Circle from 3 points

circleFrom3Points.tq

let det₃((a₁₁,a₁₂,a₁₃),(a₂₁,a₂₂,a₂₃),(a₃₁,a₃₂,a₃₃)) =
  -a₁₃*a₂₂*a₃₁ + a₁₂*a₂₃*a₃₁ + a₁₃*a₂₁*a₃₂ -
   a₁₁*a₂₃*a₃₂ - a₁₂*a₂₁*a₃₃ + a₁₁*a₂₂*a₃₃

let createCircle ((x₁, y₁), (x₂, y₂), (x₃, y₃)) =
  let a = det₃((x₁, y₁, 1), (x₂, y₂, 1), (x₃, y₃, 1)) in
  let d = -det₃((sqr x₁ + sqr y₁, y₁, 1), (sqr x₂ + sqr y₂, y₂, 1), (sqr x₃ + sqr y₃, y₃, 1)) in
  let e = det₃((sqr x₁ + sqr y₁, x₁, 1), (sqr x₂ + sqr y₂, x₂, 1), (sqr x₃ + sqr y₃, x₃, 1)) in
  let f = -det₃((sqr x₁ + sqr y₁, x₁, y₁), (sqr x₂ + sqr y₂, x₂, y₂), (sqr x₃ + sqr y₃, x₃, y₃)) in
  let r = (sqr d + sqr e)/(4 * sqr a) - f/a @ sqrt in
  Circle((-d/(2*a), -e/(2*a)), r)

let () =
  let p₁, p₂, p₃ = ((150, 100), (350, 200), (300, 50)) in
  let geometry = createCircle (p₁, p₂, p₃) in
  {p₁; p₂; p₃}
  @ Array.map [p -> Shape(Style(Fill White, Stroke(Black, 3)), Circle(p, 5))]
  @ Array.prepend (Shape(Style(Fill Red, Stroke(Black, 3)), geometry))
  @ Html.ofSvg (600, 300)
  @ yield