Rotační kužel
Author: Radka Hamříková
Date: 11. leden 2012

Sestrojte průmět rotačního kužele, který má osu o = UV, U [0;-4.5;2], V [4;0;7]. Podstava prochází bodem M [-1;1;2] a hlavní vrchol leží v průmětně.

o_1

V_1(7)

U_1(2)

M_1(2)

h_1^α(2)

= s_1^α

2

(U)

(V)

(o)

W_1

(2)

(s)

P_1

(S)

S_1

p_1^α

[M]

[S]

r

A_1

B_1

I

II

b

C_1

D_1

E_1

F_1

A = Point(xAxis)
B = (0, -4.5)
a = Line(A, B)
C = (-1, -1)
b = OrthogonalLine(C, a)
D = Intersect(a, b)
c = OrthogonalLine(B, a)
d = OrthogonalLine(A, a)
e = Circle(B, 2)
f = Circle(A, 7)
E = Intersect(e, c, 2)
F = Intersect(f, d, 2)
g = Line(E, F)
h = Circle(D, 2)
W = Intersect(a, g)
G = Intersect(h, b, 2)
i = OrthogonalLine(G, g)
H = Intersect(a, i)
I = Intersect(g, i)
j = OrthogonalLine(I, a)
J = Intersect(a, j)
k = OrthogonalLine(H, a)
l = Segment(J, C)
m = OrthogonalLine(C, l)
n = OrthogonalLine(J, l)
p = Circle(C, 2)
K, L = Intersect(p, m)
q = Circle(J, I)
M = Intersect(q, n, 2)
r = Segment(L, M)
s = Circle(J, r)
N, O = Intersect(s, j)
t = Circle(C, r)
P, Q = Intersect(t, a)
a_1 = Line(Q, C)
R = Intersect(j, a_1)
b_1 = Segment(R, C)
c_1 = Circle(J, b_1)
S, T = Intersect(c_1, a)
d_1 = Circle(S, r)
U, V = Intersect(d_1, j)
e_1 = Ellipse(U, V, C)
f_1, g_1 = Tangent(W, e_1)
Z = Intersect(e_1, g_1)
A_1 = Intersect(e_1, f_1)
h_1 = Segment(W, Z)
i_1 = Segment(W, A_1)