vpMath.cpp

/****************************************************************************
 *
 * ViSP, open source Visual Servoing Platform software.
 * Copyright (C) 2005 - 2019 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 http://visp.inria.fr for more information.
 *
 * This software was developed at:
 * Inria Rennes - Bretagne Atlantique
 * Campus Universitaire de Beaulieu
 * 35042 Rennes Cedex
 * France
 *
 * If you have questions regarding the use of this file, please contact
 * 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:
 * Simple mathematical function not available in the C math library (math.h).
 *
 *****************************************************************************/
 
#include <cmath>
#include <functional>
#include <numeric>
#include <stdint.h>
#include <cassert>
 
#include <visp3/core/vpException.h>
#include <visp3/core/vpMath.h>
#include <visp3/core/vpMatrix.h>
 
#if defined(VISP_HAVE_FUNC__FINITE)
#include <float.h>
#endif
 
#if !(defined(VISP_HAVE_FUNC_ISNAN) || defined(VISP_HAVE_FUNC_STD_ISNAN)) ||                                           \
    !(defined(VISP_HAVE_FUNC_ISINF) || defined(VISP_HAVE_FUNC_STD_ISINF)) ||                                           \
    !(defined(VISP_HAVE_FUNC_ISFINITE) || defined(VISP_HAVE_FUNC_STD_ISFINITE) || defined(VISP_HAVE_FUNC__FINITE))
#if defined _MSC_VER || defined __BORLANDC__
typedef __int64 int64;
typedef unsigned __int64 uint64;
#else
typedef int64_t int64;
typedef uint64_t uint64;
#endif
 
#ifndef DOXYGEN_SHOULD_SKIP_THIS
typedef union Vp64suf {
  //  int64 i; //Unused variable, should be harmless to comment it
  uint64 u;
  double f;
} Vp64suf;
 
typedef union Vp32suf {
  // int i; //Unused variable, should be harmless to comment it
  unsigned u;
  float f;
} Vp32suf;
#endif
#endif
 
const double vpMath::ang_min_sinc = 1.0e-8;
const double vpMath::ang_min_mc = 2.5e-4;
 
bool vpMath::isNaN(double value)
{
#if defined(VISP_HAVE_FUNC_ISNAN)
  return isnan(value);
#elif defined(VISP_HAVE_FUNC_STD_ISNAN)
  return std::isnan(value);
#elif defined(VISP_HAVE_FUNC__ISNAN)
  return (_isnan(value) != 0);
#else
  // Taken from OpenCV source code CvIsNan()
  Vp64suf ieee754;
  ieee754.f = value;
  return (((unsigned)(ieee754.u >> 32) & 0x7fffffff) + ((unsigned)ieee754.u != 0) > 0x7ff00000) != 0;
#endif
}
 
bool vpMath::isNaN(float value)
{
#if defined(VISP_HAVE_FUNC_ISNAN)
  return isnan(value);
#elif defined(VISP_HAVE_FUNC_STD_ISNAN)
  return std::isnan(value);
#elif defined(VISP_HAVE_FUNC__ISNAN)
  return (_isnan(value) != 0);
#else
  // Taken from OpenCV source code CvIsNan()
  Vp32suf ieee754;
  ieee754.f = value;
  return ((unsigned)ieee754.u & 0x7fffffff) > 0x7f800000;
#endif
}
 
bool vpMath::isInf(double value)
{
#if defined(VISP_HAVE_FUNC_ISINF)
  return isinf(value);
#elif defined(VISP_HAVE_FUNC_STD_ISINF)
  return std::isinf(value);
#else
  // Taken from OpenCV source code CvIsInf()
  Vp64suf ieee754;
  ieee754.f = value;
  return ((unsigned)(ieee754.u >> 32) & 0x7fffffff) == 0x7ff00000 && (unsigned)ieee754.u == 0;
#endif
}
 
bool vpMath::isInf(float value)
{
#if defined(VISP_HAVE_FUNC_ISINF)
  return isinf(value);
#elif defined(VISP_HAVE_FUNC_STD_ISINF)
  return std::isinf(value);
#else
  // Taken from OpenCV source code CvIsInf()
  Vp32suf ieee754;
  ieee754.f = value;
  return ((unsigned)ieee754.u & 0x7fffffff) == 0x7f800000;
#endif
}
 
bool vpMath::isFinite(double value)
{
#if defined(VISP_HAVE_FUNC_ISFINITE)
  return isfinite(value);
#elif defined(VISP_HAVE_FUNC_STD_ISFINITE)
  return std::isfinite(value);
#elif defined(VISP_HAVE_FUNC__FINITE)
  return _finite(value);
#else
  return !vpMath::isInf(value) && !vpMath::isNaN(value);
#endif
}
 
bool vpMath::isFinite(float value)
{
#if defined(VISP_HAVE_FUNC_ISFINITE)
  return isfinite(value);
#elif defined(VISP_HAVE_FUNC_STD_ISFINITE)
  return std::isfinite(value);
#elif defined(VISP_HAVE_FUNC__FINITE)
  return _finitef(value);
#else
  return !vpMath::isInf(value) && !vpMath::isNaN(value);
#endif
}
 
double vpMath::mcosc(double cosx, double x)
{
  if (fabs(x) < ang_min_mc)
    return 0.5;
  else
    return ((1.0 - cosx) / x / x);
}
 
double vpMath::msinc(double sinx, double x)
{
  if (fabs(x) < ang_min_mc)
    return (1. / 6.0);
  else
    return ((1.0 - sinx / x) / x / x);
}
 
double vpMath::sinc(double x)
{
  if (fabs(x) < ang_min_sinc)
    return 1.0;
  else
    return sin(x) / x;
}
double vpMath::sinc(double sinx, double x)
{
  if (fabs(x) < ang_min_sinc)
    return 1.0;
  else
    return (sinx / x);
}
 
double vpMath::getMean(const std::vector<double> &v)
{
  if (v.empty()) {
    throw vpException(vpException::notInitialized, "Empty vector !");
  }
 
  size_t size = v.size();
 
  double sum = std::accumulate(v.begin(), v.end(), 0.0);
 
  return sum / (double)size;
}
 
double vpMath::getMedian(const std::vector<double> &v)
{
  if (v.empty()) {
    throw vpException(vpException::notInitialized, "Empty vector !");
  }
 
  std::vector<double> v_copy = v;
  size_t size = v_copy.size();
 
  size_t n = size / 2;
  std::nth_element(v_copy.begin(), v_copy.begin() + n, v_copy.end());
  double val_n = v_copy[n];
 
  if (size % 2 == 1) {
    return val_n;
  } else {
    std::nth_element(v_copy.begin(), v_copy.begin() + n - 1, v_copy.end());
    return 0.5 * (val_n + v_copy[n - 1]);
  }
}
 
double vpMath::getStdev(const std::vector<double> &v, bool useBesselCorrection)
{
  if (v.empty()) {
    throw vpException(vpException::notInitialized, "Empty vector !");
  }
 
  double mean = getMean(v);
 
  std::vector<double> diff(v.size());
#if VISP_CXX_STANDARD > VISP_CXX_STANDARD_98
  std::transform(v.begin(), v.end(), diff.begin(), std::bind(std::minus<double>(), std::placeholders::_1, mean));
#else
  std::transform(v.begin(), v.end(), diff.begin(), std::bind2nd(std::minus<double>(), mean));
#endif
 
  double sq_sum = std::inner_product(diff.begin(), diff.end(), diff.begin(), 0.0);
  double divisor = (double)v.size();
  if (useBesselCorrection && v.size() > 1) {
    divisor = divisor - 1;
  }
 
  return std::sqrt(sq_sum / divisor);
}
 
double vpMath::lineFitting(const std::vector<vpImagePoint> &imPts, double &a, double &b, double &c)
{
  if (imPts.size() < 3) {
    throw vpException(vpException::dimensionError, "Number of image points must be greater or equal to 3.");
  }
 
  double x_mean = 0, y_mean = 0;
  for (size_t i = 0; i < imPts.size(); i++) {
    const vpImagePoint &imPt = imPts[i];
    x_mean += imPt.get_u();
    y_mean += imPt.get_v();
  }
  x_mean /= imPts.size();
  y_mean /= imPts.size();
 
  vpMatrix AtA(2, 2, 0.0);
  for (size_t i = 0; i < imPts.size(); i++) {
    const vpImagePoint &imPt = imPts[i];
    AtA[0][0] += (imPt.get_u() - x_mean) * (imPt.get_u() - x_mean);
    AtA[0][1] += (imPt.get_u() - x_mean) * (imPt.get_v() - y_mean);
    AtA[1][1] += (imPt.get_v() - y_mean) * (imPt.get_v() - y_mean);
  }
  AtA[1][0] = AtA[0][1];
 
  vpColVector eigenvalues;
  vpMatrix eigenvectors;
  AtA.eigenValues(eigenvalues, eigenvectors);
 
  a = eigenvectors[0][0];
  b = eigenvectors[1][0];
  c = a * x_mean + b * y_mean;
 
  double error = 0;
  for (size_t i = 0; i < imPts.size(); i++) {
    double x0 = imPts[i].get_u();
    double y0 = imPts[i].get_v();
 
    error += std::fabs(a * x0 + b * y0 - c);
  }
 
  return error / imPts.size();
}
 
int vpMath::modulo(int a, int n) { return ((a % n) + n) % n; }
 
vpHomogeneousMatrix vpMath::ned2ecef(double lonDeg, double latDeg, double radius)
{
  double lon = vpMath::rad(lonDeg);
  double lat = vpMath::rad(latDeg);
 
  vpHomogeneousMatrix ecef_M_ned;
  ecef_M_ned[0][0] = -sin(lat)*cos(lon); ecef_M_ned[0][1] = -sin(lon); ecef_M_ned[0][2] = -cos(lat)*cos(lon); ecef_M_ned[0][3] = radius*cos(lon)*cos(lat);
  ecef_M_ned[1][0] = -sin(lat)*sin(lon); ecef_M_ned[1][1] =  cos(lon); ecef_M_ned[1][2] = -cos(lat)*sin(lon); ecef_M_ned[1][3] = radius*sin(lon)*cos(lat);
  ecef_M_ned[2][0] =  cos(lat);          ecef_M_ned[2][1] = 0;         ecef_M_ned[2][2] = -sin(lat);          ecef_M_ned[2][3] = radius*sin(lat);
 
  return ecef_M_ned;
}
 
vpHomogeneousMatrix vpMath::enu2ecef(double lonDeg, double latDeg, double radius)
{
  double lon = vpMath::rad(lonDeg);
  double lat = vpMath::rad(latDeg);
 
  vpHomogeneousMatrix ecef_M_enu;
  ecef_M_enu[0][0] = -sin(lon); ecef_M_enu[0][1] = -sin(lat)*cos(lon); ecef_M_enu[0][2] = cos(lat)*cos(lon); ecef_M_enu[0][3] = radius*cos(lon)*cos(lat);
  ecef_M_enu[1][0] =  cos(lon); ecef_M_enu[1][1] = -sin(lat)*sin(lon); ecef_M_enu[1][2] = cos(lat)*sin(lon); ecef_M_enu[1][3] = radius*sin(lon)*cos(lat);
  ecef_M_enu[2][0] =  0;        ecef_M_enu[2][1] =  cos(lat);          ecef_M_enu[2][2] = sin(lat);          ecef_M_enu[2][3] = radius*sin(lat);
 
  return ecef_M_enu;
}
 
std::vector<std::pair<double, double> > vpMath::computeRegularPointsOnSphere(unsigned int maxPoints)
{
  assert(maxPoints > 0);
 
  double a = 4.0 * M_PI / maxPoints;
  double d = sqrt(a);
  int m_theta = int(round(M_PI / d));
  double d_theta = M_PI / m_theta;
  double d_phi = a / d_theta;
 
  std::vector<std::pair<double, double> > lonlat_vec;
#if (VISP_CXX_STANDARD > VISP_CXX_STANDARD_98)
  lonlat_vec.reserve(static_cast<unsigned int>(std::sqrt(maxPoints)));
#else
  lonlat_vec.reserve(static_cast<unsigned int>(std::sqrt(static_cast<double>(maxPoints))));
#endif
  for (int m = 0; m < m_theta; m++) {
    double theta = M_PI * (m + 0.5) / m_theta;
    int m_phi = static_cast<int>(round(2.0 * M_PI * sin(theta) / d_phi));
 
    for (int n = 0; n < m_phi; n++) {
      double phi = 2.0 * M_PI * n / m_phi;
      double lon = phi;
      double lat = M_PI_2 - theta;
      lonlat_vec.push_back(std::make_pair(deg(lon), deg(lat)));
    }
  }
 
  return lonlat_vec;
}
 
std::vector<vpHomogeneousMatrix> vpMath::getLocalTangentPlaneTransformations(const std::vector<std::pair<double, double> > &lonlatVec, double radius,
                                                                             vpHomogeneousMatrix (*toECEF)(double lonDeg_, double latDeg_, double radius_))
{
  std::vector<vpHomogeneousMatrix> ecef_M_local_vec;
  ecef_M_local_vec.reserve(lonlatVec.size());
  for (size_t i = 0; i < lonlatVec.size(); i++) {
    double lonDeg = lonlatVec[i].first;
    double latDeg = lonlatVec[i].second;
 
    vpHomogeneousMatrix ecef_M_local = toECEF(lonDeg, latDeg, radius);
    ecef_M_local_vec.push_back(ecef_M_local);
  }
  return ecef_M_local_vec;
}
 
vpHomogeneousMatrix vpMath::lookAt(const vpColVector &from, const vpColVector &to, vpColVector tmp)
{
  assert(from.size() == 3);
  assert(to.size() == 3);
  assert(tmp.size() == 3);
  vpColVector forward = (from - to).normalize();
  vpColVector right = vpColVector::crossProd(tmp.normalize(), forward).normalize();
  vpColVector up = vpColVector::crossProd(forward, right).normalize();
 
  vpHomogeneousMatrix wMc;
  wMc[0][0] = right[0]; wMc[0][1] = up[0]; wMc[0][2] = forward[0]; wMc[0][3] = from[0];
  wMc[1][0] = right[1]; wMc[1][1] = up[1]; wMc[1][2] = forward[1]; wMc[1][3] = from[1];
  wMc[2][0] = right[2]; wMc[2][1] = up[2]; wMc[2][2] = forward[2]; wMc[2][3] = from[2];
 
  return wMc;
}
 
vpColVector vpMath::deg(const vpRotationVector &r)
{
  if (r.size() == 4) {
    throw(vpException(vpException::fatalError, "Cannot convert angles of a quaternion vector in degrees!"));
  }
  vpColVector r_deg(r.size());
  for (unsigned int i = 0; i < r.size(); i++)  {
    r_deg[i] = vpMath::deg(r[i]);
  }
  return r_deg;
}
 
vpColVector vpMath::deg(const vpColVector &r)
{
  vpColVector r_deg(r.size());
  for (unsigned int i = 0; i < r.size(); i++)  {
    r_deg[i] = vpMath::deg(r[i]);
  }
  return r_deg;
}
 
vpColVector vpMath::enu2ned(const vpRxyzVector &enu)
{
  vpColVector ned(3);
  ned[0] = enu[0];
  ned[1] = -enu[1];
  ned[2] = -enu[2] + M_PI_2;
  return ned;
}
 
vpColVector vpMath::enu2ned(const vpTranslationVector &enu)
{
  vpColVector ned(3);
  ned[0] = enu[1];
  ned[1] = enu[0];
  ned[2] = -enu[2];
  return ned;
}