vpThetaUVector.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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 * Campus Universitaire de Beaulieu
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 * Description:
 * Theta U parameterization for the rotation.
 *
*****************************************************************************/
 
#include <cmath>  // std::fabs
#include <limits> // numeric_limits
 
#include <visp3/core/vpThetaUVector.h>
 
const double vpThetaUVector::minimum = 0.0001;
 
vpThetaUVector::vpThetaUVector() : vpRotationVector(3) { }
vpThetaUVector::vpThetaUVector(const vpThetaUVector &tu) : vpRotationVector(tu) { }
vpThetaUVector::vpThetaUVector(const vpColVector &tu) : vpRotationVector(3) { buildFrom(tu); }
vpThetaUVector::vpThetaUVector(const vpHomogeneousMatrix &M) : vpRotationVector(3) { buildFrom(M); }
vpThetaUVector::vpThetaUVector(const vpPoseVector &p) : vpRotationVector(3) { buildFrom(p); }
vpThetaUVector::vpThetaUVector(const vpRotationMatrix &R) : vpRotationVector(3) { buildFrom(R); }
 
vpThetaUVector::vpThetaUVector(const vpRzyxVector &rzyx) : vpRotationVector(3) { buildFrom(rzyx); }
vpThetaUVector::vpThetaUVector(const vpRzyzVector &rzyz) : vpRotationVector(3) { buildFrom(rzyz); }
vpThetaUVector::vpThetaUVector(const vpRxyzVector &rxyz) : vpRotationVector(3) { buildFrom(rxyz); }
vpThetaUVector::vpThetaUVector(const vpQuaternionVector &q) : vpRotationVector(3) { buildFrom(q); }
 
vpThetaUVector::vpThetaUVector(double tux, double tuy, double tuz) : vpRotationVector(3) { buildFrom(tux, tuy, tuz); }
 
vpThetaUVector::vpThetaUVector(const std::vector<double> &tu) { buildFrom(tu); }
 
vpThetaUVector vpThetaUVector::buildFrom(const vpHomogeneousMatrix &M)
{
  vpRotationMatrix R;
 
  M.extract(R);
  buildFrom(R);
 
  return *this;
}
vpThetaUVector vpThetaUVector::buildFrom(const vpPoseVector &p)
{
  for (unsigned int i = 0; i < 3; i++)
    data[i] = p[i + 3];
 
  return *this;
}
 
vpThetaUVector vpThetaUVector::buildFrom(const vpRotationMatrix &R)
{
  double s, c, theta;
 
  s = (R[1][0] - R[0][1]) * (R[1][0] - R[0][1]) + (R[2][0] - R[0][2]) * (R[2][0] - R[0][2]) +
    (R[2][1] - R[1][2]) * (R[2][1] - R[1][2]);
  s = sqrt(s) / 2.0;
  c = (R[0][0] + R[1][1] + R[2][2] - 1.0) / 2.0;
  theta = atan2(s, c); /* theta in [0, PI] since s > 0 */
 
  // General case when theta != pi. If theta=pi, c=-1
  if ((1 + c) > minimum) // Since -1 <= c <= 1, no fabs(1+c) is required
  {
    double sinc = vpMath::sinc(s, theta);
 
    data[0] = (R[2][1] - R[1][2]) / (2 * sinc);
    data[1] = (R[0][2] - R[2][0]) / (2 * sinc);
    data[2] = (R[1][0] - R[0][1]) / (2 * sinc);
  }
  else /* theta near PI */
  {
    double x = 0;
    if ((R[0][0] - c) > std::numeric_limits<double>::epsilon())
      x = sqrt((R[0][0] - c) / (1 - c));
 
    double y = 0;
    if ((R[1][1] - c) > std::numeric_limits<double>::epsilon())
      y = sqrt((R[1][1] - c) / (1 - c));
 
    double z = 0;
    if ((R[2][2] - c) > std::numeric_limits<double>::epsilon())
      z = sqrt((R[2][2] - c) / (1 - c));
 
    if (x > y && x > z) {
      if ((R[2][1] - R[1][2]) < 0)
        x = -x;
      if (vpMath::sign(x) * vpMath::sign(y) != vpMath::sign(R[0][1] + R[1][0]))
        y = -y;
      if (vpMath::sign(x) * vpMath::sign(z) != vpMath::sign(R[0][2] + R[2][0]))
        z = -z;
    }
    else if (y > z) {
      if ((R[0][2] - R[2][0]) < 0)
        y = -y;
      if (vpMath::sign(y) * vpMath::sign(x) != vpMath::sign(R[1][0] + R[0][1]))
        x = -x;
      if (vpMath::sign(y) * vpMath::sign(z) != vpMath::sign(R[1][2] + R[2][1]))
        z = -z;
    }
    else {
      if ((R[1][0] - R[0][1]) < 0)
        z = -z;
      if (vpMath::sign(z) * vpMath::sign(x) != vpMath::sign(R[2][0] + R[0][2]))
        x = -x;
      if (vpMath::sign(z) * vpMath::sign(y) != vpMath::sign(R[2][1] + R[1][2]))
        y = -y;
    }
    data[0] = theta * x;
    data[1] = theta * y;
    data[2] = theta * z;
  }
 
  return *this;
}
vpThetaUVector vpThetaUVector::buildFrom(const vpRzyxVector &rzyx)
{
  vpRotationMatrix R(rzyx);
 
  buildFrom(R);
  return *this;
}
vpThetaUVector vpThetaUVector::buildFrom(const vpRzyzVector &rzyz)
{
  vpRotationMatrix R(rzyz);
 
  buildFrom(R);
  return *this;
}
vpThetaUVector vpThetaUVector::buildFrom(const vpRxyzVector &rxyz)
{
  vpRotationMatrix R(rxyz);
 
  buildFrom(R);
  return *this;
}
 
vpThetaUVector vpThetaUVector::buildFrom(const vpQuaternionVector &q)
{
  vpRotationMatrix R(q);
 
  buildFrom(R);
  return *this;
}
 
vpThetaUVector vpThetaUVector::buildFrom(const std::vector<double> &tu)
{
  if (tu.size() != 3) {
    throw(vpException(vpException::dimensionError, "Cannot construct a theta-u vector from a %d-dimension std::vector",
                      tu.size()));
  }
  for (unsigned int i = 0; i < 3; i++)
    data[i] = tu[i];
 
  return *this;
}
 
vpThetaUVector vpThetaUVector::buildFrom(const vpColVector &tu)
{
  if (tu.size() != 3) {
    throw(vpException(vpException::dimensionError, "Cannot construct a theta-u vector from a %d-dimension std::vector",
                      tu.size()));
  }
  for (unsigned int i = 0; i < 3; i++)
    data[i] = tu[i];
 
  return *this;
}
 
vpThetaUVector &vpThetaUVector::operator=(double v)
{
  for (unsigned int i = 0; i < dsize; i++)
    data[i] = v;
 
  return *this;
}
 
vpThetaUVector &vpThetaUVector::operator=(const vpColVector &tu)
{
  if (tu.size() != size()) {
    throw(vpException(vpException::dimensionError, "Cannot set a theta-u vector from a %d-dimension col vector",
                      tu.size()));
  }
  for (unsigned int i = 0; i < size(); i++)
    data[i] = tu[i];
 
  return *this;
}
 
void vpThetaUVector::extract(double &theta, vpColVector &u) const
{
  u.resize(3);
 
  theta = getTheta();
  // if (theta == 0) {
  if (std::fabs(theta) <= std::numeric_limits<double>::epsilon()) {
    u = 0;
    return;
  }
  for (unsigned int i = 0; i < 3; i++)
    u[i] = data[i] / theta;
}
 
double vpThetaUVector::getTheta() const { return sqrt(data[0] * data[0] + data[1] * data[1] + data[2] * data[2]); }
 
vpColVector vpThetaUVector::getU() const
{
  vpColVector u(3);
 
  double theta = getTheta();
  // if (theta == 0) {
  if (std::fabs(theta) <= std::numeric_limits<double>::epsilon()) {
    u = 0;
    return u;
  }
  for (unsigned int i = 0; i < 3; i++)
    u[i] = data[i] / theta;
  return u;
}
 
void vpThetaUVector::buildFrom(double tux, double tuy, double tuz)
{
  data[0] = tux;
  data[1] = tuy;
  data[2] = tuz;
}
 
vpThetaUVector vpThetaUVector::operator*(const vpThetaUVector &tu_b) const
{
  double a_2 = getTheta() / 2;
  vpColVector a_hat = getU();
  double b_2 = tu_b.getTheta() / 2;
  vpColVector b_hat = tu_b.getU();
 
  vpColVector a_hat_sin_2 = a_hat * std::sin(a_2);
  vpColVector b_hat_sin_2 = b_hat * std::sin(b_2);
  double c = 2 * std::acos(std::cos(a_2) * std::cos(b_2) - vpColVector::dotProd(a_hat_sin_2, b_hat_sin_2));
  vpColVector d = std::sin(a_2) * std::cos(b_2) * a_hat + std::cos(a_2) * std::sin(b_2) * b_hat +
    std::sin(a_2) * std::sin(b_2) * vpColVector::crossProd(a_hat, b_hat);
  d = c * d / std::sin(c / 2);
 
  return vpThetaUVector(d);
}
 
vpThetaUVector &vpThetaUVector::operator=(const std::initializer_list<double> &list)
{
  if (list.size() > size()) {
    throw(vpException(
      vpException::dimensionError,
      "Cannot set theta u 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;
}