- 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
+ member this.Contains x y =
+ ((x - cx) * cos alpha + (y - cy) * sin alpha) ** 2.f / a ** 2.f + ((x - cx) * sin alpha - (y - cy) * cos alpha) ** 2.f / b ** 2.f <= 1.f
+
+ member this.CutAVericalLine (y: float32) : bool =
+ a ** 2.f + b ** 2.f - 2.f * y ** 2.f + 4.f * y * cx - 2.f * cx ** 2.f + a ** 2.f * cos (2.f * alpha) - b ** 2.f * cos (2.f * alpha) > 0.f
+
+ member this.CutAnHorizontalLine (x: float32) : bool =
+ a ** 2.f + b ** 2.f - 2.f * x ** 2.f + 4.f * x * cy - 2.f * cy ** 2.f - a ** 2.f * cos (2.f * alpha) + b ** 2.f * cos (2.f * alpha) > 0.f
+
+ member this.isOutside (width: float32) (height: float32) =
+ this.Cx < 0.f || this.Cx >= width ||
+ this.Cy < 0.f || this.Cy >= height ||
+ this.CutAVericalLine 0.f || this.CutAVericalLine width ||
+ this.CutAnHorizontalLine 0.f || this.CutAnHorizontalLine height
+
+ member this.Scale (factor: float32) =
+ Ellipse(this.Cx, this.Cy, this.A * factor, this.B * factor, alpha)
+
+ // Approximation of Ramanujan.
+ member this.Perimeter =
+ PI * (3.f * (this.A + this.B) - sqrt ((3.f * this.A + this.B) * (this.A + 3.f * this.B)))