Kocka forgatása
Author: Nagy Gábor Péter

Az u és v vektor segítségével meghatározhatjuk az α és β szögeket, majd a kokát elforgatuk tengelyesen ezen szögekkel.

Feladat: Mit tudunk mondani a forgatás tengelyéről?

E1 = Point(xAxis)
O1 = (10, 0)
f = Circle(O1, E1)
I = Point(f)
u = Vector(O1, I)
α = Angle(E1, O1, I)
O2 = Point(xAxis)
E2 = Point(xAxis)
t_1 = Circle(O2, E2)
O = Point(t_1)
v = Vector(O2, O)
β = Angle(E2, O2, O)
B = (4, 4)
C = (-4, 4)
D = (-4, -4)
A = (4, -4)
G = Intersect(yAxis, xAxis)
C' = Rotate(C, α, G)
D' = Rotate(D, α, G)
A' = Rotate(A, α, G)
B' = Rotate(B, α, G)
j = Line(C, B)
k = Line(D, A)
l = OrthogonalLine(C', xAxis)
m = OrthogonalLine(B', xAxis)
n = OrthogonalLine(A', xAxis)
p = OrthogonalLine(D', xAxis)
C1 = Intersect(l, j)
B1 = Intersect(m, j)
D1 = Intersect(p, j)
A1 = Intersect(n, j)
A2 = Intersect(n, k)
D2 = Intersect(p, k)
B2 = Intersect(m, k)
C2 = Intersect(l, k)
C1' = Rotate(C1, β, G)
B1' = Rotate(B1, β, G)
D1' = Rotate(D1, β, G)
A1' = Rotate(A1, β, G)
A2' = Rotate(A2, β, G)
D2' = Rotate(D2, β, G)
B2' = Rotate(B2, β, G)
C2' = Rotate(C2, β, G)
i_1 = OrthogonalLine(B', yAxis)
j_1 = OrthogonalLine(C', yAxis)
k_1 = OrthogonalLine(D', yAxis)
l_1 = OrthogonalLine(A', yAxis)
a = Segment(C', B')
b = Segment(B', A')
c = Segment(A', D')
d = Segment(D', C')
e = OrthogonalLine(C1', xAxis)
g = OrthogonalLine(A1', xAxis)
h = OrthogonalLine(B1', xAxis)
i = OrthogonalLine(D1', xAxis)
q = OrthogonalLine(A2', xAxis)
r = OrthogonalLine(B2', xAxis)
s = OrthogonalLine(C2', xAxis)
t = OrthogonalLine(D2', xAxis)
E = Intersect(e, j_1)
F = Intersect(s, j_1)
H = Intersect(i_1, h)
J = Intersect(i_1, r)
K = Intersect(g, l_1)
L = Intersect(l_1, q)
P = Intersect(k_1, t)
Q = Intersect(k_1, i)
a_1 = Segment(H, J)
b_1 = Segment(J, F)
c_1 = Segment(F, E)
d_1 = Segment(E, H)
e_1 = Segment(J, L)
f_1 = Segment(L, P)
g_1 = Segment(P, F)
h_1 = Segment(E, Q)
m_1 = Segment(Q, P)
n_1 = Segment(H, K)
p_1 = Segment(K, L)
q_1 = Segment(K, Q)
r_1 = Segment(O1, E1)
s_1 = Segment(O2, E2)