+let ellipse2 (p1x: float) (p1y: float) (m1: float) (p2x: float) (p2y: float) (m2: float) (p3x: float) (p3y: float) : Types.Ellipse option =
+ let p0 = pointFromTwoLines (Types.Line(float32 m1, float32 (p1y - m1 * p1x))) (Types.Line(float32 m2, float32(p2y - m2 * p2x)))
+ let p0x, p0y = float p0.X, float p0.Y
+
+ let s = matrix [[ 1.; 0.; 0. ]
+ [ 0.; 0.; -0.5 ]
+ [ 0.; -0.5; 0. ]]
+
+ let v0 = matrix [[ 1.; p0x; p0y ]]
+ let v1 = matrix [[ 1.; p1x; p1y ]]
+ let v2 = matrix [[ 1.; p2x; p2y ]]
+ let v3 = matrix [[ 1.; p3x; p3y ]]
+
+ let p = (v3.Stack(v1).Stack(v2).Determinant() * v0).Stack(v0.Stack(v3).Stack(v2).Determinant() * v1).Stack(v0.Stack(v1).Stack(v3).Determinant() * v2).Transpose()
+ let conicMat = p * s.Inverse() * p.Transpose()
+ let a = conicMat.[0, 0]
+ let b = conicMat.[0, 1]
+ let c = conicMat.[1, 1]
+ let d = conicMat.[0, 2]
+ let e = conicMat.[1, 2]
+ let f = conicMat.[2, 2]
+
+ // Center.
+ let cx = b / a
+ let cy = d / a
+
+ let at = c * f - e ** 2. + (e * d - b * f) * cx + (b * e - c * d) * cy
+ if at = 0.
+ then
+ None
+ else
+ let q = (-1. / at) * (matrix [[ a * f - d ** 2.0; b * d - a * e ]; [ b * d - a * e; a * c - b ** 2.0 ]])
+ let eigen = q.Evd()
+ let eigenValues = eigen.EigenValues
+ let lambda = eigenValues.[1].Real
+ let mu = eigenValues.[0].Real
+
+ if lambda <= 0. || mu <= 0.
+ then
+ None
+ else
+ let r1, r2 = 1. / (sqrt lambda), 1. / (sqrt mu)
+
+ let eigenVectors = eigen.EigenVectors
+ let v_a = eigenVectors.[0, 0]
+ let v_b = eigenVectors.[1, 0] // [0, 1]
+
+ // Angle against the longest axis.
+ let phi = (if r2 > r1 then atan (v_b / v_a) else atan (v_a / v_b))
+
+ let phi' = if phi < 0. then phi + Math.PI else phi
+ let majorAxis, minorAxis = if r1 > r2 then r1, r2 else r2, r1
+
+ Some (Types.Ellipse(float32 cx, float32 cy, float32 majorAxis, float32 minorAxis, float32 phi'))
+