Ανακλαστική Ιδιότητα Έλλειψης
Author: Μπουμπούλης Παντελής

E_1

E_2

a = 2.9 (slider from 0 to 5, step 0.1)
γ = 1.6 (slider from 0 to 3, step 0.1)
b: sqrt(a^(2.0) - γ^(2.0))
A: (-(γ), 0.0)
B: (γ, 0.0)
φ = 0.5 (slider from 0 to 6.283185307179586, step 0.1)
c: y - y(A) = tan(φ) * (x - x(A))
d: x^(2.0) / a^(a) + y^(2.0) / b^(2.0) = 1.0
C, M = Intersect(d, c)
t = 0 (slider from 0 to 4, step 0.0010)
B' = Rotate(B, φ, A)
α = Angle(B, A, B')
e = Ray(A, B')
N = Intersect(d, e)
f = Segment(A, N)
g = Segment(N, B)
K = If(t ≤ 1.0, A + t * (x(N) - x(A), y(N) - y(A)), If[t ≤ 2.0, N + (t - 1.0) * (x(B) - x(N), y(B) - y(N)), If[t ≤ 2.0, B]])
L = If(t ≤ 2.0 ∧ t ≥ 1.0, A + (t - 1.0) * (x(N) - x(A), y(N) - y(A)), If[t ≥ 2.0 ∧ t ≤ 3.0, N + (t - 2.0) * (x(B) - x(N), y(B) - y(N)), If[t ≥ 1.0 ∧ t ≤ 3.0, B]])
I = If(t ≤ 3.0 ∧ t ≥ 2.0, A + (t - 2.0) * (x(N) - x(A), y(N) - y(A)), If[t ≥ 3.0 ∧ t ≤ 4.0, N + (t - 3.0) * (x(B) - x(N), y(B) - y(N)), If[t ≥ 2.0 ∧ t ≤ 4.0, B]])
h = Segment(A, B)