vpBSpline.cpp

/****************************************************************************
 *
 * ViSP, open source Visual Servoing Platform software.
 * Copyright (C) 2005 - 2023 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.
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 * For using ViSP with software that can not be combined with the GNU
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 * Edition License.
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 *
 * This software was developed at:
 * Inria Rennes - Bretagne Atlantique
 * Campus Universitaire de Beaulieu
 * 35042 Rennes Cedex
 * 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:
 * This class implements the B-Spline
 *
*****************************************************************************/
 
#include <visp3/core/vpBSpline.h>
#include <visp3/core/vpDebug.h>
 
vpBSpline::vpBSpline()
  : controlPoints(), knots(), p(3), // By default : p=3 for clubic spline
  crossingPoints()
{ }
 
vpBSpline::vpBSpline(const vpBSpline &bspline)
  : controlPoints(bspline.controlPoints), knots(bspline.knots), p(bspline.p), // By default : p=3 for clubic spline
  crossingPoints(bspline.crossingPoints)
{ }
vpBSpline::~vpBSpline() { }
 
unsigned int vpBSpline::findSpan(double l_u, unsigned int l_p, std::vector<double> &l_knots)
{
  unsigned int m = (unsigned int)l_knots.size() - 1;
 
  if (l_u > l_knots.back()) {
    // vpTRACE("l_u higher than the maximum value in the knot vector  :
    // %lf",l_u);
    return ((unsigned int)(m - l_p - 1));
  }
 
  // if (l_u == l_knots.back())
  if (std::fabs(l_u - l_knots.back()) <=
      std::fabs(vpMath::maximum(l_u, l_knots.back())) * std::numeric_limits<double>::epsilon())
    return ((unsigned int)(m - l_p - 1));
 
  double low = l_p;
  double high = m - l_p;
  double middle = (low + high) / 2.0;
 
  while (l_u < l_knots[(unsigned int)middle] || l_u >= l_knots[(unsigned int)middle + 1]) {
    if (l_u < l_knots[(unsigned int)vpMath::round(middle)])
      high = middle;
    else
      low = middle;
    middle = (low + high) / 2.0;
  }
 
  return (unsigned int)middle;
}
 
unsigned int vpBSpline::findSpan(double u) { return findSpan(u, p, knots); }
 
vpBasisFunction *vpBSpline::computeBasisFuns(double l_u, unsigned int l_i, unsigned int l_p,
                                             std::vector<double> &l_knots)
{
  vpBasisFunction *N = new vpBasisFunction[l_p + 1];
 
  N[0].value = 1.0;
 
  double *left = new double[l_p + 1];
  double *right = new double[l_p + 1];
  double temp = 0.0;
 
  for (unsigned int j = 1; j <= l_p; j++) {
    left[j] = l_u - l_knots[l_i + 1 - j];
    right[j] = l_knots[l_i + j] - l_u;
    double saved = 0.0;
 
    for (unsigned int r = 0; r < j; r++) {
      temp = N[r].value / (right[r + 1] + left[j - r]);
      N[r].value = saved + right[r + 1] * temp;
      saved = left[j - r] * temp;
    }
    N[j].value = saved;
  }
  for (unsigned int j = 0; j < l_p + 1; j++) {
    N[j].i = l_i - l_p + j;
    N[j].p = l_p;
    N[j].u = l_u;
    N[j].k = 0;
  }
 
  delete[] left;
  delete[] right;
 
  return N;
}
 
vpBasisFunction *vpBSpline::computeBasisFuns(double u)
{
  unsigned int i = findSpan(u);
  return computeBasisFuns(u, i, p, knots);
}
 
vpBasisFunction **vpBSpline::computeDersBasisFuns(double l_u, unsigned int l_i, unsigned int l_p, unsigned int l_der,
                                                  std::vector<double> &l_knots)
{
  vpBasisFunction **N;
  N = new vpBasisFunction *[l_der + 1];
  for (unsigned int j = 0; j <= l_der; j++)
    N[j] = new vpBasisFunction[l_p + 1];
 
  vpMatrix a(2, l_p + 1);
  vpMatrix ndu(l_p + 1, l_p + 1);
  ndu[0][0] = 1.0;
 
  double *left = new double[l_p + 1];
  double *right = new double[l_p + 1];
  double temp = 0.0;
 
  for (unsigned int j = 1; j <= l_p; j++) {
    left[j] = l_u - l_knots[l_i + 1 - j];
    right[j] = l_knots[l_i + j] - l_u;
    double saved = 0.0;
 
    for (unsigned int r = 0; r < j; r++) {
      ndu[j][r] = right[r + 1] + left[j - r];
      temp = ndu[r][j - 1] / ndu[j][r];
      ndu[r][j] = saved + right[r + 1] * temp;
      saved = left[j - r] * temp;
    }
    ndu[j][j] = saved;
  }
 
  for (unsigned int j = 0; j <= l_p; j++) {
    N[0][j].value = ndu[j][l_p];
    N[0][j].i = l_i - l_p + j;
    N[0][j].p = l_p;
    N[0][j].u = l_u;
    N[0][j].k = 0;
  }
 
  if (l_der > l_p) {
    vpTRACE("l_der must be under or equal to l_p");
    l_der = l_p;
  }
 
  double d;
  int rk;
  unsigned int pk;
  unsigned int j1, j2;
 
  for (unsigned int r = 0; r <= l_p; r++) {
    unsigned int s1 = 0;
    unsigned int s2 = 1;
    a[0][0] = 1.0;
    for (unsigned int k = 1; k <= l_der; k++) {
      d = 0.0;
      rk = (int)(r - k);
      pk = l_p - k;
      if (r >= k) {
        a[s2][0] = a[s1][0] / ndu[pk + 1][rk];
        d = a[s2][0] * ndu[(unsigned int)rk][pk];
      }
 
      if (rk >= -1)
        j1 = 1;
      else
        j1 = (unsigned int)(-rk);
 
      if (r - 1 <= pk)
        j2 = k - 1;
      else
        j2 = l_p - r;
 
      for (unsigned int j = j1; j <= j2; j++) {
        a[s2][j] = (a[s1][j] - a[s1][j - 1]) / ndu[pk + 1][(unsigned int)rk + j];
        d += a[s2][j] * ndu[(unsigned int)rk + j][pk];
      }
 
      if (r <= pk) {
        a[s2][k] = -a[s1][k - 1] / ndu[pk + 1][r];
        d += a[s2][k] * ndu[r][pk];
      }
      N[k][r].value = d;
      N[k][r].i = l_i - l_p + r;
      N[k][r].p = l_p;
      N[k][r].u = l_u;
      N[k][r].k = k;
 
      s1 = (s1 + 1) % 2;
      s2 = (s2 + 1) % 2;
    }
  }
 
  double r = l_p;
  for (unsigned int k = 1; k <= l_der; k++) {
    for (unsigned int j = 0; j <= l_p; j++)
      N[k][j].value *= r;
    r *= (l_p - k);
  }
 
  delete[] left;
  delete[] right;
 
  return N;
}
 
vpBasisFunction **vpBSpline::computeDersBasisFuns(double u, unsigned int der)
{
  unsigned int i = findSpan(u);
  return computeDersBasisFuns(u, i, p, der, knots);
}
 
vpImagePoint vpBSpline::computeCurvePoint(double l_u, unsigned int l_i, unsigned int l_p, std::vector<double> &l_knots,
                                          std::vector<vpImagePoint> &l_controlPoints)
{
  vpBasisFunction *N = computeBasisFuns(l_u, l_i, l_p, l_knots);
  vpImagePoint pt;
 
  double ic = 0;
  double jc = 0;
  for (unsigned int j = 0; j <= l_p; j++) {
    ic = ic + N[j].value * (l_controlPoints[l_i - l_p + j]).get_i();
    jc = jc + N[j].value * (l_controlPoints[l_i - l_p + j]).get_j();
  }
 
  pt.set_i(ic);
  pt.set_j(jc);
 
  delete[] N;
 
  return pt;
}
 
vpImagePoint vpBSpline::computeCurvePoint(double u)
{
  vpBasisFunction *N = computeBasisFuns(u);
  vpImagePoint pt;
 
  double ic = 0;
  double jc = 0;
  for (unsigned int j = 0; j <= p; j++) {
    ic = ic + N[j].value * (controlPoints[N[0].i + j]).get_i();
    jc = jc + N[j].value * (controlPoints[N[0].i + j]).get_j();
  }
 
  pt.set_i(ic);
  pt.set_j(jc);
 
  delete[] N;
 
  return pt;
}
 
vpImagePoint *vpBSpline::computeCurveDers(double l_u, unsigned int l_i, unsigned int l_p, unsigned int l_der,
                                          std::vector<double> &l_knots, std::vector<vpImagePoint> &l_controlPoints)
{
  vpImagePoint *derivate = new vpImagePoint[l_der + 1];
  vpBasisFunction **N;
  N = computeDersBasisFuns(l_u, l_i, l_p, l_der, l_knots);
 
  unsigned int du;
  if (l_p < l_der) {
    vpTRACE("l_der must be under or equal to l_p");
    du = l_p;
  }
  else
    du = l_der;
 
  for (unsigned int k = 0; k <= du; k++) {
    derivate[k].set_ij(0.0, 0.0);
    for (unsigned int j = 0; j <= l_p; j++) {
      derivate[k].set_i(derivate[k].get_i() + N[k][j].value * (l_controlPoints[l_i - l_p + j]).get_i());
      derivate[k].set_j(derivate[k].get_j() + N[k][j].value * (l_controlPoints[l_i - l_p + j]).get_j());
    }
  }
 
  for (unsigned int j = 0; j <= l_der; j++)
    delete[] N[j];
  delete[] N;
 
  return derivate;
}
 
vpImagePoint *vpBSpline::computeCurveDers(double u, unsigned int der)
{
  vpImagePoint *derivate = new vpImagePoint[der + 1];
  vpBasisFunction **N;
  N = computeDersBasisFuns(u, der);
 
  unsigned int du;
  if (p < der) {
    vpTRACE("der must be under or equal to p");
    du = p;
  }
  else
    du = der;
 
  for (unsigned int k = 0; k <= du; k++) {
    derivate[k].set_ij(0.0, 0.0);
    for (unsigned int j = 0; j <= p; j++) {
      derivate[k].set_i(derivate[k].get_i() + N[k][j].value * (controlPoints[N[0][0].i - p + j]).get_i());
      derivate[k].set_j(derivate[k].get_j() + N[k][j].value * (controlPoints[N[0][0].i - p + j]).get_j());
    }
  }
 
  for (unsigned int j = 0; j <= der; j++)
    delete[] N[j];
  delete[] N;
 
  return derivate;
}