let x = (b + a) / 2.0
x, f x
+// Ellipse.A is always equal or greater than Ellipse.B.
+// Ellipse.Alpha is between 0 and Pi.
let ellipse (p1x: float) (p1y: float) (m1: float) (p2x: float) (p2y: float) (m2: float) (p3x: float) (p3y: float) : Types.Ellipse option =
let accuracy_extremum_search_1 = 4
let accuracy_extremum_search_2 = 3
let alpha1 = atan m1
let alpha2 = atan m2
- let r1 = sqrt (p1x**2.0 + p1y**2.0)
+ let r1 = sqrt (p1x ** 2.0 + p1y ** 2.0)
let theta1 = atan2 p1y p1x
let r2 = sqrt (p2x**2.0 + p2y**2.0)
let valid =
4.0 * sin (alpha1 - theta1) * (-r1 * sin (alpha1 - theta1) + r2 * sin (alpha1 - theta2)) *
sin (alpha2 - theta2) * (-r1 * sin (alpha2 - theta1) + r2 * sin (alpha2 - theta2)) +
- r1 * r2 * sin (alpha1 - alpha2) **2.0 * sin (theta1 - theta2) **2.0 < 0.0
+ r1 * r2 * sin (alpha1 - alpha2) ** 2.0 * sin (theta1 - theta2) ** 2.0 < 0.0
if valid
then
let r theta =
(r1 * r2 * (r1 * (cos (alpha2 + theta - theta1 - theta2) - cos (alpha2 - theta) * cos (theta1 - theta2)) * sin (alpha1 - theta1) + r2 * (-cos (alpha1 + theta - theta1 - theta2) + cos (alpha1 - theta) * cos (theta1 - theta2)) * sin (alpha2 - theta2)) * sin (theta1 - theta2)) /
- (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2))**2.0 - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2)**2.0)
+ (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2)) ** 2.0 - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2) ** 2.0)
let rabs = r >> abs
let rellipse theta =
sqrt (
- rc**2.0 + (r1**2.0 * r2**2.0 * (r1 * (cos (alpha2 + theta - theta1 - theta2) - cos (alpha2 - theta) * cos (theta1 - theta2)) * sin (alpha1 - theta1) + r2 * (-cos (alpha1 + theta - theta1 - theta2) + cos (alpha1 - theta) * cos (theta1 - theta2)) * sin (alpha2 - theta2))**2.0 * sin (theta1 - theta2)**2.0) /
- (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2))**2.0 - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2)**2.0)**2.0 -
+ rc ** 2.0 + (r1 ** 2.0 * r2 ** 2.0 * (r1 * (cos (alpha2 + theta - theta1 - theta2) - cos (alpha2 - theta) * cos (theta1 - theta2)) * sin (alpha1 - theta1) + r2 * (-cos (alpha1 + theta - theta1 - theta2) + cos (alpha1 - theta) * cos (theta1 - theta2)) * sin (alpha2 - theta2)) ** 2.0 * sin (theta1 - theta2) ** 2.0) /
+ (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2)) ** 2.0 - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2) ** 2.0) ** 2.0 -
(2.0 * r1 * r2 * rc * cos (theta - psi) * (r1 * (cos (alpha2 + theta - theta1 - theta2) - cos (alpha2 - theta) * cos (theta1 - theta2)) * sin (alpha1 - theta1) + r2 * (-cos (alpha1 + theta - theta1 - theta2) + cos (alpha1 - theta) * cos (theta1 - theta2)) * sin (alpha2 - theta2)) * sin (theta1 - theta2)) /
- (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2))**2.0 - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2)**2.0))
+ (sin (alpha1 - theta1) * sin (alpha2 - theta2) * (r1 * sin (theta - theta1) - r2 * sin (theta - theta2)) ** 2.0 - r1 * r2 * sin (alpha1 - theta) * sin (alpha2 - theta) * sin (theta1 - theta2) ** 2.0))
// We search for an interval [theta_a, theta_b] and assume the function is unimodal in this interval.
let r1eTheta, r1e = goldenSectionSearch rellipse accuracy_extremum_search_2 0.0 (Math.PI / 2.0) Maximum // Pi/2 and not pi because the period is Pi.
else
Some (m1, m2)
-
let find (edges: Matrix<byte>)
(xDir: Image<Gray, float>)
(yDir: Image<Gray, float>)