tasks a-s

Task/Problem-of-Apollonius/OCaml/problem-of-apollonius.ocaml

@@ -0,0 +1,76 @@
+type point = { x:float; y:float }
+type circle = {
+  center: point;
+  radius: float;
+}
+
+let new_circle ~x ~y ~r =
+  { center = { x=x; y=y };
+    radius = r }
+
+let print_circle ~c =
+  Printf.printf "Circle(x=%.2f, y=%.2f, r=%.2f)\n"
+    c.center.x c.center.y c.radius
+
+let defxyr c =
+  (c.center.x,
+   c.center.y,
+   c.radius)
+
+let solve_apollonius ~c1 ~c2 ~c3
+                     ~s1 ~s2 ~s3 =
+  let ( * ) = ( *. ) in
+  let ( / ) = ( /. ) in
+  let ( + ) = ( +. ) in
+  let ( - ) = ( -. ) in
+
+  let x1, y1, r1 = defxyr c1
+  and x2, y2, r2 = defxyr c2
+  and x3, y3, r3 = defxyr c3 in
+
+  let v11 = 2.0 * x2 - 2.0 * x1
+  and v12 = 2.0 * y2 - 2.0 * y1
+  and v13 = x1*x1 - x2*x2 + y1*y1 - y2*y2 - r1*r1 + r2*r2
+  and v14 = (2.0 * s2 * r2) - (2.0 * s1 * r1)
+
+  and v21 = 2.0 * x3 - 2.0 * x2
+  and v22 = 2.0 * y3 - 2.0 * y2
+  and v23 = x2*x2 - x3*x3 + y2*y2 - y3*y3 - r2*r2 + r3*r3
+  and v24 = (2.0 * s3 * r3) - (2.0 * s2 * r2) in
+
+  let w12 = v12 / v11
+  and w13 = v13 / v11
+  and w14 = v14 / v11 in
+
+  let w22 = v22 / v21 - w12
+  and w23 = v23 / v21 - w13
+  and w24 = v24 / v21 - w14 in
+
+  let p = -. w23 / w22
+  and q = w24 / w22 in
+  let m = -. w12 * p - w13
+  and n = w14 - w12 * q in
+
+  let a = n*n + q*q - 1.0
+  and b = 2.0*m*n - 2.0*n*x1 + 2.0*p*q - 2.0*q*y1 + 2.0*s1*r1
+  and c = x1*x1 + m*m - 2.0*m*x1 + p*p + y1*y1 - 2.0*p*y1 - r1*r1 in
+
+  let d = b * b - 4.0 * a * c in
+  let rs = (-. b - (sqrt d)) / (2.0 * a) in
+
+  let xs = m + n * rs
+  and ys = p + q * rs in
+
+  (new_circle xs ys rs)
+
+let () =
+  let c1 = new_circle 0.0 0.0 1.0
+  and c2 = new_circle 4.0 0.0 1.0
+  and c3 = new_circle 2.0 4.0 2.0 in
+
+  let r1 = solve_apollonius c1 c2 c3 1.0 1.0 1.0 in
+  print_circle r1;
+
+  let r2 = solve_apollonius c1 c2 c3 (-1.) (-1.) (-1.) in
+  print_circle r2;
+;;