/**************************************************************
*  The function Circle_Euler draws the Euler's circle of a    *
*  triangle ABC with automatic scales.                        *
*                                                             *
*                                      By J-P Moreau, Paris.  *
*                                       (www.jpmoreau.fr)     *
**************************************************************/
#include <math.h>

void OutText(int ix,int iy,char *s);

//Functions used here of Graph2D.cpp
void Cercle(double xc,double yc,double r,int trait);
void Initwindow(int,double,double,double,double);
void MoveXY(double,double);
void LineXY(double,double);
void Legendes (int,char *,char *,char *,int,int,char *,int,int,char *);

double a, b; //see Draw_Circle()
extern MaxX, MaxY;

//Solve linear system ax+b=c and a1x+b1y=c1.
void System2D(double a,double b,double c,double a1,double b1,double c1,
              double *x, double *y) {
  if (fabs(b*a1-a*b1)<1e-12)
    OutText(10,10," * Error in System2D - System is singular!");
  else {
    *y = (c*a1-c1*a)/(b*a1-a*b1);
    if (a!=0.0) *x = (c-b*(*y))/a; else *x = (c1-b1*(*y))/a1;
  }             
}

//determine coefficients a, b of y=ax+b straight line passing
//through 2 points (x1,y1) and (x2,y2).
void Line2D(double x1,double y1,double x2,double y2, double *a,
            double *b) {
  System2D(x1,1.0,y1,x2,1.0,y2,a,b);
}

//Draw line y=ax+b from (x1,y1) to (x2,y2).
void Draw_Line(double x1,double x2,double a,double b) {
  MoveXY(x1,a*x1+b); LineXY(x2,a*x2+b);
}

//Draw a circle passing through 3 points (x1,y1),(x2,y2),(x3,y3).
void Draw_Circle3P(double x1,double y1,double x2,double y2,double x3,double y3) {
  double c,r; //coefficient c of circle equation
              //x²+y²-2ax-2by+c=0 and radius r.
  System2D(2.0*(x2-x1),2.0*(y2-y1),(x2*x2+y2*y2-x1*x1-y1*y1),
           2.0*(x3-x1),2.0*(y3-y1),(x3*x3+y3*y3-x1*x1-y1*y1),&a,&b);
  c=2.0*a*x1+2.0*b*y1-x1*x1-y1*y1;
  r=sqrt(a*a+b*b-c);

  Cercle(a,b,r,0);
  Cercle(a,b,r/100.0,0);

}

void Circle_Euler() {

  double ax,ay,bx,by,cx,cy;
  double a1x,a1y,b1x,b1y,c1x,c1y;
  double x0,y0,x1,y1,x2,y2;
  
//define 3 points A, B, C in plane (Ox,Oy)
  ax=0.3333; ay=1.6666;
  bx=0.0; by=0.0;
  cx=1.5; cy=0.0;

  Initwindow(10,-0.5,2.0,-0.5,2.0);

/*TextXY(ax-0.05,ay+0.1,"A");
  TextXY(bx-0.05,by-0.05,"B");
  TextXY(cx+0.025,cy-0.025,"C"); */

  MoveXY(ax,ay); LineXY(bx,by);
  LineXY(cx,cy); LineXY(ax,ay);
  Draw_Circle3P(ax,ay,bx,by,cx,cy);
//TextXY(ax+0.05,ay+0.3,"Circumscribed Circle");
  x1=a; y1=b;

//define 3 points of Euler's circle
  a1x=(ax+bx)/2.0; a1y=(ay+by)/2.0;
  b1x=(cx+bx)/2.0; b1y=(cy+by)/2.0;
  c1x=(ax+cx)/2.0; c1y=(ay+cy)/2.0;

//draw the 3 bisectors of triangle ABC}
  MoveXY(ax,ay); LineXY(b1x,b1y);
  MoveXY(bx,by); LineXY(c1x,c1y);
  MoveXY(cx,cy); LineXY(a1x,a1y);

//drax euler circle of triangle ABC
  Draw_Circle3P(a1x,a1y,b1x,b1y,c1x,c1y);
//TextXY(0.3,0.55,"Euler's Circle");
  x2=a; y2=b;

  Line2D(x1,y1,x2,y2,&a,&b);
  Draw_Line(ax,0.7*cx,a,b);
//TextXY(ax+0.39,ay-0.3,"Euler's Line");
  
  Legendes(10,"Euler's Circle of triangle ABC","X","Y",0.56*MaxX,0.18*MaxY,"Circumscribed Circle",
	       0.55*MaxX, 0.4*MaxX,"Euler's Line");
  Legendes(10,"","","",0.33*MaxX,0.48*MaxY,"Euler's Circle",
	       0,0,"");
  Legendes(10,"","","",0.37*MaxX,0.2*MaxY,"A",
	       0.25*MaxX,0.74*MaxY,"B");
  Legendes(10,"","","",0.39*MaxX,0.67*MaxY,"H",
	       0.77*MaxX,0.74*MaxY,"C");
  Legendes(10,"","","",0.42*MaxX,0.58*MaxY,"O1",
	       0.5*MaxX,0.5*MaxY,"O");
  Legendes(10,"","","",0.37*MaxX,0.74*MaxY,"HA",
	       0.49*MaxX,0.55*MaxY,"G");
  Legendes(10,"","","",0.61*MaxX,0.5*MaxY,"HB",
	       0.31*MaxX,0.62*MaxY,"HC");

//Draw line C-Hc perpendicular to side AB
  Line2D(ax,ay,bx,by,&a,&b);
  System2D(a,-1,-b,(-1.0/a),-1.0,-(cy+cx/a),&x0,&y0); // Hc is in (x0,y0)
  MoveXY(cx,cy); LineXY(x0,y0);

//Draw line B-Hb perpendicular to side AC
  Line2D(ax,ay,cx,cy,&a,&b);
  System2D(a,-1,-b,(-1.0/a),-1.0,-(by+bx/a),&x0,&y0); // Hb is in (x0,y0)
  MoveXY(bx,by); LineXY(x0,y0);

/*Draw line A-Ha perpendicular to side BC (here a=0}
  Line2D(bx,by,cx,cy,&a,&b);
  System2D(a,-1,-b,(-1.0/a),-1.0,-(ay+ax/a),&x0,&y0); // Hb is in (x0,y0)
  MoveXY(ax,ay); LineXY(x0,y0); */
  MoveXY(ax,ay); LineXY(ax,0.0); //special case a=0

}

//end of file gceuler.cpp