This file is indexed.

/usr/include/openvdb/math/Quat.h is in libopenvdb-dev 3.1.0-2.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

  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
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2012-2015 DreamWorks Animation LLC
//
// All rights reserved. This software is distributed under the
// Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
//
// Redistributions of source code must retain the above copyright
// and license notice and the following restrictions and disclaimer.
//
// *     Neither the name of DreamWorks Animation 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 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.
// IN NO EVENT SHALL THE COPYRIGHT HOLDERS' AND CONTRIBUTORS' AGGREGATE
// LIABILITY FOR ALL CLAIMS REGARDLESS OF THEIR BASIS EXCEED US$250.00.
//
///////////////////////////////////////////////////////////////////////////

#ifndef OPENVDB_MATH_QUAT_H_HAS_BEEN_INCLUDED
#define OPENVDB_MATH_QUAT_H_HAS_BEEN_INCLUDED

#include <iostream>
#include <cmath>

#include "Mat.h"
#include "Mat3.h"
#include "Math.h"
#include "Vec3.h"
#include <openvdb/Exceptions.h>


namespace openvdb {
OPENVDB_USE_VERSION_NAMESPACE
namespace OPENVDB_VERSION_NAME {
namespace math {

template<typename T> class Quat;

/// Linear interpolation between the two quaternions
template <typename T>
Quat<T> slerp(const Quat<T> &q1, const Quat<T> &q2, T t, T tolerance=0.00001)
{
    T qdot, angle, sineAngle;

    qdot = q1.dot(q2);

    if (fabs(qdot) >= 1.0) {
        angle     = 0; // not necessary but suppresses compiler warning
        sineAngle = 0;
    } else {
        angle     = acos(qdot);
        sineAngle = sin(angle);
    }

    //
    // Denominator close to 0 corresponds to the case where the
    // two quaternions are close to the same rotation. In this
    // case linear interpolation is used but we normalize to
    // guarantee unit length
    //
    if (sineAngle <= tolerance) {
        T s = 1.0 - t;

        Quat<T> qtemp(s * q1[0] + t * q2[0], s * q1[1] + t * q2[1],
                      s * q1[2] + t * q2[2], s * q1[3] + t * q2[3]);
        //
        // Check the case where two close to antipodal quaternions were
        // blended resulting in a nearly zero result which can happen,
        // for example, if t is close to 0.5. In this case it is not safe
        // to project back onto the sphere.
        //
        double lengthSquared = qtemp.dot(qtemp);

        if (lengthSquared <= tolerance * tolerance) {
            qtemp = (t < 0.5) ? q1 : q2;
        } else {
            qtemp *= 1.0 / sqrt(lengthSquared);
        }
        return qtemp;
    } else {

        T sine  = 1.0 / sineAngle;
        T a = sin((1.0 - t) * angle) * sine;
        T b = sin(t * angle) * sine;
        return Quat<T>(a * q1[0] + b * q2[0], a * q1[1] + b * q2[1],
                       a * q1[2] + b * q2[2], a * q1[3] + b * q2[3]);
    }

}

template<typename T>
class Quat
{
public:
    /// Trivial constructor, the quaternion is NOT initialized
    Quat() {}

    /// Constructor with four arguments, e.g.   Quatf q(1,2,3,4);
    Quat(T x, T y, T z, T w)
    {
        mm[0] = x;
        mm[1] = y;
        mm[2] = z;
        mm[3] = w;

    }

    /// Constructor with array argument, e.g.   float a[4]; Quatf q(a);
    Quat(T *a)
    {
        mm[0] = a[0];
        mm[1] = a[1];
        mm[2] = a[2];
        mm[3] = a[3];

    }

    /// Constructor given rotation as axis and angle, the axis must be
    /// unit vector
    Quat(const Vec3<T> &axis, T angle)
    {
        // assert( REL_EQ(axis.length(), 1.) );

        T s = T(sin(angle*T(0.5)));

        mm[0] = axis.x() * s;
        mm[1] = axis.y() * s;
        mm[2] = axis.z() * s;

        mm[3] = T(cos(angle*T(0.5)));

    }

    /// Constructor given rotation as axis and angle
    Quat(math::Axis axis, T angle)
    {
        T s = T(sin(angle*T(0.5)));

        mm[0] = (axis==math::X_AXIS) * s;
        mm[1] = (axis==math::Y_AXIS) * s;
        mm[2] = (axis==math::Z_AXIS) * s;

        mm[3] = T(cos(angle*T(0.5)));
    }

    /// Constructor given a rotation matrix
    template<typename T1>
    Quat(const Mat3<T1> &rot) {

        // verify that the matrix is really a rotation
        if(!isUnitary(rot)) {  // unitary is reflection or rotation
             OPENVDB_THROW(ArithmeticError,
                "A non-rotation matrix can not be used to construct a quaternion");
        }
        if (!isApproxEqual(rot.det(), (T1)1)) { // rule out reflection
             OPENVDB_THROW(ArithmeticError,
                "A reflection matrix can not be used to construct a quaternion");
        }

        T trace = (T)rot.trace();
        if (trace > 0) {

            T q_w = 0.5 * std::sqrt(trace+1);
            T factor = 0.25 / q_w;

            mm[0] = factor * (rot(1,2) - rot(2,1));
            mm[1] = factor * (rot(2,0) - rot(0,2));
            mm[2] = factor * (rot(0,1) - rot(1,0));
            mm[3] = q_w;
        }  else if (rot(0,0) > rot(1,1) && rot(0,0) > rot(2,2)) {

            T q_x = 0.5 * sqrt(rot(0,0)- rot(1,1)-rot(2,2)+1);
            T factor = 0.25 / q_x;

            mm[0] = q_x;
            mm[1] = factor * (rot(0,1) + rot(1,0));
            mm[2] = factor * (rot(2,0) + rot(0,2));
            mm[3] = factor * (rot(1,2) - rot(2,1));
        } else if (rot(1,1) > rot(2,2)) {

            T q_y = 0.5 * sqrt(rot(1,1)-rot(0,0)-rot(2,2)+1);
            T factor = 0.25 / q_y;

            mm[0] =  factor * (rot(0,1) + rot(1,0));
            mm[1] = q_y;
            mm[2] = factor * (rot(1,2) + rot(2,1));
            mm[3] = factor * (rot(2,0) - rot(0,2));
        } else {

            T q_z = 0.5 * sqrt(rot(2,2)-rot(0,0)-rot(1,1)+1);
            T factor = 0.25 / q_z;

            mm[0] = factor * (rot(2,0) + rot(0,2));
            mm[1] = factor * (rot(1,2) + rot(2,1));
            mm[2] = q_z;
            mm[3] = factor * (rot(0,1) - rot(1,0));
        }
    }

    /// Copy constructor
    Quat(const Quat &q)
    {
        mm[0] = q.mm[0];
        mm[1] = q.mm[1];
        mm[2] = q.mm[2];
        mm[3] = q.mm[3];

    }

    /// Reference to the component, e.g.   q.x() = 4.5f;
    T& x() { return mm[0]; }
    T& y() { return mm[1]; }
    T& z() { return mm[2]; }
    T& w() { return mm[3]; }

    /// Get the component, e.g.   float f = q.w();
    T x() const { return mm[0]; }
    T y() const { return mm[1]; }
    T z() const { return mm[2]; }
    T w() const { return mm[3]; }

    // Number of elements
    static unsigned numElements() { return 4; }

    /// Array style reference to the components, e.g.   q[3] = 1.34f;
    T& operator[](int i) { return mm[i]; }

    /// Array style constant reference to the components, e.g.  float f = q[1];
    T operator[](int i) const { return mm[i]; }

    /// Cast to T*
    operator T*() { return mm; }
    operator const T*() const { return mm; }

    /// Alternative indexed reference to the elements
    T& operator()(int i) { return mm[i]; }

    /// Alternative indexed constant reference to the elements,
    T operator()(int i) const { return mm[i]; }

    /// Return angle of rotation
    T angle() const
    {
        T sqrLength = mm[0]*mm[0] + mm[1]*mm[1] + mm[2]*mm[2];

        if ( sqrLength > 1.0e-8 ) {

            return T(T(2.0) * acos(mm[3]));

        } else {

            return T(0.0);
        }
    }

    /// Return axis of rotation
    Vec3<T> axis() const
    {
        T sqrLength = mm[0]*mm[0] + mm[1]*mm[1] + mm[2]*mm[2];

        if ( sqrLength > 1.0e-8 ) {

            T invLength = T(T(1)/sqrt(sqrLength));

            return Vec3<T>( mm[0]*invLength, mm[1]*invLength, mm[2]*invLength );
        } else {

            return Vec3<T>(1,0,0);
        }
    }


    /// "this" quaternion gets initialized to [x, y, z, w]
    Quat& init(T x, T y, T z, T w)
    {
        mm[0] = x; mm[1] = y; mm[2] = z; mm[3] = w;
        return *this;
    }

    /// "this" quaternion gets initialized to identity, same as setIdentity()
    Quat& init() { return setIdentity(); }

    /// Set "this" quaternion to rotation specified by axis and angle,
    /// the axis must be unit vector
    Quat& setAxisAngle(const Vec3<T>& axis, T angle)
    {

        T s = T(sin(angle*T(0.5)));

        mm[0] = axis.x() * s;
        mm[1] = axis.y() * s;
        mm[2] = axis.z() * s;

        mm[3] = T(cos(angle*T(0.5)));

        return *this;
    } // axisAngleTest

    /// Set "this" vector to zero
    Quat& setZero()
    {
        mm[0] = mm[1] = mm[2] = mm[3] = 0;
        return *this;
    }

    /// Set "this" vector to identity
    Quat& setIdentity()
    {
        mm[0] = mm[1] = mm[2] = 0;
        mm[3] = 1;
        return *this;
    }

    /// Returns vector of x,y,z rotational components
    Vec3<T> eulerAngles(RotationOrder rotationOrder) const
    { return math::eulerAngles(Mat3<T>(*this), rotationOrder); }

    /// Assignment operator
    Quat& operator=(const Quat &q)
    {
        mm[0] = q.mm[0];
        mm[1] = q.mm[1];
        mm[2] = q.mm[2];
        mm[3] = q.mm[3];

        return *this;
    }

    /// Equality operator, does exact floating point comparisons
    bool operator==(const Quat &q) const
    {
        return (isExactlyEqual(mm[0],q.mm[0]) &&
                isExactlyEqual(mm[1],q.mm[1]) &&
                isExactlyEqual(mm[2],q.mm[2]) &&
                isExactlyEqual(mm[3],q.mm[3]) );
    }

    /// Test if "this" is equivalent to q with tolerance of eps value
    bool eq(const Quat &q, T eps=1.0e-7) const
    {
        return isApproxEqual(mm[0],q.mm[0],eps) && isApproxEqual(mm[1],q.mm[1],eps) &&
            isApproxEqual(mm[2],q.mm[2],eps) && isApproxEqual(mm[3],q.mm[3],eps) ;
    } // trivial

    /// Add quaternion q to "this" quaternion, e.g.   q += q1;
    Quat& operator+=(const Quat &q)
    {
        mm[0] += q.mm[0];
        mm[1] += q.mm[1];
        mm[2] += q.mm[2];
        mm[3] += q.mm[3];

        return *this;
    }

    /// Subtract quaternion q from "this" quaternion, e.g.   q -= q1;
    Quat& operator-=(const Quat &q)
    {
        mm[0] -= q.mm[0];
        mm[1] -= q.mm[1];
        mm[2] -= q.mm[2];
        mm[3] -= q.mm[3];

        return *this;
    }

    /// Scale "this" quaternion by scalar, e.g.   q *= scalar;
    Quat& operator*=(T scalar)
    {
        mm[0] *= scalar;
        mm[1] *= scalar;
        mm[2] *= scalar;
        mm[3] *= scalar;

        return *this;
    }

    /// Return (this+q), e.g.   q = q1 + q2;
    Quat operator+(const Quat &q) const
    {
        return Quat<T>(mm[0]+q.mm[0], mm[1]+q.mm[1], mm[2]+q.mm[2], mm[3]+q.mm[3]);
    }

    /// Return (this-q), e.g.   q = q1 - q2;
    Quat operator-(const Quat &q) const
    {
        return Quat<T>(mm[0]-q.mm[0], mm[1]-q.mm[1], mm[2]-q.mm[2], mm[3]-q.mm[3]);
    }

    /// Return (this*q), e.g.   q = q1 * q2;
    Quat operator*(const Quat &q) const
    {
        Quat<T> prod;

        prod.mm[0] = mm[3]*q.mm[0] + mm[0]*q.mm[3] + mm[1]*q.mm[2] - mm[2]*q.mm[1];
        prod.mm[1] = mm[3]*q.mm[1] + mm[1]*q.mm[3] + mm[2]*q.mm[0] - mm[0]*q.mm[2];
        prod.mm[2] = mm[3]*q.mm[2] + mm[2]*q.mm[3] + mm[0]*q.mm[1] - mm[1]*q.mm[0];
        prod.mm[3] = mm[3]*q.mm[3] - mm[0]*q.mm[0] - mm[1]*q.mm[1] - mm[2]*q.mm[2];

        return prod;

    }

    /// Assigns this to (this*q), e.g.   q *= q1;
    Quat operator*=(const Quat &q)
    {
        *this = *this * q;
        return *this;
    }

    /// Return (this*scalar), e.g.   q = q1 * scalar;
    Quat operator*(T scalar) const
    {
        return Quat<T>(mm[0]*scalar, mm[1]*scalar, mm[2]*scalar, mm[3]*scalar);
    }

    /// Return (this/scalar), e.g.   q = q1 / scalar;
    Quat operator/(T scalar) const
    {
        return Quat<T>(mm[0]/scalar, mm[1]/scalar, mm[2]/scalar, mm[3]/scalar);
    }

    /// Negation operator, e.g.   q = -q;
    Quat operator-() const
    { return Quat<T>(-mm[0], -mm[1], -mm[2], -mm[3]); }

    /// this = q1 + q2
    /// "this", q1 and q2 need not be distinct objects, e.g. q.add(q1,q);
    Quat& add(const Quat &q1, const Quat &q2)
    {
        mm[0] = q1.mm[0] + q2.mm[0];
        mm[1] = q1.mm[1] + q2.mm[1];
        mm[2] = q1.mm[2] + q2.mm[2];
        mm[3] = q1.mm[3] + q2.mm[3];

        return *this;
    }

    /// this = q1 - q2
    /// "this", q1 and q2 need not be distinct objects, e.g. q.sub(q1,q);
    Quat& sub(const Quat &q1, const Quat &q2)
    {
        mm[0] = q1.mm[0] - q2.mm[0];
        mm[1] = q1.mm[1] - q2.mm[1];
        mm[2] = q1.mm[2] - q2.mm[2];
        mm[3] = q1.mm[3] - q2.mm[3];

        return *this;
    }

    /// this = q1 * q2
    /// q1 and q2 must be distinct objects than "this", e.g.  q.mult(q1,q2);
    Quat& mult(const Quat &q1, const Quat &q2)
    {
        mm[0] = q1.mm[3]*q2.mm[0] + q1.mm[0]*q2.mm[3] +
                q1.mm[1]*q2.mm[2] - q1.mm[2]*q2.mm[1];
        mm[1] = q1.mm[3]*q2.mm[1] + q1.mm[1]*q2.mm[3] +
                q1.mm[2]*q2.mm[0] - q1.mm[0]*q2.mm[2];
        mm[2] = q1.mm[3]*q2.mm[2] + q1.mm[2]*q2.mm[3] +
                q1.mm[0]*q2.mm[1] - q1.mm[1]*q2.mm[0];
        mm[3] = q1.mm[3]*q2.mm[3] - q1.mm[0]*q2.mm[0] -
                q1.mm[1]*q2.mm[1] - q1.mm[2]*q2.mm[2];

        return *this;
    }

    /// this =  scalar*q, q need not be distinct object than "this",
    /// e.g. q.scale(1.5,q1);
    Quat& scale(T scale, const Quat &q)
    {
        mm[0] = scale * q.mm[0];
        mm[1] = scale * q.mm[1];
        mm[2] = scale * q.mm[2];
        mm[3] = scale * q.mm[3];

        return *this;
    }

    /// Dot product
    T dot(const Quat &q) const
    {
        return (mm[0]*q.mm[0] + mm[1]*q.mm[1] + mm[2]*q.mm[2] + mm[3]*q.mm[3]);
    }

    /// Return the quaternion rate corrsponding to the angular velocity omega
    /// and "this" current rotation
    Quat derivative(const Vec3<T>& omega) const
    {
        return Quat<T>( +w()*omega.x() -z()*omega.y() +y()*omega.z() ,
                        +z()*omega.x() +w()*omega.y() -x()*omega.z() ,
                        -y()*omega.x() +x()*omega.y() +w()*omega.z() ,
                        -x()*omega.x() -y()*omega.y() -z()*omega.z() );
    }

    /// this = normalized this
    bool normalize(T eps = T(1.0e-8))
    {
        T d = T(sqrt(mm[0]*mm[0] + mm[1]*mm[1] + mm[2]*mm[2] + mm[3]*mm[3]));
        if( isApproxEqual(d, T(0.0), eps) ) return false;
        *this *= ( T(1)/d );
        return true;
    }

    /// this = normalized this
    Quat unit() const
    {
        T d = sqrt(mm[0]*mm[0] + mm[1]*mm[1] + mm[2]*mm[2] + mm[3]*mm[3]);
        if( isExactlyEqual(d , T(0.0) ) )
            OPENVDB_THROW(ArithmeticError,
                "Normalizing degenerate quaternion");
        return *this / d;
    }

    /// returns inverse of this
    Quat inverse(T tolerance = T(0))
    {
        T d = mm[0]*mm[0] + mm[1]*mm[1] + mm[2]*mm[2] + mm[3]*mm[3];
        if( isApproxEqual(d, T(0.0), tolerance) )
            OPENVDB_THROW(ArithmeticError,
                "Cannot invert degenerate quaternion");
        Quat result = *this/-d;
        result.mm[3] = -result.mm[3];
        return result;
    }


    /// Return the conjugate of "this", same as invert without
    /// unit quaternion test
    Quat conjugate() const
    {
        return Quat<T>(-mm[0], -mm[1], -mm[2], mm[3]);
    }

    /// Return rotated vector by "this" quaternion
    Vec3<T> rotateVector(const Vec3<T> &v) const
    {
        Mat3<T> m(*this);
        return m.transform(v);
    }

    /// Predefined constants, e.g.   Quat q = Quat::identity();
    static Quat zero() { return Quat<T>(0,0,0,0); }
    static Quat identity() { return Quat<T>(0,0,0,1); }

     /// @return string representation of Classname
    std::string
    str() const {
        std::ostringstream buffer;

        buffer << "[";

        // For each column
        for (unsigned j(0); j < 4; j++) {
            if (j) buffer << ", ";
            buffer << mm[j];
        }

        buffer << "]";

        return buffer.str();
    }

    /// Output to the stream, e.g.   std::cout << q << std::endl;
    friend std::ostream& operator<<(std::ostream &stream, const Quat &q)
    {
        stream << q.str();
        return stream;
    }

    friend Quat slerp<>(const Quat &q1, const Quat &q2, T t, T tolerance);


    void write(std::ostream& os) const {
        os.write((char*)&mm, sizeof(T)*4);
    }
    void read(std::istream& is) {
        is.read((char*)&mm, sizeof(T)*4);
    }

protected:
    T mm[4];
};

/// Returns V, where \f$V_i = v_i * scalar\f$ for \f$i \in [0, 3]\f$
template <typename S, typename T>
Quat<T> operator*(S scalar, const Quat<T> &q) { return q*scalar; }


/// @brief Interpolate between m1 and m2.
/// Converts to quaternion  form and uses slerp
/// m1 and m2 must be rotation matrices!
template <typename T, typename T0>
Mat3<T> slerp(const Mat3<T0> &m1, const Mat3<T0> &m2, T t)
{
    typedef Mat3<T> MatType;

    Quat<T> q1(m1);
    Quat<T> q2(m2);

    if (q1.dot(q2) < 0) q2 *= -1;

    Quat<T> qslerp = slerp<T>(q1, q2, static_cast<T>(t));
    MatType m = rotation<MatType>(qslerp);
    return m;
}



/// Interpolate between m1 and m4 by converting m1 ... m4  into
/// quaternions and treating them as control points of a Bezier
/// curve using slerp in place of lerp in the De Castlejeau evaluation
/// algorithm. Just like a cubic Bezier curve, this will interpolate
/// m1 at t = 0 and m4 at t = 1 but in general will not pass through
/// m2 and m3.  Unlike a standard Bezier curve this curve will not have
/// the convex hull property.
/// m1 ... m4 must be rotation matrices!
template <typename T, typename T0>
Mat3<T> bezLerp(const Mat3<T0> &m1, const Mat3<T0> &m2,
                const Mat3<T0> &m3, const Mat3<T0> &m4,
                T t)
{
    Mat3<T> m00, m01, m02, m10, m11;

    m00 = slerp(m1, m2, t);
    m01 = slerp(m2, m3, t);
    m02 = slerp(m3, m4, t);

    m10 = slerp(m00, m01, t);
    m11 = slerp(m01, m02, t);

    return slerp(m10, m11, t);
}

typedef Quat<float> Quats;
typedef Quat<double> Quatd;

} // namespace math
} // namespace OPENVDB_VERSION_NAME
} // namespace openvdb

#endif //OPENVDB_MATH_QUAT_H_HAS_BEEN_INCLUDED

// ---------------------------------------------------------------------------
// Copyright (c) 2012-2015 DreamWorks Animation LLC
// All rights reserved. This software is distributed under the
// Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )