module Types

open System

type Ellipse (cx: float, cy: float, a: float, b: float, alpha: float) =
    member this.Cx = cx
    member this.Cy = cy
    member this.A = a
    member this.B = b
    member this.Alpha = alpha
    member this.Area = a * b * Math.PI

    // Does the ellipse contain the point (x, y)?.
    member this.Contains x y = 
        ((x - cx) * cos alpha + (y - cy) * sin alpha) ** 2.0 / a ** 2.0 + ((x - cx) * sin alpha - (y - cy) * cos alpha) ** 2.0 / b ** 2.0 <= 1.0