Řez hranolu rovinou
Author: Radka Hamříková
Date: 2. leden 2012

Sestrojte řez kosého šestibokého hranolu rovinou ρ.

Dolní podstava hranolu - pravidelný šestiúhelník - je dána středem S [0,4,0] a vrcholem A [0,0,0], podstava leží v průmětně. Střed horní podstavy je S' [8,6,7]. 

Rovina řezu má souřadnice ρ (8,12,4).

S_1(0)

A_1

B_1

C_1

D_1

E_1

F_1

S'_1(7)

A'_1

B'_1

C'_1

D'_1

E'_1

F'_1

p_1^ρ

h_1^ρ(4)

p_1^α

h_1^α(7)

4

h_1^α(4)

C''_1

D''_1

I

E''_1

II

F''_1

A''_1

B''_1

A = (0, -4)
c = Circle(A, 4)
B = Intersect(c, xAxis, 1)
B' = Rotate(B, 60*°, A)
α = Angle(B, A, B')
mnohoúhelník1, b, b', a, d, e, f, C, D, E, F = Polygon(B, B', 6)
G = (8, -6)
g = Segment(A, G)
h = Line(B, g)
i = Line(F, g)
j = Line(B', g)
k = Line(C, g)
l = Line(D, g)
m = Line(E, g)
p = Circle(B, g)
H = Intersect(p, h, 2)
n = Segment(B, H)
q = Circle(B', g)
I = Intersect(q, j, 2)
r = Circle(C, g)
J = Intersect(r, k, 2)
s = Circle(D, g)
K = Intersect(s, l, 2)
t = Circle(E, g)
L = Intersect(t, m, 2)
c_1 = Circle(F, g)
M = Intersect(c_1, i, 2)
a_1 = Segment(H, I)
b_1 = Segment(I, J)
d_1 = Segment(J, K)
e_1 = Segment(K, L)
f_1 = Segment(L, M)
g_1 = Segment(M, H)
h_1 = Segment(B', I)
i_1 = Segment(C, J)
j_1 = Segment(D, K)
k_1 = Segment(E, L)
l_1 = Segment(F, M)
N = Point(xAxis)
O = (0, -12)
m_1 = Line(N, O)
n_1 = Line(B, m_1)
p_1 = Line(C, D)
q_1 = Line(K, p_1)
D' = Dilate(D, 0.14285714285714285, K)
K' = Mirror(K, D')
D'' = Mirror(D', K')
K'' = Mirror(K', D'')
D''' = Mirror(D'', K'')
K''' = Mirror(K'', D''')
r_1 = Line(D'', p_1)
P = Intersect(m_1, p_1)
Q = Intersect(n_1, r_1)
s_1 = Line(Q, P)
R = Intersect(k, s_1)
S = Intersect(s_1, l)
t_1 = Segment(R, S)
a_2 = Line(D, E)
T = Intersect(m_1, a_2)
b_2 = Line(S, T)
U = Intersect(b_2, m)
c_2 = Segment(U, S)
d_2 = Line(F, E)
V = Intersect(d_2, m_1)
e_2 = Line(V, U)
W = Intersect(e_2, i)
f_2 = Segment(U, W)
g_2 = Line(W, t_1)
Z = Intersect(h, g_2)
h_2 = Segment(W, Z)
i_2 = Line(Z, c_2)
A_1 = Intersect(j, i_2)
j_2 = Segment(Z, A_1)
k_2 = Segment(R, A_1)
mnohoúhelník2, z, a_3, r_2, s_2, u, w = Polygon(Z, A_1, R, S, U, W)