vpThetaUVector.cpp

/*
 * ViSP, open source Visual Servoing Platform software.
 * Copyright (C) 2005 - 2024 by Inria. All rights reserved.
 *
 * This software is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 * See the file LICENSE.txt at the root directory of this source
 * distribution for additional information about the GNU GPL.
 *
 * For using ViSP with software that can not be combined with the GNU
 * GPL, please contact Inria about acquiring a ViSP Professional
 * Edition License.
 *
 * See https://visp.inria.fr for more information.
 *
 * This software was developed at:
 * Inria Rennes - Bretagne Atlantique
 * Campus Universitaire de Beaulieu
 * 35042 Rennes Cedex
 * France
 *
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 * Inria at visp@inria.fr
 *
 * 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:
 * Theta U parameterization for the rotation.
 */

 
#include <cmath>  // std::fabs
#include <limits> // numeric_limits
 
#include <visp3/core/vpThetaUVector.h>
 
BEGIN_VISP_NAMESPACE
 
const double vpThetaUVector::minimum = 0.0001;
const unsigned int vpThetaUVector::constr_val_3 = 3;

vpThetaUVector::vpThetaUVector() : vpRotationVector(constr_val_3) { }
vpThetaUVector::vpThetaUVector(const vpColVector &tu) : vpRotationVector(constr_val_3) { buildFrom(tu); }
vpThetaUVector::vpThetaUVector(const vpHomogeneousMatrix &M) : vpRotationVector(constr_val_3) { buildFrom(M); }
vpThetaUVector::vpThetaUVector(const vpPoseVector &p) : vpRotationVector(constr_val_3) { buildFrom(p); }
vpThetaUVector::vpThetaUVector(const vpRotationMatrix &R) : vpRotationVector(constr_val_3) { buildFrom(R); }

vpThetaUVector::vpThetaUVector(const vpRzyxVector &rzyx) : vpRotationVector(constr_val_3) { buildFrom(rzyx); }
vpThetaUVector::vpThetaUVector(const vpRzyzVector &rzyz) : vpRotationVector(constr_val_3) { buildFrom(rzyz); }
vpThetaUVector::vpThetaUVector(const vpRxyzVector &rxyz) : vpRotationVector(constr_val_3) { buildFrom(rxyz); }
vpThetaUVector::vpThetaUVector(const vpQuaternionVector &q) : vpRotationVector(constr_val_3) { buildFrom(q); }

vpThetaUVector::vpThetaUVector(double tux, double tuy, double tuz) : vpRotationVector(constr_val_3) { buildFrom(tux, tuy, tuz); }

vpThetaUVector::vpThetaUVector(const std::vector<double> &tu) : vpRotationVector(constr_val_3) { buildFrom(tu); }

vpThetaUVector &vpThetaUVector::buildFrom(const vpHomogeneousMatrix &M)
{
  vpRotationMatrix R;
 
  M.extract(R);
  buildFrom(R);
 
  return *this;
}

vpThetaUVector &vpThetaUVector::buildFrom(const vpPoseVector &p)
{
  const unsigned int val_3 = 3;
  const unsigned int index_3 = 3;
  for (unsigned int i = 0; i < val_3; ++i) {
    data[i] = p[i + index_3];
  }
 
  return *this;
}

vpThetaUVector &vpThetaUVector::buildFrom(const vpRotationMatrix &R)
{
  double s, c, theta;
  const unsigned int index_0 = 0;
  const unsigned int index_1 = 1;
  const unsigned int index_2 = 2;
 
  s = ((R[1][0] - R[0][1]) * (R[1][0] - R[0][1])) + ((R[index_2][0] - R[0][index_2]) * (R[index_2][0] - R[0][index_2])) +
    ((R[index_2][index_1] - R[index_1][index_2]) * (R[index_2][index_1] - R[index_1][index_2]));
  s = sqrt(s) / 2.0;
  c = ((R[index_0][index_0] + R[index_1][index_1] + R[index_2][index_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[index_0] = (R[index_2][index_1] - R[index_1][index_2]) / (2.0 * sinc);
    data[index_1] = (R[index_0][index_2] - R[index_2][index_0]) / (2.0 * sinc);
    data[index_2] = (R[index_1][index_0] - R[index_0][index_1]) / (2.0 * 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[index_2][index_2] - c) > std::numeric_limits<double>::epsilon()) {
      z = sqrt((R[index_2][index_2] - c) / (1 - c));
    }
 
    if ((x > y) && (x > z)) {
      if ((R[index_2][index_1] - R[index_1][index_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[index_0][index_2] + R[index_2][index_0]))) {
        z = -z;
      }
    }
    else if (y > z) {
      if ((R[index_0][index_2] - R[index_2][index_0]) < 0) {
        y = -y;
      }
      if ((vpMath::sign(y) * vpMath::sign(x)) != (vpMath::sign(R[index_1][index_0] + R[index_0][index_1]))) {
        x = -x;
      }
      if ((vpMath::sign(y) * vpMath::sign(z)) != (vpMath::sign(R[index_1][index_2] + R[index_2][index_1]))) {
        z = -z;
      }
    }
    else {
      if ((R[1][0] - R[0][1]) < 0) {
        z = -z;
      }
      if ((vpMath::sign(z) * vpMath::sign(x)) != (vpMath::sign(R[index_2][index_0] + R[index_0][index_2]))) {
        x = -x;
      }
      if ((vpMath::sign(z) * vpMath::sign(y)) != (vpMath::sign(R[index_2][index_1] + R[index_1][index_2]))) {
        y = -y;
      }
    }
    data[index_0] = theta * x;
    data[index_1] = theta * y;
    data[index_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)
{
  const unsigned int val_3 = 3;
  if (tu.size() != val_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 < val_3; ++i) {
    data[i] = tu[i];
  }
 
  return *this;
}

vpThetaUVector &vpThetaUVector::buildFrom(const vpColVector &tu)
{
  const unsigned int val_3 = 3;
  if (tu.size() != val_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 < val_3; ++i) {
    data[i] = tu[i];
  }
 
  return *this;
}

vpThetaUVector &vpThetaUVector::buildFrom(const double &tux, const double &tuy, const double &tuz)
{
  const unsigned int index_0 = 0;
  const unsigned int index_1 = 1;
  const unsigned int index_2 = 2;
  data[index_0] = tux;
  data[index_1] = tuy;
  data[index_2] = tuz;
  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()));
  }
 
  unsigned int l_size = size();
  for (unsigned int i = 0; i < l_size; ++i) {
    data[i] = tu[i];
  }
 
  return *this;
}

void vpThetaUVector::extract(double &theta, vpColVector &u) const
{
  const unsigned int val_3 = 3;
  u.resize(val_3);
 
  theta = getTheta();
  // --comment: if theta equals 0
  if (std::fabs(theta) <= std::numeric_limits<double>::epsilon()) {
    u = 0;
    return;
  }
  for (unsigned int i = 0; i < val_3; ++i) {
    u[i] = data[i] / theta;
  }
}

double vpThetaUVector::getTheta() const
{
  const unsigned int index_0 = 0;
  const unsigned int index_1 = 1;
  const unsigned int index_2 = 2;
  return sqrt((data[index_0] * data[index_0]) + (data[index_1] * data[index_1]) + (data[index_2] * data[index_2]));
}

vpColVector vpThetaUVector::getU() const
{
  vpColVector u(3);
 
  double theta = getTheta();
  // --comment: if theta equals 0
  if (std::fabs(theta) <= std::numeric_limits<double>::epsilon()) {
    u = 0;
    return u;
  }
  const unsigned int val_3 = 3;
  for (unsigned int i = 0; i < val_3; ++i) {
    u[i] = data[i] / theta;
  }
  return u;
}

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 / 2.0);
 
  return vpThetaUVector(d);
}
 
#if (VISP_CXX_STANDARD >= VISP_CXX_STANDARD_11)
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;
}
#endif
END_VISP_NAMESPACE