Task: Problem of Apollonius

C: #include <stdio.h>
#include <tgmath.h>

#define VERBOSE 0
#define for3 for(int i = 0; i < 3; i++)

typedef complex double vec;
typedef struct { vec c; double r; } circ;

#define re(x) creal(x)
#define im(x) cimag(x)
#define cp(x) re(x), im(x)
#define CPLX "(%6.3f,%6.3f)"
#define CPLX3 CPLX" "CPLX" "CPLX

double cross(vec a, vec b) { return re(a) * im(b) - im(a) * re(b); }
double abs2(vec a) { return a * conj(a); }
 
int apollonius_in(circ aa[], int ss[], int flip, int divert)
{
	vec n[3], x[3], t[3], a, b, center;
	int s[3], iter = 0, res = 0;
	double diff = 1, diff_old = -1, axb, d, r;
 
	for3 {
		s[i] = ss[i] ? 1 : -1;
		x[i] = aa[i].c;
	}
 
	while (diff > 1e-20) {
		a = x[0] - x[2], b = x[1] - x[2];
		diff = 0;
		axb = -cross(a, b);
		d = sqrt(abs2(a) * abs2(b) * abs2(a - b));

		if (VERBOSE) {
			const char *z = 1 + "-0+";
			printf("%c%c%c|%c%c|",
				z[s[0]], z[s[1]], z[s[2]], z[flip], z[divert]);
			printf(CPLX3, cp(x[0]), cp(x[1]), cp(x[2]));
		}

		
		r = fabs(d / (2 * axb));
		center = (abs2(a)*b - abs2(b)*a) / (2 * axb) * I + x[2];
 
 		
		if (!axb && flip != -1 && !divert) {
			if (!d) { 
				printf("Given conditions confused me.\n");
				return 0;
			}

			if (VERBOSE) puts("\n[divert]");
			divert = 1;
			res = apollonius_in(aa, ss, -1, 1);
		}

 		
		for3 n[i] = axb ? aa[i].c - center : a * I * flip;
		for3 t[i] = aa[i].c + n[i] / cabs(n[i]) * aa[i].r * s[i];

		
		for3 diff += abs2(t[i] - x[i]), x[i] = t[i];

		if (VERBOSE) printf(" %g\n", diff);
 
 		
		if (diff >= diff_old && diff_old >= 0)
			if (iter++ > 20) return res;

		diff_old = diff;
	}

	printf("found: ");
	if (axb) printf("circle "CPLX", r = %f\n", cp(center), r);
	else	 printf("line "CPLX3"\n", cp(x[0]), cp(x[1]), cp(x[2]));

	return res + 1;
}
 
int apollonius(circ aa[])
{
	int s[3], i, sum = 0;
	for (i = 0; i < 8; i++) {
		s[0] = i & 1, s[1] = i & 2, s[2] = i & 4;

		
		if (s[0] && !aa[0].r) continue;
		if (s[1] && !aa[1].r) continue;
		if (s[2] && !aa[2].r) continue;
		sum += apollonius_in(aa, s, 1, 0);
	}
	return sum;
}
 
int main()
{
	circ a[3] = {{0, 1}, {4, 1}, {2 + 4 * I, 1}};
	circ b[3] = {{-3, 2}, {0, 1}, {3, 2}};
	circ c[3] = {{-2, 1}, {0, 1}, {2 * I, 1}};
	
 
	puts("set 1"); apollonius(a);
	puts("set 2"); apollonius(b);
	puts("set 3"); apollonius(c);
}










Fortran: program Apollonius
  implicit none

  integer, parameter :: dp = selected_real_kind(15)

  type circle
    real(dp) :: x
    real(dp) :: y
    real(dp) :: radius
  end type
       
  type(circle) :: c1 , c2, c3, r

  c1 = circle(0.0, 0.0, 1.0)
  c2 = circle(4.0, 0.0, 1.0)
  c3 = circle(2.0, 4.0, 2.0)

  write(*, "(a,3f12.8))") "External tangent:", SolveApollonius(c1, c2, c3, 1, 1, 1)
  write(*, "(a,3f12.8))") "Internal tangent:", SolveApollonius(c1, c2, c3, -1, -1, -1)
 
contains

function SolveApollonius(c1, c2, c3, s1, s2, s3) result(res)
  type(circle) :: res
  type(circle), intent(in) :: c1, c2, c3
  integer, intent(in) :: s1, s2, s3
 
  real(dp) :: x1, x2, x3, y1, y2, y3, r1, r2, r3
  real(dp) :: v11, v12, v13, v14
  real(dp) :: v21, v22, v23, v24
  real(dp) :: w12, w13, w14
  real(dp) :: w22, w23, w24
  real(dp) :: p, q, m, n, a, b, c, det
  
  x1 = c1%x; x2 = c2%x; x3 = c3%x
  y1 = c1%y; y2 = c2%y; y3 = c3%y
  r1 = c1%radius; r2 = c2%radius; r3 = c3%radius

  v11 = 2*x2 - 2*x1
  v12 = 2*y2 - 2*y1
  v13 = x1*x1 - x2*x2 + y1*y1 - y2*y2 - r1*r1 + r2*r2
  v14 = 2*s2*r2 - 2*s1*r1
 
  v21 = 2*x3 - 2*x2
  v22 = 2*y3 - 2*y2
  v23 = x2*x2 - x3*x3 + y2*y2 - y3*y3 - r2*r2 + r3*r3
  v24 = 2*s3*r3 - 2*s2*r2
 
  w12 = v12/v11
  w13 = v13/v11
  w14 = v14/v11
 
  w22 = v22/v21-w12
  w23 = v23/v21-w13
  w24 = v24/v21-w14
 
  p = -w23/w22
  q = w24/w22
  m = -w12*P - w13
  n = w14 - w12*q
 
  a = n*n + q*q - 1
  b = 2*m*n - 2*n*x1 + 2*p*q - 2*q*y1 + 2*s1*r1
  c = x1*x1 + m*m - 2*m*x1 + p*p + y1*y1 - 2*p*y1 - r1*r1
 
  det = b*b - 4*a*c
  res%radius = (-b-sqrt(det)) / (2*a)
  res%x = m + n*res%radius
  res%y = p + q*res%radius

end function
end program