vpQuaternionVector.cpp

/****************************************************************************
 *
 * ViSP, open source Visual Servoing Platform software.
 * Copyright (C) 2005 - 2023 by Inria. All rights reserved.
 *
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 * it under the terms of the GNU General Public License as published by
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 * Inria Rennes - Bretagne Atlantique
 * Campus Universitaire de Beaulieu
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 * France
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 *
 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 *
 * Description:
 * Quaternion vector.
 *
 * Authors:
 * Filip Novotny
 *
*****************************************************************************/
 
#include <algorithm>
#include <cassert>
#include <stdio.h>
#include <string.h>
#include <visp3/core/vpMath.h>
#include <visp3/core/vpQuaternionVector.h>
 
// minimum value of sine
const double vpQuaternionVector::minimum = 0.0001;
 
vpQuaternionVector::vpQuaternionVector() : vpRotationVector(4) { }
 
vpQuaternionVector::vpQuaternionVector(const vpQuaternionVector &q) : vpRotationVector(q) { }
 
vpQuaternionVector::vpQuaternionVector(double x_, double y_, double z_, double w_) : vpRotationVector(4)
{
  set(x_, y_, z_, w_);
}
 
vpQuaternionVector::vpQuaternionVector(const vpColVector &q) : vpRotationVector(4) { buildFrom(q); }
 
vpQuaternionVector::vpQuaternionVector(const std::vector<double> &q) : vpRotationVector(4) { buildFrom(q); }
 
vpQuaternionVector::vpQuaternionVector(const vpRotationMatrix &R) : vpRotationVector(4) { buildFrom(R); }
 
vpQuaternionVector::vpQuaternionVector(const vpThetaUVector &tu) : vpRotationVector(4) { buildFrom(tu); }
 
void vpQuaternionVector::set(double qx, double qy, double qz, double qw)
{
  data[0] = qx;
  data[1] = qy;
  data[2] = qz;
  data[3] = qw;
}
vpQuaternionVector vpQuaternionVector::buildFrom(double qx, double qy, double qz, double qw)
{
  set(qx, qy, qz, qw);
  return *this;
}
 
vpQuaternionVector vpQuaternionVector::buildFrom(const vpThetaUVector &tu)
{
  vpRotationMatrix R(tu);
  buildFrom(R);
 
  return *this;
}
 
vpQuaternionVector vpQuaternionVector::buildFrom(const vpColVector &q)
{
  if (q.size() != 4) {
    throw(vpException(vpException::dimensionError,
                      "Cannot construct a quaternion vector from a %d-dimension col vector", q.size()));
  }
  for (unsigned int i = 0; i < 4; ++i) {
    data[i] = q[i];
  }
 
  return *this;
}
 
vpQuaternionVector vpQuaternionVector::buildFrom(const std::vector<double> &q)
{
  if (q.size() != 4) {
    throw(vpException(vpException::dimensionError,
                      "Cannot construct a quaternion vector from a %d-dimension std::vector", q.size()));
  }
  for (unsigned int i = 0; i < 4; ++i) {
    data[i] = q[i];
  }
 
  return *this;
}
 
vpQuaternionVector vpQuaternionVector::operator+(const vpQuaternionVector &q) const
{
  return vpQuaternionVector(x() + q.x(), y() + q.y(), z() + q.z(), w() + q.w());
}
vpQuaternionVector vpQuaternionVector::operator-(const vpQuaternionVector &q) const
{
  return vpQuaternionVector(x() - q.x(), y() - q.y(), z() - q.z(), w() - q.w());
}
 
vpQuaternionVector vpQuaternionVector::operator-() const { return vpQuaternionVector(-x(), -y(), -z(), -w()); }
 
vpQuaternionVector vpQuaternionVector::operator*(double l) const
{
  return vpQuaternionVector(l * x(), l * y(), l * z(), l * w());
}
 
vpQuaternionVector vpQuaternionVector::operator*(const vpQuaternionVector &rq) const
{
  return vpQuaternionVector(((w() * rq.x()) + (x() * rq.w()) + (y() * rq.z())) - (z() * rq.y()),
                            ((w() * rq.y()) + (y() * rq.w()) + (z() * rq.x())) - (x() * rq.z()),
                            ((w() * rq.z()) + (z() * rq.w()) + (x() * rq.y())) - (y() * rq.x()),
                            ((w() * rq.w()) - (x() * rq.x()) - (y() * rq.y())) - (z() * rq.z()));
}
 
vpQuaternionVector vpQuaternionVector::operator/(double l) const
{
  if (vpMath::nul(l, std::numeric_limits<double>::epsilon())) {
    throw vpException(vpException::fatalError, "Division by scalar l==0 !");
  }
 
  return vpQuaternionVector(x() / l, y() / l, z() / l, w() / l);
}
vpQuaternionVector &vpQuaternionVector::operator=(const vpColVector &q)
{
  if (q.size() != 4) {
    throw(vpException(vpException::dimensionError, "Cannot set a quaternion vector from a %d-dimension col vector",
                      q.size()));
  }
  for (unsigned int i = 0; i < 4; ++i) {
    data[i] = q[i];
  }
 
  return *this;
}
 
vpQuaternionVector vpQuaternionVector::buildFrom(const vpRotationMatrix &R)
{
  vpThetaUVector tu(R);
  vpColVector u;
  double theta;
  tu.extract(theta, u);
 
  theta *= 0.5;
 
  double sinTheta_2 = sin(theta);
  set(u[0] * sinTheta_2, u[1] * sinTheta_2, u[2] * sinTheta_2, cos(theta));
  return *this;
}
 
vpQuaternionVector vpQuaternionVector::conjugate() const { return vpQuaternionVector(-x(), -y(), -z(), w()); }
 
vpQuaternionVector vpQuaternionVector::inverse() const
{
  vpQuaternionVector q_inv;
 
  double mag_square = (w() * w()) + (x() * x()) + (y() * y()) + (z() * z());
  if (!vpMath::nul(mag_square, std::numeric_limits<double>::epsilon())) {
    q_inv = this->conjugate() / mag_square;
  }
  else {
    std::cerr << "The current quaternion is null ! The inverse cannot be computed !" << std::endl;
  }
 
  return q_inv;
}
 
double vpQuaternionVector::magnitude() const { return sqrt((w() * w()) + (x() * x()) + (y() * y()) + (z() * z())); }
 
void vpQuaternionVector::normalize()
{
  double mag = magnitude();
  if (!vpMath::nul(mag, std::numeric_limits<double>::epsilon())) {
    set(x() / mag, y() / mag, z() / mag, w() / mag);
  }
}
 
double vpQuaternionVector::dot(const vpQuaternionVector &q0, const vpQuaternionVector &q1)
{
  return (q0.x() * q1.x()) + (q0.y() * q1.y()) + (q0.z() * q1.z()) + (q0.w() * q1.w());
}
 
const double &vpQuaternionVector::x() const { return data[0]; }
const double &vpQuaternionVector::y() const { return data[1]; }
const double &vpQuaternionVector::z() const { return data[2]; }
const double &vpQuaternionVector::w() const { return data[3]; }
 
double &vpQuaternionVector::x() { return data[0]; }
double &vpQuaternionVector::y() { return data[1]; }
double &vpQuaternionVector::z() { return data[2]; }
double &vpQuaternionVector::w() { return data[3]; }
 
#if (VISP_CXX_STANDARD >= VISP_CXX_STANDARD_11)
vpQuaternionVector &vpQuaternionVector::operator=(const std::initializer_list<double> &list)
{
  if (list.size() > size()) {
    throw(vpException(
      vpException::dimensionError,
      "Cannot set quaternion vector out of bounds. It has only %d values while you try to initialize with %d values",
      size(), list.size()));
  }
  std::copy(list.begin(), list.end(), data);
  return *this;
}
#endif
 
vpQuaternionVector vpQuaternionVector::lerp(const vpQuaternionVector &q0, const vpQuaternionVector &q1, double t)
{
  assert(t >= 0 && t <= 1);
 
  double cosHalfTheta = dot(q0, q1);
  vpQuaternionVector q1_ = q1;
  if (cosHalfTheta < 0) {
    cosHalfTheta = -cosHalfTheta;
    q1_ = -q1;
  }
 
  vpQuaternionVector qLerp;
  qLerp.x() = q0.x() - (t * (q0.x() - q1.x()));
  qLerp.y() = q0.y() - (t * (q0.y() - q1.y()));
  qLerp.z() = q0.z() - (t * (q0.z() - q1.z()));
  qLerp.w() = q0.w() - (t * (q0.w() - q1.w()));
 
  return qLerp;
}
 
vpQuaternionVector vpQuaternionVector::nlerp(const vpQuaternionVector &q0, const vpQuaternionVector &q1, double t)
{
  assert(t >= 0 && t <= 1);
 
  vpQuaternionVector qLerp = lerp(q0, q1, t);
  qLerp.normalize();
 
  return qLerp;
}
 
vpQuaternionVector vpQuaternionVector::slerp(const vpQuaternionVector &q0, const vpQuaternionVector &q1, double t)
{
  assert(t >= 0 && t <= 1);
  // Some additional references:
  // https://splines.readthedocs.io/en/latest/rotation/slerp.html
  // https://zeux.io/2015/07/23/approximating-slerp/
  // https://github.com/eigenteam/eigen-git-mirror/blob/36b95962756c1fce8e29b1f8bc45967f30773c00/Eigen/src/Geometry/Quaternion.h#L753-L790
  // https://www.euclideanspace.com/maths/algebra/realNormedAlgebra/quaternions/slerp/index.htm
  // http://number-none.com/product/Understanding%20Slerp,%20Then%20Not%20Using%20It/
  // https://www.3dgep.com/understanding-quaternions/
  // https://blog.magnum.graphics/backstage/the-unnecessarily-short-ways-to-do-a-quaternion-slerp/
 
  double cosHalfTheta = dot(q0, q1);
  vpQuaternionVector q1_ = q1;
  if (cosHalfTheta < 0) {
    cosHalfTheta = -cosHalfTheta;
    q1_ = -q1;
  }
 
  double scale0 = 1 - t;
  double scale1 = t;
 
  if ((1 - cosHalfTheta) > 0.1) {
    double theta = std::acos(cosHalfTheta);
    double invSinTheta = 1 / std::sin(theta);
 
    scale0 = std::sin((1 - t) * theta) * invSinTheta;
    scale1 = std::sin(t * theta) * invSinTheta;
  }
 
  vpQuaternionVector qSlerp;
  qSlerp.x() = (scale0 * q0.x()) + (scale1 * q1_.x());
  qSlerp.y() = (scale0 * q0.y()) + (scale1 * q1_.y());
  qSlerp.z() = (scale0 * q0.z()) + (scale1 * q1_.z());
  qSlerp.w() = (scale0 * q0.w()) + (scale1 * q1_.w());
  qSlerp.normalize();
 
  return qSlerp;
}