/****************************************************
* This program allows calculating the 4 parameters  *
* of an arc of circle knowing two of them.          *
*  R:radius of circle S:curvilinear abscissa of arc *
*  C:length of chord  T:angle of arc of circle (rad)*
* ------------------------------------------------- *
* Ref.: "Mathématiques en Turbo-Pascal By M. Ducamp *
* and A. Reverchon (vol 2), Eyrolles, Paris, 1988"  *
* [BIBLI 05].                                       *
* ------------------------------------------------- *
* SAMPLE RUN:                                       *
*                                                   *
*   R=0                                             *
*   S=0                                             *
*   C=2                                             *
*   T=1                                             *
*                                                   *
* SUCCESS: YES.                                     *
*                                                   *
* Radius              :   2.0858296429              *
* Curvilinear abscissa:   2.0858296429              *
* Chord               :   2.0000000000              *
* Angle (radians)     :   1.0000000000              *
*                                                   *
* Surface of angular sector     :   2.1753426497    *
* Surface between arc and chord :   0.3448549280    *
*                                                   *
*                       C++ Version By J-P Moreau.  *
*                           (www.jpmoreau.fr)       *
****************************************************/
#include <stdio.h>
#include <math.h>

#define  FALSE  0
#define  TRUE   1
#define  PI     3.14159265359

// LABEL fin

double  c,r,s,t,s1,s2;
double  a,b,u,x,y;
int     ndata;
bool    done;


void main() {
  printf("\n             ARC OF CIRCLE\n");
  printf(" -----------------------------------------\n");
  printf("  Give two parameters between:\n");
  printf("    R: radius of circle\n");
  printf("    S: curvilinear abscissa\n");
  printf("    C: chord\n");
  printf("    T: angle of arc in radians\n");
  printf("  The other two must be given as zero.\n");
  printf("  The program then calculates the\n");
  printf("  missing parameters and the two surfaces:\n");
  printf("    S1: total surface of angular sector\n");
  printf("    S2: surface between chord and arc s.\n");
  printf(" -----------------------------------------\n");
  printf("     R= "); scanf("%lf",&r);
  printf("     S= "); scanf("%lf",&s);
  printf("     C= "); scanf("%lf",&c);
  printf("     T= "); scanf("%lf",&t);
  printf("\n");;
  done=FALSE; ndata=0;
  // verify consistency of data r,s,c,t
  if (r!=0) ndata++;
  if (s!=0) ndata++;
  if (c!=0) ndata++;
  if (t!=0) ndata++;
  if (ndata!=2) {
    printf(" Too many data != 0 (maximum two).\n");
    goto fin;
  }
  if (t<0 || t>PI) {
    printf(" Angle t(radians) must be between 0 && PI.\n");
    goto fin;
  }
  if (s>0 && c>=s) {
    printf(" Chord c must be smaller than curvilinear abscissa s.\n");
    goto fin;
  }
  if (c>0 && s>c*PI/2) {
    printf(" Curvilinear abscissa s must be smaller than chord times PI/2.\n");
    goto fin;
  }
  if (r>0 && s>PI*r) {
    printf(" Curvilinear abscissa s must be smaller then radius r times PI.\n");
    goto fin;
  }
  //end of verify data
  if (t>0) 
    if (r>0) {
      //---------------------- t && r are given ----
      s=r*t; c=2*r*sin(t/2);
	}
    else
      if (s>0) {
      //---------------------- t && s are given ----
        r=s/t; c=2*r*sin(t/2);
      }
      else {
      //---------------------- t && c are given ----
        r=c/2/sin(t/2); s=r*t;
      }
  else  // t is not given
    if (c==0) {
      //---------------------- r && s are given ----
      t=s/r; c=2*r*sin(t/2);
	}
    else
      if (r>0) {
		//---------------------- r && c are given ----
        if (c<2*r) 
          t=2*atan(c/sqrt(4*r*r-c*c));
        else
          t=PI;
        s=r*t;
      }
      else {
		//---------------------- s && c are given
        y=c;
        do {
          x=y;        u=s/x;
          a=s*cos(u); b=x*sin(u)-a;
          if ((c-a)*b<=0) goto fin;
          y=x*(c-a)/b;
        } while (fabs(x-y)>1e-8);
        r=y/2; t=s/r;
      }
  // calculate surfaces s1 && s2
  s1=s*r/2;
  s2=(s-c*cos(t/2))*r/2;
  done=TRUE;

  // print results
  if (done) {
    printf("\n SUCCESS: YES.\n\n");
    printf(" Radius              : %15.10f\n", r);
    printf(" Curvilinear abscissa: %15.10f\n", s);
    printf(" Chord               : %15.10f\n", c);
    printf(" Angle (radians)     : %15.10f\n", t);
    printf("\n");
    printf(" Sector surface                : %15.10f\n", s1);
    printf(" Surface between arc and chord : %15.10f\n\n", s2);
  }
  else
    printf("\n SUCCESS: NO.\n\n");

fin: printf("\n");
}

// end of file arcircle.cpp