$\vec{n}$

Punkt A

Punkt B

Punkt C

Punkt D

Untersuche:

P: (0 | 0 | 4)
N = (2, 4, 12)
n = Vector(P, N)
u = If(x(n) ≟ 0, (1 | 0 | 0), If[y(n) ≟ 0, (0 | 1 | 0), If[z(n) ≟ 0, (0 | 0 | 1), ((-y(n)) | x(n) | 0)]])
v: n ⊗ u
v0: v / abs(v)
u0: u / abs(u)
Q1: P + (8 * u0) + (8 * v0)
Q3: P - (8 * u0) - (8 * v0)
Q4: P + (8 * u0) - (8 * v0)
Q2: P - (8 * u0) + (8 * v0)
v1, q2, q3, q4, q1 = Polygon(Q2, Q3, Q4, Q1)
a: (u0 * n)
b: (v0 * n)
c: (u0 * v0)
g1 = Line((1 | 1 | 4), (3 | 5 | 12))
g2 = Line((1 | -1 | 4), (3 | 3 | 12))
g3 = Line((-1 | 1 | 4), (1 | 5 | 12))
A: (4 | 4 | 1)
B: (-4 | 6 | 3)
C: (-2 | -3 | 7)
D: (4 | -4 | 5)
A0: (x(A) | y(A) | 0)
B0: (x(B) | y(B) | 0)
C0: (x(C) | y(C) | 0)
D0: (x(D) | y(D) | 0)
f = Segment(A, A0)
g = Segment(B, B0)
h = Segment(C, C0)
i = Segment(D, D0)
vPA = Vector(P, A)
vPB = Vector(P, B)
vPD = Vector(P, D)
vPC = Vector(P, C)
α = Angle(n, vPA)
β = Angle(n, vPB)
γ = Angle(n, vPC)
δ = Angle(n, vPD)
k = true
l = false
m = false
o = false