Visual Servoing Platform  version 3.6.1 under development (2024-03-18)
vpBSpline.cpp
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30  *
31  * Description:
32  * This class implements the B-Spline
33  *
34 *****************************************************************************/
35 
36 #include <visp3/core/vpBSpline.h>
37 #include <visp3/core/vpDebug.h>
38 
46  : controlPoints(), knots(), p(3), // By default : p=3 for clubic spline
47  crossingPoints()
48 { }
49 
55  : controlPoints(bspline.controlPoints), knots(bspline.knots), p(bspline.p), // By default : p=3 for clubic spline
56  crossingPoints(bspline.crossingPoints)
57 { }
62 
79 unsigned int vpBSpline::findSpan(double l_u, unsigned int l_p, std::vector<double> &l_knots)
80 {
81  unsigned int m = (unsigned int)l_knots.size() - 1;
82 
83  if (l_u > l_knots.back()) {
84  // vpTRACE("l_u higher than the maximum value in the knot vector :
85  // %lf",l_u);
86  return ((unsigned int)(m - l_p - 1));
87  }
88 
89  // if (l_u == l_knots.back())
90  if (std::fabs(l_u - l_knots.back()) <=
91  std::fabs(vpMath::maximum(l_u, l_knots.back())) * std::numeric_limits<double>::epsilon())
92  return ((unsigned int)(m - l_p - 1));
93 
94  double low = l_p;
95  double high = m - l_p;
96  double middle = (low + high) / 2.0;
97 
98  while (l_u < l_knots[(unsigned int)middle] || l_u >= l_knots[(unsigned int)middle + 1]) {
99  if (l_u < l_knots[(unsigned int)vpMath::round(middle)])
100  high = middle;
101  else
102  low = middle;
103  middle = (low + high) / 2.0;
104  }
105 
106  return (unsigned int)middle;
107 }
108 
123 unsigned int vpBSpline::findSpan(double u) { return findSpan(u, p, knots); }
124 
142 vpBasisFunction *vpBSpline::computeBasisFuns(double l_u, unsigned int l_i, unsigned int l_p,
143  std::vector<double> &l_knots)
144 {
145  vpBasisFunction *N = new vpBasisFunction[l_p + 1];
146 
147  N[0].value = 1.0;
148 
149  double *left = new double[l_p + 1];
150  double *right = new double[l_p + 1];
151  double temp = 0.0;
152 
153  for (unsigned int j = 1; j <= l_p; j++) {
154  left[j] = l_u - l_knots[l_i + 1 - j];
155  right[j] = l_knots[l_i + j] - l_u;
156  double saved = 0.0;
157 
158  for (unsigned int r = 0; r < j; r++) {
159  temp = N[r].value / (right[r + 1] + left[j - r]);
160  N[r].value = saved + right[r + 1] * temp;
161  saved = left[j - r] * temp;
162  }
163  N[j].value = saved;
164  }
165  for (unsigned int j = 0; j < l_p + 1; j++) {
166  N[j].i = l_i - l_p + j;
167  N[j].p = l_p;
168  N[j].u = l_u;
169  N[j].k = 0;
170  }
171 
172  delete[] left;
173  delete[] right;
174 
175  return N;
176 }
177 
193 vpBasisFunction *vpBSpline::computeBasisFuns(double u)
194 {
195  unsigned int i = findSpan(u);
196  return computeBasisFuns(u, i, p, knots);
197 }
198 
228 vpBasisFunction **vpBSpline::computeDersBasisFuns(double l_u, unsigned int l_i, unsigned int l_p, unsigned int l_der,
229  std::vector<double> &l_knots)
230 {
231  vpBasisFunction **N;
232  N = new vpBasisFunction *[l_der + 1];
233  for (unsigned int j = 0; j <= l_der; j++)
234  N[j] = new vpBasisFunction[l_p + 1];
235 
236  vpMatrix a(2, l_p + 1);
237  vpMatrix ndu(l_p + 1, l_p + 1);
238  ndu[0][0] = 1.0;
239 
240  double *left = new double[l_p + 1];
241  double *right = new double[l_p + 1];
242  double temp = 0.0;
243 
244  for (unsigned int j = 1; j <= l_p; j++) {
245  left[j] = l_u - l_knots[l_i + 1 - j];
246  right[j] = l_knots[l_i + j] - l_u;
247  double saved = 0.0;
248 
249  for (unsigned int r = 0; r < j; r++) {
250  ndu[j][r] = right[r + 1] + left[j - r];
251  temp = ndu[r][j - 1] / ndu[j][r];
252  ndu[r][j] = saved + right[r + 1] * temp;
253  saved = left[j - r] * temp;
254  }
255  ndu[j][j] = saved;
256  }
257 
258  for (unsigned int j = 0; j <= l_p; j++) {
259  N[0][j].value = ndu[j][l_p];
260  N[0][j].i = l_i - l_p + j;
261  N[0][j].p = l_p;
262  N[0][j].u = l_u;
263  N[0][j].k = 0;
264  }
265 
266  if (l_der > l_p) {
267  vpTRACE("l_der must be under or equal to l_p");
268  l_der = l_p;
269  }
270 
271  double d;
272  int rk;
273  unsigned int pk;
274  unsigned int j1, j2;
275 
276  for (unsigned int r = 0; r <= l_p; r++) {
277  unsigned int s1 = 0;
278  unsigned int s2 = 1;
279  a[0][0] = 1.0;
280  for (unsigned int k = 1; k <= l_der; k++) {
281  d = 0.0;
282  rk = (int)(r - k);
283  pk = l_p - k;
284  if (r >= k) {
285  a[s2][0] = a[s1][0] / ndu[pk + 1][rk];
286  d = a[s2][0] * ndu[(unsigned int)rk][pk];
287  }
288 
289  if (rk >= -1)
290  j1 = 1;
291  else
292  j1 = (unsigned int)(-rk);
293 
294  if (r - 1 <= pk)
295  j2 = k - 1;
296  else
297  j2 = l_p - r;
298 
299  for (unsigned int j = j1; j <= j2; j++) {
300  a[s2][j] = (a[s1][j] - a[s1][j - 1]) / ndu[pk + 1][(unsigned int)rk + j];
301  d += a[s2][j] * ndu[(unsigned int)rk + j][pk];
302  }
303 
304  if (r <= pk) {
305  a[s2][k] = -a[s1][k - 1] / ndu[pk + 1][r];
306  d += a[s2][k] * ndu[r][pk];
307  }
308  N[k][r].value = d;
309  N[k][r].i = l_i - l_p + r;
310  N[k][r].p = l_p;
311  N[k][r].u = l_u;
312  N[k][r].k = k;
313 
314  s1 = (s1 + 1) % 2;
315  s2 = (s2 + 1) % 2;
316  }
317  }
318 
319  double r = l_p;
320  for (unsigned int k = 1; k <= l_der; k++) {
321  for (unsigned int j = 0; j <= l_p; j++)
322  N[k][j].value *= r;
323  r *= (l_p - k);
324  }
325 
326  delete[] left;
327  delete[] right;
328 
329  return N;
330 }
331 
358 vpBasisFunction **vpBSpline::computeDersBasisFuns(double u, unsigned int der)
359 {
360  unsigned int i = findSpan(u);
361  return computeDersBasisFuns(u, i, p, der, knots);
362 }
363 
375 vpImagePoint vpBSpline::computeCurvePoint(double l_u, unsigned int l_i, unsigned int l_p, std::vector<double> &l_knots,
376  std::vector<vpImagePoint> &l_controlPoints)
377 {
378  vpBasisFunction *N = computeBasisFuns(l_u, l_i, l_p, l_knots);
379  vpImagePoint pt;
380 
381  double ic = 0;
382  double jc = 0;
383  for (unsigned int j = 0; j <= l_p; j++) {
384  ic = ic + N[j].value * (l_controlPoints[l_i - l_p + j]).get_i();
385  jc = jc + N[j].value * (l_controlPoints[l_i - l_p + j]).get_j();
386  }
387 
388  pt.set_i(ic);
389  pt.set_j(jc);
390 
391  delete[] N;
392 
393  return pt;
394 }
395 
405 {
406  vpBasisFunction *N = computeBasisFuns(u);
407  vpImagePoint pt;
408 
409  double ic = 0;
410  double jc = 0;
411  for (unsigned int j = 0; j <= p; j++) {
412  ic = ic + N[j].value * (controlPoints[N[0].i + j]).get_i();
413  jc = jc + N[j].value * (controlPoints[N[0].i + j]).get_j();
414  }
415 
416  pt.set_i(ic);
417  pt.set_j(jc);
418 
419  delete[] N;
420 
421  return pt;
422 }
423 
445 vpImagePoint *vpBSpline::computeCurveDers(double l_u, unsigned int l_i, unsigned int l_p, unsigned int l_der,
446  std::vector<double> &l_knots, std::vector<vpImagePoint> &l_controlPoints)
447 {
448  vpImagePoint *derivate = new vpImagePoint[l_der + 1];
449  vpBasisFunction **N;
450  N = computeDersBasisFuns(l_u, l_i, l_p, l_der, l_knots);
451 
452  unsigned int du;
453  if (l_p < l_der) {
454  vpTRACE("l_der must be under or equal to l_p");
455  du = l_p;
456  }
457  else
458  du = l_der;
459 
460  for (unsigned int k = 0; k <= du; k++) {
461  derivate[k].set_ij(0.0, 0.0);
462  for (unsigned int j = 0; j <= l_p; j++) {
463  derivate[k].set_i(derivate[k].get_i() + N[k][j].value * (l_controlPoints[l_i - l_p + j]).get_i());
464  derivate[k].set_j(derivate[k].get_j() + N[k][j].value * (l_controlPoints[l_i - l_p + j]).get_j());
465  }
466  }
467 
468  for (unsigned int j = 0; j <= l_der; j++)
469  delete[] N[j];
470  delete[] N;
471 
472  return derivate;
473 }
474 
492 vpImagePoint *vpBSpline::computeCurveDers(double u, unsigned int der)
493 {
494  vpImagePoint *derivate = new vpImagePoint[der + 1];
495  vpBasisFunction **N;
496  N = computeDersBasisFuns(u, der);
497 
498  unsigned int du;
499  if (p < der) {
500  vpTRACE("der must be under or equal to p");
501  du = p;
502  }
503  else
504  du = der;
505 
506  for (unsigned int k = 0; k <= du; k++) {
507  derivate[k].set_ij(0.0, 0.0);
508  for (unsigned int j = 0; j <= p; j++) {
509  derivate[k].set_i(derivate[k].get_i() + N[k][j].value * (controlPoints[N[0][0].i - p + j]).get_i());
510  derivate[k].set_j(derivate[k].get_j() + N[k][j].value * (controlPoints[N[0][0].i - p + j]).get_j());
511  }
512  }
513 
514  for (unsigned int j = 0; j <= der; j++)
515  delete[] N[j];
516  delete[] N;
517 
518  return derivate;
519 }
Class that provides tools to compute and manipulate a B-Spline curve.
Definition: vpBSpline.h:106
static vpBasisFunction ** computeDersBasisFuns(double l_u, unsigned int l_i, unsigned int l_p, unsigned int l_der, std::vector< double > &l_knots)
Definition: vpBSpline.cpp:228
static vpBasisFunction * computeBasisFuns(double l_u, unsigned int l_i, unsigned int l_p, std::vector< double > &l_knots)
Definition: vpBSpline.cpp:142
virtual ~vpBSpline()
Definition: vpBSpline.cpp:61
static vpImagePoint computeCurvePoint(double l_u, unsigned int l_i, unsigned int l_p, std::vector< double > &l_knots, std::vector< vpImagePoint > &l_controlPoints)
Definition: vpBSpline.cpp:375
static vpImagePoint * 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)
Definition: vpBSpline.cpp:445
static unsigned int findSpan(double l_u, unsigned int l_p, std::vector< double > &l_knots)
Definition: vpBSpline.cpp:79
Class that defines a 2D point in an image. This class is useful for image processing and stores only ...
Definition: vpImagePoint.h:82
void set_j(double jj)
Definition: vpImagePoint.h:304
void set_ij(double ii, double jj)
Definition: vpImagePoint.h:315
void set_i(double ii)
Definition: vpImagePoint.h:293
static Type maximum(const Type &a, const Type &b)
Definition: vpMath.h:252
static int round(double x)
Definition: vpMath.h:403
Implementation of a matrix and operations on matrices.
Definition: vpMatrix.h:146
#define vpTRACE
Definition: vpDebug.h:405