!*****************************************************
!* 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              :    2.085830                 *
!* Curvilinear abscissa:    2.085830                 *
!* Chord               :    2.000000                 *
!* Angle (radians)     :    1.000000                 *
!*                                                   *
!* Surface of angular sector     :   2.175343        *
!* Surface between arc and chord :  0.3448550        *
!*                                                   *
!*                        F90 Version By J-P Moreau. *
!*                            (www.jpmoreau.fr)      *
!*****************************************************
Program arc_of_circle

parameter(FALSE=0,TRUE=1,PI=3.14159265359)

  print *,''
  print *,'             ARC OF CIRCLE'
  print *,' -----------------------------------------'
  print *,'  Give two parameters between:'
  print *,'    R: radius of circle'
  print *,'    S: curvilinear abscissa'
  print *,'    C: chord'
  print *,'    T: angle of arc in radians'
  print *,'  The other two must be given as zero.'
  print *,'  The program then calculates the'
  print *,'  missing parameters and the two surfaces:'
  print *,'    S1: total surface of angular sector'
  print *,'    S2: surface between chord and arc s.'
  print *,' -----------------------------------------'
  write(*,100,advance='no'); read *, r
  write(*,110,advance='no'); read *, s
  write(*,115,advance='no'); read *, c
  write(*,120,advance='no'); read *, t
  print *,''
  done=FALSE; ndata=0
  !verify consistency of data r,s,c,t
  if (r.ne.0.) ndata=ndata+1
  if (s.ne.0.) ndata=ndata+1
  if (c.ne.0.) ndata=ndata+1
  if (t.ne.0.) ndata=ndata+1
  if (ndata > 2) then
    print *,' Too many data <> 0 (maximum two).'
    goto 500
  end if
  if (ndata < 2) then
    print *,' Not enough data <> 0 (minimum two).'
    goto 500
  end if
  if (t<0.or.t>PI) then
    print *,' Angle t(radians) must be between 0 and PI.'
    goto 500
  end if
  if (s>0.and.c>=s) then
    print *,' Chord c must be smaller than curvilinear abscissa s.'
    goto 500
  end if
  if (c>0.and.s>c*PI/2) then
    print *,' Curvilinear abscissa s must be smaller than chord times PI/2.'
    goto 500
  end if
  if (r>0.and.s>PI*r) then
    print *,' Curvilinear abscissa s must be smaller then radius r times PI.'
    goto 500
  end if
  !end of verify data

  x=1; y=0           !to ensure initial abs(x-y)<>0

  if (t>0) then
    if (r>0) then
      !---------------------- t and r are given ----
      s=r*t; c=2*r*sin(t/2)
    else
      if (s>0) then
      !---------------------- t and s are given ----
        r=s/t; c=2*r*sin(t/2)
      else
      !---------------------- t and c are given ----
        r=c/2/sin(t/2); s=r*t
      end if
    end if
  else  !t is not given
    if (c.eq.0.) then
      !---------------------- r and s are given ----
      t=s/r; c=2*r*sin(t/2)
    else
      if (r>0.) then
        !---------------------- r and c are given ----
        if (c<2*r) then
          t=2*atan(c/sqrt(4*r*r-c*c))
        else
          t=PI
        end if
        s=r*t
      else
      !---------------------- s and c are given
        y=c
        do while(abs(x-y)>1.E-8)
          x=y;        u=s/x
          a=s*cos(u); b=x*sin(u)-a
          if ((c-a)*b<=0.) goto 500
          y=x*(c-a)/b
        end do
        r=y/2; t=s/r
      end if
    end if
  end if	 
  !calculate surfaces s1 and s2
  s1=s*r/2
  s2=(s-c*cos(t/2))*r/2
  done=TRUE

  !print results
  if (done.eq.TRUE) then
    print *,''
    print *,' SUCCESS:  Yes.'
    print *,''
    print *,' Radius              : ', r
    print *,' Curvilinear abscissa: ', s
    print *,' Chord               : ', c
    print *,' Angle (radians)     : ', t
    print *,''
    print *,' Surface of angular sector     : ',s1
    print *,' Surface between arc and chord : ',s2
  else
    print *,' SUCCESS:  No.'
  end if

500 print *,''
    stop

100 format('     R= ')
110 format('     S= ')
115 format('     C= ')
120 format('     T= ')

END

! end of file arcircle.f90