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 355 of file FrechetShortcut.h.

Member Function Documentation

angleVectVect()

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

double DGtal::FrechetShortcut< TIterator, TInteger >::Tools::angleVectVect ( Vector u, Vector v )

inlinestatic

Angle between two vectors

Parameters

u	and
v	two vectors

Returns

an angle

Definition at line 579 of file FrechetShortcut.h.

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

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

chainCode2Vect()

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

Vector DGtal::FrechetShortcut< TIterator, TInteger >::Tools::chainCode2Vect ( int d )

inlinestatic

Converts a chain code into a vector

Parameters

d

an int

Returns

a vector

Definition at line 690 of file FrechetShortcut.h.

    {
      Vector v;
      switch(d){
        
      case 0:{
        v[0] = 1;
        v[1] = 0;
        break;
      }
      case 1:{
        v[0] = 1;
        v[1] = 1;
        break;
      }
      case 2:{
        v[0] = 0;
        v[1] = 1;
        break;
      }
      case 3:{
        v[0] = -1;
        v[1] = 1;
        break;
      }
      case 4:{
        v[0] = -1;
        v[1] = 0;
        break;
      }
      case 5:{
        v[0] = -1;
        v[1] = -1;
        break;
      }
      case 6:{
        v[0] = 0;
        v[1] = -1;
        break;
      }
      case 7:{
        v[0] = 1;
        v[1] = -1;
        break;
      } 
        
      }
      
      return v;
    }

circle_circle_intersection()

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

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 401 of file FrechetShortcut.h.

      {
        // I. Sivignon 05/2024: fix to handle the case where r0=0 or
        // r1=0. Enables the case where error=0. 
        // Other special cases where circles are tangent are treated
        // below. 
        if(r0==0)
          {
            *xi = x0; *yi = y0;
            *xi_prime = x0 ; *yi_prime = y0;
            return 1;
          }
        else
          if(r1==0)
            {
              *xi = x1; *yi = y1;
              *xi_prime = x1 ; *yi_prime = y1;
              return 1;
            }
        
        double a, dx, dy, d, h, rx, ry;
        double x2, y2;
        
        /* dx and dy are the vertical and horizontal distances between
         * the circle centers.
         */
        dx = x1 - x0;
        dy = y1 - y0;
 
        /* Determine the straight-line distance between the centers. */
        //d = sqrt((dy*dy) + (dx*dx));
        d = hypot(dx,dy); // Suggested by Keith Briggs
 
        if((r0+r1)*(r0+r1)-((dy*dy)+(dx*dx)) < PRECISION)   
          {  // I. Sivignon 05/2024: fix to handle the case where
             // circles are tangent but radii are non zero.
            
            double alpha= r0/d;
            *xi = x0 + dx*alpha;
            *yi = y0 + dy*alpha;
            *xi_prime = *xi; *yi_prime = *yi; 
            return 1;
          }
        
        /* Check for solvability. */
        if (d > (r0 + r1))
        {
          /* no solution. circles do not intersect. */
          std::cerr  << "Warning : the two circles do not intersect -> should never happen" << std::endl;
          return 0; //I. Sivignon 05/2010 should never happen for our specific use.
        }
        if (d < fabs(r0 - r1))
          {
            /* no solution. one circle is contained in the other */
            return 0;
          }
 
        //   }
        /* 'point 2' is the point where the line through the circle
         * intersection points crosses the line between the circle
         * centers.  
         */
        
        /* Determine the distance from point 0 to point 2. */
        a = ((r0*r0) - (r1*r1) + (d*d)) / (2.0 * d) ;
 
        /* Determine the coordinates of point 2. */
        x2 = x0 + (dx * a/d);
        y2 = y0 + (dy * a/d);
 
 
        /* Determine the distance from point 2 to either of the
       * intersection points.
       */
        h = sqrt((r0*r0) - (a*a));
 
        /* Now determine the offsets of the intersection points from
         * point 2.
         */
        rx = -dy * (h/d);
        ry = dx * (h/d);
        
        /* Determine the absolute intersection points. */
        *xi = x2 + rx;
        *xi_prime = x2 - rx;
        *yi = y2 + ry;
        *yi_prime = y2 - ry;
        
        return 1;
      }

Referenced by circleTangentPoints().

circleTangentPoints()

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

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]	x	the first coordinate of X.
[in]	y	the second coordinate of X.
[in]	x1	the first coordinate of the circle center X1.
[in]	y1	the second coordinate of the circle center X1.
[in]	r1	the circle radius.
[out]	xi	pointer to the first coordinate of the first intersection point.
[out]	yi	pointer to the second coordinate of the first intersection point.
[out]	xi_prime	pointer to the first coordinate of the second intersection point.
[out]	yi_prime	pointer to the second coordinate of the second intersection point.

Returns

result of the call to circle_circle_intersection

Definition at line 516 of file FrechetShortcut.h.

      {
        double x0 = (x+x1)/2;
        double y0 = (y+y1)/2;
        double r0 = sqrt((x-x1)*(x-x1) + (y-y1)*(y-y1))/2;
        
        int res =
          circle_circle_intersection(x0,y0,r0,x1,y1,r1,xi,yi,xi_prime,yi_prime);
 
        
        return res;
        
      }

References circle_circle_intersection().

computeAngle()

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

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

x0	x0
y0	y0
x1	x1
y1	y1

Returns

an angle

Definition at line 541 of file FrechetShortcut.h.

      {
        double x = x1-x0;
        double y = y1-y0;
        
        if(x!=0)
          {
            double alpha = y/x;
          
            if(x>0 && y>=0)
              return atan(alpha);
            else
              if(x>0 && y<0)
                return atan(alpha)+2*M_PI;
              else
                if(x<0)
                  return atan(alpha)+M_PI;
          }
        else
          {
            if(y==0)
              return 0;
            else 
              if(y>0)
                return M_PI_2;
              else
                return 3*M_PI_2;
          }
        return -1;
      }      

computeChainCode()

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

int DGtal::FrechetShortcut< TIterator, TInteger >::Tools::computeChainCode ( Point p, Point q )

inlinestatic

Computes the chain code between two 8-connected pixels

Parameters

p	and
q	two points

Returns

an int

Definition at line 590 of file FrechetShortcut.h.

      {
        int d;
        Coordinate x2 = q[0];
        Coordinate y2 = q[1];
        Coordinate x1 = p[0];
        Coordinate y1 = p[1];
        
        if(x2-x1==0)
          if(y2-y1==1)
            d=2;
          else
            d=6;
        else
          if(x2-x1==1)
            if(y2-y1==0)
              d=0;
            else
              if(y2-y1==1)
                d=1;
              else
                d=7;
          else
            if(y2-y1==0)
              d=4;
            else
              if(y2-y1==1)
                d=3;
              else
                d=5;
        return d;
      }

computeOctant()

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

int DGtal::FrechetShortcut< TIterator, TInteger >::Tools::computeOctant ( Point p, Point q )

inlinestatic

Computes the octant of the direction pq

Parameters

p	and
q	two points

Returns

an int

Definition at line 628 of file FrechetShortcut.h.

    {
      int d = 0;
      Coordinate x = q[0]-p[0];
      Coordinate y = q[1]-p[1];
      
      if(x>=0)
        {
          if(y>=0)
            {
              if(x>y)
                d=0; // 0 <= y < x  
              else
                if(x!=0)
                  d=1; // 0 <= x <= y
            }
          else
            {
              if(x>=abs(y)) 
                d=7; // 0 < abs(y) <= x 
              else
                d=6; // 0 <= x < abs(y)
            }
        }
      if(x<=0)
        {
          if(y>0)
            if(abs(x)>=y)
              d=3; // 
            else
              d=2;
          else
            {
              if(abs(x)>abs(y))
                d=4;
              else
                if(x!=0)
                  d=5;
            }
        }
      return d;
      
    }

isBetween()

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

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

i	i
a	a
b	b
n	n

Returns

true if i is between a anb d, false otherwise

Definition at line 366 of file FrechetShortcut.h.

      {
        if(a<=b)
          return (i>=a && i<=b);
        else
          return ((i>=a && i<=n) || (i>=0 && i<=b));
      }

rot()

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

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

d	a chain code
quad	the octant

Returns

an int (the new chain code)

Definition at line 680 of file FrechetShortcut.h.

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

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The documentation for this struct was generated from the following file:

• FrechetShortcut.h