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vpQuaternionVector.cpp
1/****************************************************************************
2 *
3 * ViSP, open source Visual Servoing Platform software.
4 * Copyright (C) 2005 - 2023 by Inria. All rights reserved.
5 *
6 * This software is free software; you can redistribute it and/or modify
7 * it under the terms of the GNU General Public License as published by
8 * the Free Software Foundation; either version 2 of the License, or
9 * (at your option) any later version.
10 * See the file LICENSE.txt at the root directory of this source
11 * distribution for additional information about the GNU GPL.
12 *
13 * For using ViSP with software that can not be combined with the GNU
14 * GPL, please contact Inria about acquiring a ViSP Professional
15 * Edition License.
16 *
17 * See https://visp.inria.fr for more information.
18 *
19 * This software was developed at:
20 * Inria Rennes - Bretagne Atlantique
21 * Campus Universitaire de Beaulieu
22 * 35042 Rennes Cedex
23 * France
24 *
25 * If you have questions regarding the use of this file, please contact
26 * Inria at visp@inria.fr
27 *
28 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
29 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
30 *
31 * Description:
32 * Quaternion vector.
33 *
34 * Authors:
35 * Filip Novotny
36 *
37*****************************************************************************/
38
39#include <algorithm>
40#include <cassert>
41#include <stdio.h>
42#include <string.h>
43#include <visp3/core/vpMath.h>
44#include <visp3/core/vpQuaternionVector.h>
45
46// minimum value of sine
47const double vpQuaternionVector::minimum = 0.0001;
48
56
59
61vpQuaternionVector::vpQuaternionVector(double x_, double y_, double z_, double w_) : vpRotationVector(4)
62{
63 set(x_, y_, z_, w_);
64}
65
68
70vpQuaternionVector::vpQuaternionVector(const std::vector<double> &q) : vpRotationVector(4) { buildFrom(q); }
71
78
86
94void vpQuaternionVector::set(double qx, double qy, double qz, double qw)
95{
96 data[0] = qx;
97 data[1] = qy;
98 data[2] = qz;
99 data[3] = qw;
100}
110vpQuaternionVector vpQuaternionVector::buildFrom(double qx, double qy, double qz, double qw)
111{
112 set(qx, qy, qz, qw);
113 return *this;
114}
115
123{
124 vpRotationMatrix R(tu);
125 buildFrom(R);
126
127 return *this;
128}
129
134{
135 if (q.size() != 4) {
137 "Cannot construct a quaternion vector from a %d-dimension col vector", q.size()));
138 }
139 for (unsigned int i = 0; i < 4; i++)
140 data[i] = q[i];
141
142 return *this;
143}
144
149{
150 if (q.size() != 4) {
152 "Cannot construct a quaternion vector from a %d-dimension std::vector", q.size()));
153 }
154 for (unsigned int i = 0; i < 4; i++)
155 data[i] = q[i];
156
157 return *this;
158}
159
168{
169 return vpQuaternionVector(x() + q.x(), y() + q.y(), z() + q.z(), w() + q.w());
170}
179{
180 return vpQuaternionVector(x() - q.x(), y() - q.y(), z() - q.z(), w() - q.w());
181}
182
185
188{
189 return vpQuaternionVector(l * x(), l * y(), l * z(), l * w());
190}
191
194{
195 return vpQuaternionVector(w() * rq.x() + x() * rq.w() + y() * rq.z() - z() * rq.y(),
196 w() * rq.y() + y() * rq.w() + z() * rq.x() - x() * rq.z(),
197 w() * rq.z() + z() * rq.w() + x() * rq.y() - y() * rq.x(),
198 w() * rq.w() - x() * rq.x() - y() * rq.y() - z() * rq.z());
199}
200
203{
204 if (vpMath::nul(l, std::numeric_limits<double>::epsilon())) {
205 throw vpException(vpException::fatalError, "Division by scalar l==0 !");
206 }
207
208 return vpQuaternionVector(x() / l, y() / l, z() / l, w() / l);
209}
235{
236 if (q.size() != 4) {
237 throw(vpException(vpException::dimensionError, "Cannot set a quaternion vector from a %d-dimension col vector",
238 q.size()));
239 }
240 for (unsigned int i = 0; i < 4; i++)
241 data[i] = q[i];
242
243 return *this;
244}
245
252{
253 vpThetaUVector tu(R);
254 vpColVector u;
255 double theta;
256 tu.extract(theta, u);
257
258 theta *= 0.5;
259
260 double sinTheta_2 = sin(theta);
261 set(u[0] * sinTheta_2, u[1] * sinTheta_2, u[2] * sinTheta_2, cos(theta));
262 return *this;
263}
264
271
278{
279 vpQuaternionVector q_inv;
280
281 double mag_square = w() * w() + x() * x() + y() * y() + z() * z();
282 if (!vpMath::nul(mag_square, std::numeric_limits<double>::epsilon())) {
283 q_inv = this->conjugate() / mag_square;
284 } else {
285 std::cerr << "The current quaternion is null ! The inverse cannot be computed !" << std::endl;
286 }
287
288 return q_inv;
289}
290
296double vpQuaternionVector::magnitude() const { return sqrt(w() * w() + x() * x() + y() * y() + z() * z()); }
297
302{
303 double mag = magnitude();
304 if (!vpMath::nul(mag, std::numeric_limits<double>::epsilon())) {
305 set(x() / mag, y() / mag, z() / mag, w() / mag);
306 }
307}
308
318{
319 return q0.x() * q1.x() + q0.y() * q1.y() + q0.z() * q1.z() + q0.w() * q1.w();
320}
321
323const double& vpQuaternionVector::x() const { return data[0]; }
325const double& vpQuaternionVector::y() const { return data[1]; }
327const double& vpQuaternionVector::z() const { return data[2]; }
329const double& vpQuaternionVector::w() const { return data[3]; }
330
332double& vpQuaternionVector::x() { return data[0]; }
334double& vpQuaternionVector::y() { return data[1]; }
336double& vpQuaternionVector::z() { return data[2]; }
338double& vpQuaternionVector::w() { return data[3]; }
339
340#if (VISP_CXX_STANDARD >= VISP_CXX_STANDARD_11)
358vpQuaternionVector &vpQuaternionVector::operator=(const std::initializer_list<double> &list)
359{
360 if (list.size() > size()) {
361 throw(vpException(
363 "Cannot set quaternion vector out of bounds. It has only %d values while you try to initialize with %d values",
364 size(), list.size()));
365 }
366 std::copy(list.begin(), list.end(), data);
367 return *this;
368}
369#endif
370
386{
387 assert(t >= 0 && t <= 1);
388
389 double cosHalfTheta = dot(q0, q1);
390 vpQuaternionVector q1_ = q1;
391 if (cosHalfTheta < 0) {
392 cosHalfTheta = -cosHalfTheta;
393 q1_ = -q1;
394 }
395
396 vpQuaternionVector qLerp;
397 qLerp.x() = q0.x() - t * (q0.x() - q1.x());
398 qLerp.y() = q0.y() - t * (q0.y() - q1.y());
399 qLerp.z() = q0.z() - t * (q0.z() - q1.z());
400 qLerp.w() = q0.w() - t * (q0.w() - q1.w());
401
402 return qLerp;
403}
404
420{
421 assert(t >= 0 && t <= 1);
422
423 vpQuaternionVector qLerp = lerp(q0, q1, t);
424 qLerp.normalize();
425
426 return qLerp;
427}
428
444{
445 assert(t >= 0 && t <= 1);
446 // Some additional references:
447 // https://splines.readthedocs.io/en/latest/rotation/slerp.html
448 // https://zeux.io/2015/07/23/approximating-slerp/
449 // https://github.com/eigenteam/eigen-git-mirror/blob/36b95962756c1fce8e29b1f8bc45967f30773c00/Eigen/src/Geometry/Quaternion.h#L753-L790
450 // https://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/index.htm
451 // http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/
452 // https://www.3dgep.com/understanding-quaternions/
453 // https://blog.magnum.graphics/backstage/the-unnecessarily-short-ways-to-do-a-quaternion-slerp/
454
455 double cosHalfTheta = dot(q0, q1);
456 vpQuaternionVector q1_ = q1;
457 if (cosHalfTheta < 0) {
458 cosHalfTheta = -cosHalfTheta;
459 q1_ = -q1;
460 }
461
462 double scale0 = 1 - t;
463 double scale1 = t;
464
465 if (1 - cosHalfTheta > 0.1) {
466 double theta = std::acos(cosHalfTheta);
467 double invSinTheta = 1 / std::sin(theta);
468
469 scale0 = std::sin((1 - t) * theta) * invSinTheta;
470 scale1 = std::sin((t * theta)) * invSinTheta;
471 }
472
473 vpQuaternionVector qSlerp;
474 qSlerp.x() = (scale0 * q0.x()) + (scale1 * q1_.x());
475 qSlerp.y() = (scale0 * q0.y()) + (scale1 * q1_.y());
476 qSlerp.z() = (scale0 * q0.z()) + (scale1 * q1_.z());
477 qSlerp.w() = (scale0 * q0.w()) + (scale1 * q1_.w());
478 qSlerp.normalize();
479
480 return qSlerp;
481}
unsigned int size() const
Return the number of elements of the 2D array.
Definition vpArray2D.h:292
Implementation of column vector and the associated operations.
error that can be emitted by ViSP classes.
Definition vpException.h:59
@ dimensionError
Bad dimension.
Definition vpException.h:83
@ fatalError
Fatal error.
Definition vpException.h:84
static bool nul(double x, double threshold=0.001)
Definition vpMath.h:360
Implementation of a rotation vector as quaternion angle minimal representation.
vpQuaternionVector operator*(double l) const
Multiplication by scalar. Returns a quaternion defined by (lx,ly,lz,lw).
const double & z() const
Returns the z-component of the quaternion.
vpQuaternionVector conjugate() const
vpQuaternionVector inverse() const
vpQuaternionVector & operator=(const vpColVector &q)
void set(double x, double y, double z, double w)
static vpQuaternionVector slerp(const vpQuaternionVector &q0, const vpQuaternionVector &q1, double t)
vpQuaternionVector buildFrom(const vpThetaUVector &tu)
static vpQuaternionVector nlerp(const vpQuaternionVector &q0, const vpQuaternionVector &q1, double t)
vpQuaternionVector operator-() const
Negate operator. Returns a quaternion defined by (-x,-y,-z-,-w).
const double & x() const
Returns the x-component of the quaternion.
static double dot(const vpQuaternionVector &q0, const vpQuaternionVector &q1)
const double & y() const
Returns the y-component of the quaternion.
const double & w() const
Returns the w-component of the quaternion.
vpQuaternionVector buildFrom(const double qx, const double qy, const double qz, const double qw)
vpQuaternionVector operator+(const vpQuaternionVector &q) const
static vpQuaternionVector lerp(const vpQuaternionVector &q0, const vpQuaternionVector &q1, double t)
vpQuaternionVector operator/(double l) const
Division by scalar. Returns a quaternion defined by (x/l,y/l,z/l,w/l).
Implementation of a rotation matrix and operations on such kind of matrices.
Implementation of a generic rotation vector.
vpRowVector t() const
Implementation of a rotation vector as axis-angle minimal representation.
void extract(double &theta, vpColVector &u) const