V Mongeově projekci zobrazte sdružené 
průměty hranolu ABCDEFGH se čtvercovou 
podstavou ležící v rovině σ určenou 
úhlopříčkou AC a výškou tělesa v. 

rozvržení stránky

hlavní přímky

otočení - poloměr

otočení - afinita

nárys podstavy

výška

viditelnost

rovina podstavy 3D

3D model

0

x_{1,2}

σ_z

n_2σ

N_2

h_2σ

A_2

A

z_A

N'_2

C_2

C

(A)

(A')

z_A

S

S_2

S

N''_2

h''_2σ

B_2

D_2

(E)

(E')

E

F

G

H

E_2

F_2

G_2

H_2

1=2

2

1

3=4

3

4

j = false
o = true
t = true
u = true
t_1 = true
w = true
o_1 = true
w_3 = false
o_4 = true
šířka_{st} = 18 (slider from 0 to 21, step 0.5)
výška_{st} = 27 (slider from 0 to 29.7, step 0.5)
v = 8 (slider from 0 to 10, step 0.5)
O = Intersect(xAxis, yAxis)
B_3 = Point(xAxis)
a = Line(O, B_3)
b = OrthogonalLine(O, a)
L = Point(a)
c = Circle(L, šířka_{st})
D_3 = Intersect(c, a, 2)
d_6 = OrthogonalLine(L, a)
e = OrthogonalLine(D_3, a)
H = Point(b)
f = Circle(H, výška_{st})
F = Intersect(f, b, 1)
g = OrthogonalLine(H, b)
vzdalenostHO = Distance(H, O)
vzdalenostLO = Distance(L, O)
HL = Intersect(d_6, g)
HP = Intersect(e, g)
h = OrthogonalLine(F, b)
U_1 = Intersect(e, h)
DL = Intersect(h, d_6)
j_8 = Segment(HL, HP)
k_8 = Segment(HP, U_1)
vzdalenostAC = Distance(HL, HP)
vzdalenostAE = Distance(HL, DL)
d = Segment(L, O)
i_1 = Segment(O, H)
l_8 = Segment(U_1, DL)
m_8 = Segment(DL, HL)
vzdalenostEO{1,2} = Distance(H, O)
x_{1,2} = Point(a)
Z_1 = Point(a)
i_8 = Segment(x_{1,2}, Z_1)
vzdalenostO{1,2}E = Distance(O, H)
text2: "šířka stránky = " + vzdalenostAC + "
výška stránky = " + vzdalenostAE + "
|H0| = " + vzdalenostHO + "
|L0| = " + vzdalenostLO + ""
σ_x = Point(a)
σ_y = Point(b)
r_5 = Segment(O, σ_y)
k = Line(σ_x, σ_y)
p_1σ = Ray(σ_x, σ_y)
σ_z = Point(b)
s_5 = Segment(O, σ_z)
l = Line(σ_x, σ_z)
n_2σ = Ray(σ_x, σ_z)
text3: "σ(" + (x(σ_x)) + ";" + ((-y(σ_y))) + ";" + (y(σ_z)) + ")"
A_1 = (-7, -4)
q = OrthogonalLine(A_1, a)
W = Intersect(q, a)
j_3 = Segment(A_1, W)
text4: "A(" + (x(A_1)) + ";" + ((-y(A_1))) + ";?)"
C_1 = (-1, -3)
l_3 = Segment(A_1, C_1)
text5: "C(" + (x(C_1)) + ";" + ((-y(C_1))) + ";?)"
text6: "v=" + v + ""
a_1 = OrthogonalLine(C_1, a)
K_1 = Intersect(a_1, a)
n_3 = Segment(C_1, K_1)
t_3 = Circle(O, s_5, xAxis)
L_1, M_1 = Intersect(zAxis, t_3)
i_4 = Line(σ_x, L_1)
u_1 = Plane(σ_x, O, L_1)
v_1 = Plane(σ_x, σ_y, L_1)
m = Line(A_1, k)
N_1 = Intersect(a, m)
h_1σ = Ray(N_1, A_1)
n = OrthogonalLine(N_1, a)
N_2 = Intersect(l, n)
r_3 = Segment(N_1, N_2)
b_5 = OrthogonalLine(N_1, xOyPlane)
O_1 = Intersect(b_5, i_4)
s_6 = Segment(N_1, O_1)
h_2σ = Line(N_2, a)
t_6 = Line(O_1, xAxis)
A_2 = Intersect(h_2σ, q)
s_3 = Segment(W, A_2)
b_7 = OrthogonalLine(W, xOyPlane)
P_1 = Intersect(t_6, b_7)
f_7 = Segment(W, P_1)
h_7 = OrthogonalLine(A_1, xOyPlane)
i_7 = OrthogonalLine(P_1, u_1)
Q_1 = Intersect(h_7, i_7)
j_7 = Segment(A_1, Q_1)
k_7 = Segment(P_1, Q_1)
l_7 = Line(Q_1, O_1)
r = Line(C_1, k)
N'_1 = Intersect(a, r)
h'_1σ = Ray(N'_1, C_1)
s = OrthogonalLine(N'_1, a)
N'_2 = Intersect(l, s)
a_4 = Segment(N'_1, N'_2)
m_7 = OrthogonalLine(N'_1, xOyPlane)
R_1 = Intersect(m_7, i_4)
n_7 = Segment(N'_1, R_1)
h'_2σ = Line(N'_2, a)
p_7 = Line(R_1, xAxis)
C_2 = Intersect(a_1, h'_2σ)
b_4 = Segment(K_1, C_2)
q_7 = OrthogonalLine(K_1, xOyPlane)
T_1 = Intersect(q_7, p_7)
r_7 = Segment(K_1, T_1)
n_8 = Segment(P_1, T_1)
s_7 = OrthogonalLine(C_1, xOyPlane)
t_7 = OrthogonalLine(T_1, u_1)
V_1 = Intersect(s_7, t_7)
a_8 = Segment(V_1, C_1)
b_8 = Segment(V_1, T_1)
c_8 = Line(R_1, V_1)
m_3 = Segment(A_2, C_2)
d_8 = Segment(Q_1, V_1)
b_1 = OrthogonalLine(A_1, k)
δ = Angle(k, b_1)
s_1σ = Intersect(b_1, a)
c_4 = Ray(s_1σ, A_1)
s_σ = OrthogonalLine(Q_1, p_1σ, space)
θ = Angle(p_1σ, s_σ)
P_1s = Intersect(b_1, k)
c_1 = Circle(A_1, Segment[W, A_2])
z_A = Segment(W, A_2)
e_8 = Segment(Q_1, A_1)
K, M = Intersect(c_1, m)
p = Segment(M, A_1)
η = Angle(P_1s, A_1, K)
d_4 = Segment(A_1, K)
f_8 = CircumcircleArc(K, Q_1, M)
g_2 = Line(P_1s, K)
r_A = Segment(P_1s, K)
d_1 = Line(M, P_1s)
e_1 = Circle(P_1s, M)
A'_o, A_o = Intersect(e_1, b_1)
g_8 = CircumcircleArc(A_o, Q_1, A'_o)
f_1 = Line(A_1, C_1)
i = Intersect(k, f_1)
j_4 = Segment(C_1, i)
b_9 = Segment(V_1, i)
g_1 = Line(i, A_o)
k_4 = Segment(i, A_o)
h_1 = OrthogonalLine(C_1, k)
C_o = Intersect(g_1, h_1)
l_4 = Segment(C_1, C_o)
S_1 = Midpoint(A_1, C_1)
j_1 = OrthogonalLine(S_1, k)
S_o = Intersect(g_1, j_1)
m_4 = Segment(S_1, S_o)
n_1 = Line(A_2, C_2)
n_4 = Segment(A_2, C_2)
q_1 = OrthogonalLine(S_1, a)
S_2 = Intersect(q_1, n_1)
p_4 = Segment(S_1, S_2)
W_1 = Intersect(xAxis, p_4)
p_8 = Segment(S_1, W_1)
q_8 = OrthogonalLine(W_1, xOyPlane)
I_2 = Intersect(q_8, n_8)
r_8 = Segment(W_1, I_2)
s_8 = OrthogonalLine(S_1, xOyPlane)
J_2 = Intersect(s_8, d_8)
t_8 = Segment(S_1, J_2)
a_9 = Segment(I_2, J_2)
h_8 = OrthogonalLine(W_1, xOyPlane)
k_1 = OrthogonalLine(S_o, g_1)
p_1 = Circle(S_o, A_o)
B_o, D_o = Intersect(p_1, k_1)
q_4 = Segment(B_o, D_o)
ε = Angle(A_o, S_o, D_o)
mnohoúhelník1, a_o, b_o, c_o, d_o = Polygon(A_o, B_o, C_o, D_o)
ii = Intersect(k_1, k)
r_4 = Segment(ii, B_o)
l_1 = Line(ii, S_1)
s_4 = Segment(ii, S_1)
c_9 = Segment(ii, J_2)
m_1 = OrthogonalLine(B_o, k)
B_1 = Intersect(m_1, l_1)
t_4 = Segment(B_o, B_1)
d_9 = OrthogonalLine(B_1, xOyPlane)
B = Intersect(d_9, c_9)
e_9 = Segment(B_1, B)
D_1 = Mirror(B_1, S_1)
a_5 = Segment(S_1, D_1)
f_9 = OrthogonalLine(D_1, xOyPlane)
D = Intersect(f_9, v_1)
g_9 = Segment(B, D)
h_9 = Segment(D_1, D)
ι = Angle(d_8, g_9)
q_3 = Segment(B_1, D_1)
mnohoúhelník2, a_2, b_2, c_2, d_2 = Polygon(A_1, B_1, C_1, D_1)
mnohoúhelník8, q_9, b_{10}, v_2, d_{10} = Polygon(Q_1, B, V_1, D)
r_1 = Line(B_1, k)
N''_1 = Intersect(r_1, a)
h''_1σ = Segment(B_1, N''_1)
s_1 = OrthogonalLine(N''_1, a)
N''_2 = Intersect(s_1, l)
c_5 = Segment(N''_1, N''_2)
i_9 = OrthogonalLine(N''_1, xOyPlane)
K_2 = Intersect(i_9, i_4)
j_9 = Segment(N''_1, K_2)
h''_2σ = Line(N''_2, a)
k_9 = Line(K_2, xAxis)
e_2 = OrthogonalLine(B_1, a)
B_2 = Intersect(e_2, h''_2σ)
d_5 = Segment(B_1, B_2)
l_9 = OrthogonalLine(B_1, u_1)
L_2 = Intersect(l_9, u_1)
m_9 = Segment(B_1, L_2)
n_9 = OrthogonalLine(L_2, xOyPlane)
M_2 = Intersect(n_9, k_9)
s_9 = Segment(B, M_2)
p_9 = Segment(L_2, M_2)
f_2 = Line(B_2, S_2)
D_2 = Mirror(B_2, S_2)
e_5 = Segment(B_2, D_2)
O_2 = Mirror(M_2, I_2)
r_9 = Segment(M_2, O_2)
t_9 = Segment(D, O_2)
mnohoúhelník3, a_3, b_3, c_3, d_3 = Polygon(A_2, B_2, C_2, D_2)
mnohoúhelník9, p_{10}, m_{10}, t_{10}, o_2 = Polygon(P_1, M_2, T_1, O_2)
h_2 = OrthogonalLine(K, g_2)
k_2 = Circle(K, v)
R, S = Intersect(k_2, h_2)
α = Angle(P_1s, K, R)
i_2 = OrthogonalLine(R, b_1)
E_1 = Intersect(i_2, b_1)
f_5 = Segment(R, E_1)
ζ = Angle(R, E_1, A_1)
g_5 = Segment(A_1, E_1)
a_{10} = OrthogonalLine(Q_1, v_1)
c_{10} = OrthogonalLine(E_1, xOyPlane)
P_2 = Intersect(c_{10}, a_{10})
e_{10} = Segment(E_1, P_2)
f_{10} = Segment(Q_1, P_2)
p_2 = Circle(B_1, Segment[A_1, E_1])
T, F_1 = Intersect(p_2, m_1)
h_5 = Segment(B_1, F_1)
e_{11} = OrthogonalLine(B, v_1)
f_{11} = OrthogonalLine(F_1, xOyPlane)
W_2 = Intersect(f_{11}, e_{11})
g_{11} = Segment(B, W_2)
q_2 = Circle(C_1, Segment[A_1, E_1])
U, G_1 = Intersect(q_2, h_1)
i_5 = Segment(C_1, G_1)
h_{11} = OrthogonalLine(V_1, v_1)
i_{11} = OrthogonalLine(G_1, xOyPlane)
Z_2 = Intersect(h_{11}, i_{11})
j_{11} = Segment(V_1, Z_2)
j_2 = OrthogonalLine(D_1, k)
r_2 = Circle(D_1, Segment[A_1, E_1])
V, H_1 = Intersect(r_2, j_2)
j_5 = Segment(D_1, H_1)
k_{11} = OrthogonalLine(D, v_1)
l_{11} = OrthogonalLine(H_1, xOyPlane)
A_3 = Intersect(k_{11}, l_{11})
m_{11} = Segment(D, A_3)
mnohoúhelník4, e_3, f_3, g_3, h_3 = Polygon(E_1, F_1, G_1, H_1)
mnohoúhelník11, p_{11}, w_2, z_2, a_{12} = Polygon(P_2, W_2, Z_2, A_3)
l_2 = OrthogonalLine(A_2, l)
β = Angle(l, l_2)
A = Intersect(l_2, l)
k_5 = Ray(A_2, A)
g_{10} = OrthogonalLine(P_1, i_4, space)
κ = Angle(g_{10}, i_4)
m_2 = OrthogonalLine(E_1, a)
E_2 = Intersect(l_2, m_2)
Q_2 = Intersect(xAxis, m_2)
h_{10} = OrthogonalLine(Q_2, xOyPlane)
R_2 = Intersect(h_{10}, g_{10})
i_{10} = Segment(R_2, Q_2)
l_5 = Segment(E_1, E_2)
m_5 = Segment(A_2, E_2)
j_{10} = Segment(E_1, Q_2)
k_{10} = Segment(P_2, R_2)
n_2 = OrthogonalLine(B_2, l)
γ = Angle(l, n_2)
s_2 = Circle(B_2, Segment[A_2, E_2])
F_2, Z = Intersect(s_2, n_2)
n_5 = Segment(B_2, F_2)
l_{10} = Line(M_2, g_{10})
n_{10} = Line(R_2, p_{10})
T_2 = Intersect(n_{10}, l_{10})
q_{10} = Segment(M_2, T_2)
r_{10} = Line(T_1, g_{10})
s_{10} = Line(T_2, m_{10})
U_2 = Intersect(s_{10}, r_{10})
a_{11} = Segment(T_1, U_2)
t_2 = OrthogonalLine(C_2, l)
k_3 = Circle(C_2, Segment[A_2, E_2])
G_2, I_1 = Intersect(k_3, t_2)
p_5 = Segment(C_2, G_2)
i_3 = OrthogonalLine(D_2, l)
p_3 = Circle(D_2, Segment[A_2, E_2])
H_2, J_1 = Intersect(p_3, i_3)
q_5 = Segment(D_2, H_2)
b_{11} = Line(O_2, g_{10})
c_{11} = Line(R_2, o_2)
V_2 = Intersect(c_{11}, b_{11})
d_{11} = Segment(O_2, V_2)
mnohoúhelník5, e_4, f_4, g_4, h_4 = Polygon(E_2, F_2, G_2, H_2)
mnohoúhelník10, r_{11}, t_{11}, u_2, v_3 = Polygon(R_2, T_2, U_2, V_2)
w_1, C_3, E_3, F_3, G_3, stena1, stena3, stena4, stena2, stena5, hrana1, hrana3, hrana2, hrana4, hrana5, hrana7, hrana8, hrana6 = Prism(mnohoúhelník8, 1.0E-4)
o_3, H_3, I_3, J_3, K_3, stena6, stena8, stena9, stena7, stena10, hrana9, hrana10, hrana11, hrana12, hrana13, hrana15, hrana16, hrana14 = Prism(stena5, g_{11})
mnohoúhelník6, a_6, e_6, f_6, g_6, c_6, d_7 = Polygon(A_1, E_1, F_1, G_1, C_1, D_1)
mnohoúhelník7, a_7, b_6, c_7, g_7, h_6, e_7 = Polygon(A_2, B_2, C_2, G_2, H_2, E_2)
mnohoúhelník12, p_{12}, r_{12}, v_4, u_3, t_{12}, m_{12} = Polygon(P_1, R_2, V_2, U_2, T_1, M_2)
C = Intersect(j_5, b_2)
t_5 = OrthogonalLine(C, i_8)
E = Intersect(q_5, t_5)
G = Intersect(t_5, b_3)
i_6 = Segment(C, E)
j_6 = Segment(D_1, H_1)
k_6 = Segment(E_1, H_1)
l_6 = Segment(H_1, G_1)
I = Intersect(c_3, n_5)
J = Intersect(r_3, mnohoúhelník7)
m_6 = OrthogonalLine(I, i_8)
N = Intersect(m_6, t_4)
P = Intersect(c_2, c_6)
Q = Intersect(m_6, c_2)
n_6 = Segment(I, N)
p_6 = Segment(B_2, F_2)
n_{11} = Segment(M_2, T_2)
q_6 = Segment(E_2, F_2)
r_6 = Segment(F_2, G_2)
q_{11} = Segment(U_2, T_2)
s_{11} = Segment(T_2, R_2)