// FILE: coordsys.cpp
// written for the course 2172, 1999
#include "coordsys.h"
#include <math.h>


// constructor
coordinate::coordinate(double a,double b):_x(a),_y(b) { }

// properties
double coordinate::x() const { return _x; }
double coordinate::y() const { return _y; }

ostream& operator<<(ostream& os, const coordinate& c) {
   return os << '<' << c._x << ',' << c._y << '>';
}

// properties
double coordsys::minX() const { return xmin; }
double coordsys::minY() const { return ymin; }
double coordsys::maxX() const { return xmax; }
double coordsys::maxY() const { return ymax; }


// constructor
coordsys::coordsys(double lx, double ly, double hx, double hy)
   :xmin(lx),xmax(hx),ymin(ly),ymax(hy) { }

/* S.map(system,p1)
 * p1 is a point in system 
 * map returns the corrsponding 
 * coordinates of p1 in S
 */
coordinate coordsys::map(coordsys system,coordinate p1) {
  return coordinate(
            xmin + (p1.x()-system.xmin) / (system.xmax - system.xmin) 
                 * (xmax - xmin), // mapped x value
            ymin + (p1.y()-system.ymin) / (system.ymax - system.ymin)
                 * (ymax - ymin)  // mapped y value
         );
}


#ifndef sqr
#define sqr(A) ((A)*(A))
#endif
#ifndef pi
#define pi 3.1415926535897 
#endif

/* S.rotate(o,p,angle)
 * returns the coordinates of p rotated about p
 * by angle many degrees (not radians!) counter
 * clock-wise
 */
coordinate coordsys::rotate(coordinate p,coordinate o,double beta) {
  // if o == p then beta is irrelevant
  if ((int)p.x() == (int)o.x() && (int)p.y() == (int)o.y()) return p;

  if (beta==0) return p; // no rotation

  double betarad = (pi * beta)/180.0; // beta in radians

  // hypotenuse
  double hyp = sqrt(sqr(p.x()-o.x()) + sqr(p.y() - o.y()));

  double alpharad; // move angle to the right quadrant

  // Tricky special cases that would render tan^-1 to infinity
  if ((int)p.x() == (int)o.x()) { // on same horizontal 
    if (p.y() > o.y()) { // p above o
      alpharad = pi/2.0; // 90
    } else { // p below o
      alpharad = -pi/2.0; // -90
    } 
  } else { // not on same horizontal
    if ((int)p.y() ==  (int)o.y()) { // on same vertical
      if (p.x() < o.x()) { // p "before" o
        alpharad = pi; //  180
      } else {
        alpharad = 0; // 0
      }
    } else { // not on same vertical, not on same horizontal
      double invtan = atan((p.y()-o.y())/(p.x()-o.x()));

      if (p.x() < o.x()) { // II or III quadrant
        alpharad =  invtan + pi; // 180 - alpha
      } else { // I or IV quadrant
        alpharad = invtan;
      }
    }
  }

  
  return coordinate(o.x()+cos(alpharad+betarad)*hyp,
                    o.y()+sin(alpharad+betarad)*hyp); 
}


ostream& operator<<(ostream& os, const coordsys& s) {

   return os << '[' << coordinate(s.xmin,s.ymin) << ','
             << coordinate(s.xmax,s.ymax) << ']';
}