+ 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'))
+
+
+let private vectorRotation (p1x: float32) (p1y: float32) (v1x: float32) (v1y: float32) (px: float32) (py: float32) : float32 =
+ let mutable rotation = 1.f