Řez kosého válce rovinou
Author: Radka Hamříková
Date: 2. leden 2012

Rovina řezu je α (4;-1,5;1). Válec má dolní podstavu v průmětně, střed je S [5,5,0], poloměr je r = 4, střed horní podstavy je bod S' [-2,0,9].

S'_1(9)

S_1(0)

p_1^α

1

h_1^α(1)

(S')

1

(1)

0

(O)

O_1

K'_1

L'_1

M'_1

N'_1

M_1

N_1

L_1

K_1

M_R

U_R

h_1

v_1

a

b

A_1

B_1

C_1

D_1

A = Point(xAxis)
B = (5, -5)
a = Line(A, B)
c = Circle(A, 4)
d = Circle(B, 4)
b = OrthogonalLine(A, a)
e = OrthogonalLine(B, a)
C, D = Intersect(c, b)
E, F = Intersect(d, e)
f = Segment(D, F)
g = Segment(C, E)
h = CircleArc(B, E, F)
k = CircleArc(B, F, E)
G = Point(xAxis)
H = Point(xAxis)
I = (0, 1.5)
i = Line(H, I)
j = Line(G, i)
J = Intersect(a, j)
K = Intersect(a, i)
p = Circle(A, 9)
L = Intersect(p, b, 1)
l = Line(L, B)
m = OrthogonalLine(J, a)
q = Circle(J, 1)
M = Intersect(q, m, 1)
n = Line(M, K)
N = Intersect(l, n)
r = OrthogonalLine(N, a)
O = Intersect(a, r)
s = OrthogonalLine(B, i)
t = OrthogonalLine(B, s)
P = Intersect(d, h, 1)
Q = Intersect(d, h, 1)
R = Intersect(d, h, 1)
S = Intersect(d, h)
T = Point(d)
U = Point(d)
V = Point(d)
W = Intersect(d, t, 1)
Z = Intersect(i, s)
a_1 = Line(O, Z)
b_1 = Line(U, a)
A_1 = Intersect(a_1, b_1)
c_1 = Line(T, a)
B_1 = Intersect(a_1, c_1)
d_1 = Line(O, t)
e_1 = Line(W, a)
f_1 = Line(V, a)
C_1 = Intersect(d_1, e_1)
D_1 = Intersect(d_1, f_1)
g_1 = OrthogonalLine(O, a_1)
h_1 = Circle(O, B_1)
E_1, F_1 = Intersect(h_1, g_1)
i_1 = Line(C_1, F_1)
G_1 = Midpoint(C_1, F_1)
k_1 = Circle(G_1, O)
H_1, I_1 = Intersect(k_1, i_1)
j_1 = Line(H_1, O)
l_1 = Line(I_1, O)
vzdalenostC1I1 = Distance(C_1, I_1)
m_1 = Segment(C_1, I_1)
n_1 = Segment(H_1, C_1)
vzdalenostH1C1 = Distance(H_1, C_1)
p_1 = Circle(O, 5.01)
J_1, K_1 = Intersect(p_1, j_1)
q_1 = Circle(O, 2.7)
L_1, M_1 = Intersect(q_1, l_1)
r_1 = Conic(J_1, L_1, K_1, M_1, D_1)
N_1 = (-9.6775431272844, -2.7739635670593397)
s_1 = Line(E, F)
O_1 = Intersect(e, i)
t_1 = Line(O_1, O)
P_1 = Intersect(r_1, t_1, 2)
Q_1 = (7.118430670944086, -1.5519214802169943)
R_1 = Intersect(t_1, g)
c_2 = Conic(J_1, R_1, A_1, M_1, D_1)
d_2 = Conic(K_1, L_1, M_1, R_1, A_1)
a_2 = Segment(Q_1, F)
b_2 = Segment(E, R_1)