSin(t * angle)) / sinOfAngle;
        }
    }

    // Construct the result quaternion.
    return q1 * factor1 + q2b * factor2;
}

/*!
    Interpolates along the shortest linear path between the rotational
    positions \a q1 and \a q2.  The value \a t should be between 0 and 1,
    indicating the distance to travel between \a q1 and \a q2.
    The result will be normalized().

    If \a t is less than or equal to 0, then \a q1 will be returned.
    If \a t is greater than or equal to 1, then \a q2 will be returned.

    The nlerp() function is typically faster than slerp() and will
    give approximate results to spherical interpolation that are
    good enough for some applications.

    \sa slerp()
*/
QQuaternion QQuaternion::nlerp
    (const QQuaternion& q1, const QQuaternion& q2, qreal t)
{
    // Handle the easy cases first.
    if (t <= 0.0f)
        return q1;
    else if (t >= 1.0f)
        return q2;

    // Determine the angle between the two quaternions.
    QQuaternion q2b;
    qreal dot;
    dot = q1.xp * q2.xp + q1.yp * q2.yp + q1.zp * q2.zp + q1.wp * q2.wp;
    if (dot >= 0.0f)
        q2b = q2;
    else
        q2b = -q2;

    // Perform the linear interpolation.
    return (q1 * (1.0f - t) + q2b * t).normalized();
}

/*!
    Returns the quaternion as a QVariant.
*/
QQuaternion::operator QVariant() const
{
    return QVariant(QVariant::Quaternion, this);
}

#ifndef QT_NO_DEBUG_STREAM

QDebug operator<<(QDebug dbg, const QQuaternion &q)
{
    dbg.nospace() << "QQuaternion(scalar:" << q.scalar()
        << ", vector:(" << q.x() << ", "
        << q.y() << ", " << q.z() << "))";
    return dbg.space();
}

#endif

#ifndef QT_NO_DATASTREAM

/*!
    \fn QDataStream &operator<<(QDataStream &stream, const QQuaternion &quaternion)
    \relates QQuaternion

    Writes the given \a quaternion to the given \a stream and returns a
    reference to the stream.

    \sa {Serializing Qt Data Types}
*/

QDataStream &operator<<(QDataStream &stream, const QQuaternion &quaternion)
{
    stream << double(quaternion.scalar()) << double(quaternion.x())
           << double(quaternion.y()) << double(quaternion.z());
    return stream;
}

/*!
    \fn QDataStream &operator>>(QDataStream &stream, QQuaternion &quaternion)
    \relates QQuaternion

    Reads a quaternion from the given \a stream into the given \a quaternion
    and returns a reference to the stream.

    \sa {Serializing Qt Data Types}
*/

QDataStream &operator>>(QDataStream &stream, QQuaternion &quaternion)
{
    double scalar, x, y, z;
    stream >> scalar;
    stream >> x;
    stream >> y;
    stream >> z;
    quaternion.setScalar(qreal(scalar));
    quaternion.setX(qreal(x));
    quaternion.setY(qreal(y));
    quaternion.setZ(qreal(z));
    return stream;
}

#endif // QT_NO_DATASTREAM

#endif

QT_END_NAMESPACE