Problem of Apollonius: Difference between revisions

=={{header|F_Sharp|F#}}==

{{trans|OCaml}}

<lang fsharp>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 =

printfn "Circle(x=%.2f, y=%.2f, r=%.2f)"

c.center.x c.center.y c.radius

let xyr c = c.center.x, c.center.y, c.radius

let solve_apollonius c1 c2 c3

s1 s2 s3 =

let x1, y1, r1 = xyr c1

let x2, y2, r2 = xyr c2

let x3, y3, r3 = xyr c3

let v11 = 2. * x2 - 2. * x1

let v12 = 2. * y2 - 2. * y1

let v13 = x1*x1 - x2*x2 + y1*y1 - y2*y2 - r1*r1 + r2*r2

let v14 = (2. * s2 * r2) - (2. * s1 * r1)

let v21 = 2. * x3 - 2. * x2

let v22 = 2. * y3 - 2. * y2

let v23 = x2*x2 - x3*x3 + y2*y2 - y3*y3 - r2*r2 + r3*r3

let v24 = (2. * s3 * r3) - (2. * s2 * r2)

let w12 = v12 / v11

let w13 = v13 / v11

let w14 = v14 / v11

let w22 = v22 / v21 - w12

let w23 = v23 / v21 - w13

let w24 = v24 / v21 - w14

let p = - w23 / w22

let q = w24 / w22

let m = - w12 * p - w13

let n = w14 - w12 * q

let a = n*n + q*q - 1.

let b = 2.*m*n - 2.*n*x1 + 2.*p*q - 2.*q*y1 + 2.*s1*r1

let c = x1*x1 + m*m - 2.*m*x1 + p*p + y1*y1 - 2.*p*y1 - r1*r1

let d = b * b - 4. * a * c

let rs = (- b - (sqrt d)) / (2. * a)

let xs = m + n * rs

let ys = p + q * rs

new_circle xs ys rs

[<EntryPoint>]

let main argv =

let c1 = new_circle 0. 0. 1.

let c2 = new_circle 4. 0. 1.

let c3 = new_circle 2. 4. 2.

let r1 = solve_apollonius c1 c2 c3 1. 1. 1.

print_circle r1

let r2 = solve_apollonius c1 c2 c3 (-1.) (-1.) (-1.)

print_circle r2

0</lang>

{{out}}

<pre>Circle(x=2.00, y=2.10, r=3.90)

Circle(x=2.00, y=0.83, r=1.17)</pre>