DGtal  1.3.beta
Static Public Member Functions
DGtal::FrechetShortcut< TIterator, TInteger >::Tools Struct Reference

#include <DGtal/geometry/curves/FrechetShortcut.h>

Static Public Member Functions

static bool isBetween (double i, double a, double b, double n)
 
static int circle_circle_intersection (double x0, double y0, double r0, double x1, double y1, double r1, double *xi, double *yi, double *xi_prime, double *yi_prime)
 
static int circleTangentPoints (double x, double y, double x1, double y1, double r1, double *xi, double *yi, double *xi_prime, double *yi_prime)
 
static double computeAngle (double x0, double y0, double x1, double y1)
 
static double angleVectVect (Vector u, Vector v)
 
static int computeChainCode (Point p, Point q)
 
static int computeOctant (Point p, Point q)
 
static int rot (int d, int quad)
 
static Vector chainCode2Vect (int d)
 

Detailed Description

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>
struct DGtal::FrechetShortcut< TIterator, TInteger >::Tools

Definition at line 351 of file FrechetShortcut.h.

Member Function Documentation

◆ angleVectVect()

template<typename TIterator , typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>
static double DGtal::FrechetShortcut< TIterator, TInteger >::Tools::angleVectVect ( Vector  u,
Vector  v 
)
inlinestatic

Angle between two vectors

Parameters
uand
vtwo vectors
Returns
an angle

Definition at line 540 of file FrechetShortcut.h.

541  {
542  IntegerComputer<Integer> ic;
543  return acos((double)ic.dotProduct(u,v)/(u.norm()*v.norm()));
544  }

References DGtal::IntegerComputer< TInteger >::dotProduct().

◆ chainCode2Vect()

template<typename TIterator , typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>
static Vector DGtal::FrechetShortcut< TIterator, TInteger >::Tools::chainCode2Vect ( int  d)
inlinestatic

Converts a chain code into a vector

Parameters
dan int
Returns
a vector

Definition at line 651 of file FrechetShortcut.h.

652  {
653  Vector v;
654  switch(d){
655 
656  case 0:{
657  v[0] = 1;
658  v[1] = 0;
659  break;
660  }
661  case 1:{
662  v[0] = 1;
663  v[1] = 1;
664  break;
665  }
666  case 2:{
667  v[0] = 0;
668  v[1] = 1;
669  break;
670  }
671  case 3:{
672  v[0] = -1;
673  v[1] = 1;
674  break;
675  }
676  case 4:{
677  v[0] = -1;
678  v[1] = 0;
679  break;
680  }
681  case 5:{
682  v[0] = -1;
683  v[1] = -1;
684  break;
685  }
686  case 6:{
687  v[0] = 0;
688  v[1] = -1;
689  break;
690  }
691  case 7:{
692  v[0] = 1;
693  v[1] = -1;
694  break;
695  }
696 
697  }
698 
699  return v;
700  }

◆ circle_circle_intersection()

template<typename TIterator , typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>
static int DGtal::FrechetShortcut< TIterator, TInteger >::Tools::circle_circle_intersection ( double  x0,
double  y0,
double  r0,
double  x1,
double  y1,
double  r1,
double *  xi,
double *  yi,
double *  xi_prime,
double *  yi_prime 
)
inlinestatic

Determine the points where two circles in a common plane intersect Parameters: three doubles per circle (center, radius), pointers to the two intersection points

Returns
0 if the circles do not intersect each other, 1 otherwise

Definition at line 397 of file FrechetShortcut.h.

401  {
402  double a, dx, dy, d, h, rx, ry;
403  double x2, y2;
404 
405  /* dx and dy are the vertical and horizontal distances between
406  * the circle centers.
407  */
408  dx = x1 - x0;
409  dy = y1 - y0;
410 
411  /* Determine the straight-line distance between the centers. */
412  //d = sqrt((dy*dy) + (dx*dx));
413  d = hypot(dx,dy); // Suggested by Keith Briggs
414 
415  /* Check for solvability. */
416  if (d > (r0 + r1))
417  {
418  /* no solution. circles do not intersect. */
419  std::cerr << "Warning : the two circles do not intersect -> should never happen" << std::endl;
420  return 0; //I. Sivignon 05/2010 should never happen for our specific use.
421  }
422  if (d < fabs(r0 - r1))
423  {
424  /* no solution. one circle is contained in the other */
425  return 0;
426  }
427 
428  /* 'point 2' is the point where the line through the circle
429  * intersection points crosses the line between the circle
430  * centers.
431  */
432 
433  /* Determine the distance from point 0 to point 2. */
434  a = ((r0*r0) - (r1*r1) + (d*d)) / (2.0 * d) ;
435 
436  /* Determine the coordinates of point 2. */
437  x2 = x0 + (dx * a/d);
438  y2 = y0 + (dy * a/d);
439 
440  /* Determine the distance from point 2 to either of the
441  * intersection points.
442  */
443  h = sqrt((r0*r0) - (a*a));
444 
445  /* Now determine the offsets of the intersection points from
446  * point 2.
447  */
448  rx = -dy * (h/d);
449  ry = dx * (h/d);
450 
451  /* Determine the absolute intersection points. */
452  *xi = x2 + rx;
453  *xi_prime = x2 - rx;
454  *yi = y2 + ry;
455  *yi_prime = y2 - ry;
456 
457  return 1;
458  }

Referenced by DGtal::FrechetShortcut< TIterator, TInteger >::Tools::circleTangentPoints().

◆ circleTangentPoints()

template<typename TIterator , typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>
static int DGtal::FrechetShortcut< TIterator, TInteger >::Tools::circleTangentPoints ( double  x,
double  y,
double  x1,
double  y1,
double  r1,
double *  xi,
double *  yi,
double *  xi_prime,
double *  yi_prime 
)
inlinestatic

Given a point X and a circle of center X1, compute the two points Xi and Xi' of the circle the tangent of which go through X. Since the triangle XXiX1 is a right triangle on Xi, the middle point M between X and X1 is equidistant to X, X1 and Xi. Thus, Xi belongs to the intersection of the circle (X1,r1) and the circle of center M and radius ||XX1||/2.

Parameters
[in]xthe first coordinate of X.
[in]ythe second coordinate of X.
[in]x1the first coordinate of the circle center X1.
[in]y1the second coordinate of the circle center X1.
[in]r1the circle radius.
[out]xipointer to the first coordinate of the first intersection point.
[out]yipointer to the second coordinate of the first intersection point.
[out]xi_primepointer to the first coordinate of the second intersection point.
[out]yi_primepointer to the second coordinate of the second intersection point.
Returns
result of the call to circle_circle_intersection

Definition at line 481 of file FrechetShortcut.h.

483  {
484  double x0 = (x+x1)/2;
485  double y0 = (y+y1)/2;
486  double r0 = sqrt((x-x1)*(x-x1) + (y-y1)*(y-y1))/2;
487 
488  int res =
489  circle_circle_intersection(x0,y0,r0,x1,y1,r1,xi,yi,xi_prime,yi_prime);
490 
491  return res;
492 
493  }

References DGtal::FrechetShortcut< TIterator, TInteger >::Tools::circle_circle_intersection().

◆ computeAngle()

template<typename TIterator , typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>
static double DGtal::FrechetShortcut< TIterator, TInteger >::Tools::computeAngle ( double  x0,
double  y0,
double  x1,
double  y1 
)
inlinestatic

Compute the angle of the line passing through two points. Angle in [0,2pi]

Parameters
x0x0
y0y0
x1x1
y1y1
Returns
an angle

Definition at line 505 of file FrechetShortcut.h.

506  {
507  double x = x1-x0;
508  double y = y1-y0;
509 
510  if(x!=0)
511  {
512  double alpha = y/x;
513 
514  if(x>0 && y>=0)
515  return atan(alpha);
516  else
517  if(x>0 && y<0)
518  return atan(alpha)+2*M_PI;
519  else
520  if(x<0)
521  return atan(alpha)+M_PI;
522  }
523  else
524  {
525  if(y>0)
526  return M_PI_2;
527  else
528  return 3*M_PI_2;
529  }
530  return -1;
531  }

◆ computeChainCode()

template<typename TIterator , typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>
static int DGtal::FrechetShortcut< TIterator, TInteger >::Tools::computeChainCode ( Point  p,
Point  q 
)
inlinestatic

Computes the chain code between two 8-connected pixels

Parameters
pand
qtwo points
Returns
an int

Definition at line 551 of file FrechetShortcut.h.

552  {
553  int d;
554  Coordinate x2 = q[0];
555  Coordinate y2 = q[1];
556  Coordinate x1 = p[0];
557  Coordinate y1 = p[1];
558 
559  if(x2-x1==0)
560  if(y2-y1==1)
561  d=2;
562  else
563  d=6;
564  else
565  if(x2-x1==1)
566  if(y2-y1==0)
567  d=0;
568  else
569  if(y2-y1==1)
570  d=1;
571  else
572  d=7;
573  else
574  if(y2-y1==0)
575  d=4;
576  else
577  if(y2-y1==1)
578  d=3;
579  else
580  d=5;
581  return d;
582  }

◆ computeOctant()

template<typename TIterator , typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>
static int DGtal::FrechetShortcut< TIterator, TInteger >::Tools::computeOctant ( Point  p,
Point  q 
)
inlinestatic

Computes the octant of the direction pq

Parameters
pand
qtwo points
Returns
an int

Definition at line 589 of file FrechetShortcut.h.

590  {
591  int d = 0;
592  Coordinate x = q[0]-p[0];
593  Coordinate y = q[1]-p[1];
594 
595  if(x>=0)
596  {
597  if(y>=0)
598  {
599  if(x>y)
600  d=0; // 0 <= y < x
601  else
602  if(x!=0)
603  d=1; // 0 <= x <= y
604  }
605  else
606  {
607  if(x>=abs(y))
608  d=7; // 0 < abs(y) <= x
609  else
610  d=6; // 0 <= x < abs(y)
611  }
612  }
613  if(x<=0)
614  {
615  if(y>0)
616  if(abs(x)>=y)
617  d=3; //
618  else
619  d=2;
620  else
621  {
622  if(abs(x)>abs(y))
623  d=4;
624  else
625  if(x!=0)
626  d=5;
627  }
628  }
629  return d;
630 
631  }

◆ isBetween()

template<typename TIterator , typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>
static bool DGtal::FrechetShortcut< TIterator, TInteger >::Tools::isBetween ( double  i,
double  a,
double  b,
double  n 
)
inlinestatic

Determines if i is between a and b in the oriented toric space modulo n

Parameters
ii
aa
bb
nn
Returns
true if i is between a anb d, false otherwise

Definition at line 362 of file FrechetShortcut.h.

363  {
364  if(a<=b)
365  return (i>=a && i<=b);
366  else
367  return ((i>=a && i<=n) || (i>=0 && i<=b));
368  }

◆ rot()

template<typename TIterator , typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>
static int DGtal::FrechetShortcut< TIterator, TInteger >::Tools::rot ( int  d,
int  quad 
)
inlinestatic

Rotate the chain code d to put it in the frame where the octant 'quad' is treated as the first octant.

Parameters
da chain code
quadthe octant
Returns
an int (the new chain code)

Definition at line 641 of file FrechetShortcut.h.

642  {
643  return (d-quad+8)%8;
644  }

The documentation for this struct was generated from the following file:
DGtal::FrechetShortcut::Tools::circle_circle_intersection
static int circle_circle_intersection(double x0, double y0, double r0, double x1, double y1, double r1, double *xi, double *yi, double *xi_prime, double *yi_prime)
Definition: FrechetShortcut.h:397
Vector
FreemanChain< int >::Vector Vector
Definition: testCombinDSS.cpp:60
DGtal::functions::abs
T abs(const T &a)
Definition: BasicMathFunctions.h:116
DGtal::FrechetShortcut::Coordinate
Vector::Coordinate Coordinate
Definition: FrechetShortcut.h:127