point_utils.H

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/*
                          Aleph_w
 
  Data structures & Algorithms
  version 2.0.0b
  https://github.com/lrleon/Aleph-w
 
  This file is part of Aleph-w library
 
  Copyright (c) 2002-2026 Leandro Rabindranath Leon
 
  Permission is hereby granted, free of charge, to any person obtaining a copy
  of this software and associated documentation files (the "Software"), to deal
  in the Software without restriction, including without limitation the rights
  to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
  copies of the Software, and to permit persons to whom the Software is
  furnished to do so, subject to the following conditions:
 
  The above copyright notice and this permission notice shall be included in all
  copies or substantial portions of the Software.
 
  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
  AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
  OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  SOFTWARE.
*/
 
 
# ifndef POINT_UTILS_H
# define POINT_UTILS_H
 
inline const Geom_Number area_of_parallelogram(const Point & a, 
                 const Point & b, 
                 const Point & c)
{
  return ((b.get_x() - a.get_x()) * (c.get_y() - a.get_y()) - 
    (c.get_x() - a.get_x()) * (b.get_y() - a.get_y()));
}
 
inline const Geom_Number area_of_triangle(const Point & a, 
            const Point & b, 
            const Point & c)
{
  return mpq_abs(area_of_parallelogram(a, b, c))/2;
}
 
inline const bool points_are_colinear(const Point & a, 
              const Point & b, 
              const Point & c)
{
  return area_of_parallelogram(a, b, c) == 0;
}
 
inline const bool c_is_to_left_(const Point & a, const Point & b, const Point & c)
{
  return parallelogram_area(a, b, c) > 0;
}
 
inline const bool is_clockwise(const Point & a, 
             const Point & b, 
             const Point & c)
{
  return not left(a, b, c);
}
 
inline const bool left_on(const Point & a, const Point & b, const Point & c)
{
  return parallelogram_area(a, b, c) >= 0;
}
 
const bool proper_intersection(const Point & a, const Point & b, 
             const Point & c, const Point & d)
{
  if (colinear_points(a, b, c) or
      colinear_points(a, b, d) or
      colinear_points(c, d, a) or
      colinear_points(c, d, b))
    return false;
 
  return ((left(a, b, c) xor left(a, b, d)) and
    (left(c, d, a) xor left(c, d, b)));
}
 
const bool between(const Point & a, const Point & b, const Point & c)
{
  if (not colinear_points(a, b, c))
    return false;
  
  // If ab is not vertical, compare x coordinates
  if (a.get_x() != b.get_x())
    return (((a.get_x() <= c.get_x()) and (c.get_x() <= b.get_x())) or
      ((a.get_x() >= c.get_x()) and (c.get_x() >= b.get_x())));
 
  // Vertical segment: compare y coordinates
  return (((a.get_y() <= c.get_y()) and (c.get_y() <= b.get_y())) or
    ((a.get_y() >= c.get_y()) and (c.get_y() >= b.get_y())));
}
 
const bool intersect_improp(const Point & a, const Point & b, 
           const Point & c, const Point & d)
{
  if (between(a, b, c) or
      between(a, b, d) or
      between(c, d, a) or
      between(c, d, b))
    return true;
 
  return false;
}
 
const bool intersectp(const Point & a, const Point & b, 
           const Point & c, const Point & d)
{
  if (intersect_prop(a, b, c, d))
    return true;
 
  if (intersect_improp(a, b, c, d))
    return true;
  
  return false;
}
 
int read_pixels(ifstream &in){
    int c=0, i=0;
    char buffer[]={'\0','\0','\0','\0','\0'};
    while(!in.eof() && isdigit(c=in.get())) buffer[i++] = c;
    int num = atoi(buffer);
    return num;
   
}
 
 
# endif // POINT_UTILS_H