B_1

B_2

IMP10

Kegelschnitte in 3D

Brennpunkte

Berührkreise

Berührkreisebenen

K_2

Abstände: P - Brennpunkte

Abstände: P - Berührkreise

Ebene

Start

Leitgeraden

Abstände: P - Leitgeraden

Kugeln

Kegel

Kegelschnitt

Punkt P

Neigung

Höhe

Öffnung

k = 0.7 (slider from 0.1 to 1, step 0.1)
gl1: x^(2) + y^(2) = ((k * z))^(2)
α: atand(1 / k)
γ: α / 2
h = -1 (slider from -3 to 3, step 0.1)
m = -0.6 (slider from -10 to 10)
p: ((-m) * x) + z = h
c = IntersectPath(p, gl1)
A, B = Focus(c)
Lot_2 = OrthogonalLine(B, p)
S_2, S_1, S_3, S_4 = Vertex(c)
f_1: (Distance[B, S_1] * tan(γ))
achse = Line((0, 0, 0), (0, 0, 1))
δ: 90° - γ
f_2: (Distance[B, S_1] * tan(δ))
Lot_1 = OrthogonalLine(A, p)
M_2 = If(m ≟ 0, If[h > 0, (0, 0, h - f_1), (0, 0, h + f_1)], Intersect[Lot_2, achse])
M_1 = If(m ≟ 0, If[h > 0, (0, 0, h + f_2), (0, 0, h - f_2)], Intersect[Lot_1, achse])
K_2 = Sphere(M_1, Distance[M_1, A])
a = true
ε: abs(sin(atand(m)) / sin(atand(1 / k)))
L_3: S_1 + (1 / ε * Vector[B, S_1])
h_1: z = z(L_3)
kreis_1 = IntersectPath(h_1, gl1)
b: round(1 / k, 1)
L_4: S_2 + (1 / ε * Vector[A, S_2])
h_2: z = z(L_4)
kreis_2 = IntersectPath(h_2, gl1)
d = true
e = true
K_1 = Sphere(M_2, Distance[M_2, B])
P = Point(c)
f = Segment(P, A)
g = Segment(P, B)
i = Ray((0, 0), P)
K_4 = Intersect(i, kreis_1)
D = Intersect(i, kreis_2)
j = Segment(P, K_4)
l = Segment(P, D)
n = true
o = true
q = true
anim = false
Leitgerade_1 = IntersectPath(h_1, p)
Leitgerade_2 = IntersectPath(h_2, p)
t = true
r = OrthogonalLine(P, Leitgerade_2, space)
L_1 = Intersect(r, Leitgerade_1)
L_2 = Intersect(r, Leitgerade_2)
s_1 = Segment(P, L_1)
s_2 = Segment(P, L_2)
s = false
u = true
v = true
w = true
a_1 = true
b_1 = true
c_1 = true
d_1 = true