Lissajousovy obrazce - bodové vykreslení
Date: 5 Říjen 2013

Lissajousovy obrazce

Křivka

Malý náhled

Stopa

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$90°$

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$135°$

$150°$

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$180°$

$195°$

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$255°$

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$285°$

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$345°$

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t = 0

Automatický posun

rychlost autom. posunu

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$60°$

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$150°$

$210°$

$240°$

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$330°$

ruční posun:
jezdcem myší

Δφ = 90 (slider from 0 to 360, step 15)
ω_x = 2 (slider from 1 to 5, step 1)
ω_y = 1 (slider from 1 to 5, step 1)
t = 2.6179939 (slider from 0 to 6.283185307179586, step 0.26179939)
A_1: (sin(ω_x * t), sin(ω_y * t + Δφ * π / 180))
B_1: (0, sin(ω_y * t + Δφ * π / 180))
C: (sin(ω_x * t), 0)
b = Segment(A_1, B_1)
c = Segment(A_1, C)
f = Polynomial({(1, -1), (1, 1), (-1, 1), (-1, -1)})
text1 = FractionText(ω_x / ω_y)
d = true
g = false
D = (-1.618543908374668, -0.6362051282928071)
h = Segment((-1, 0), (1, 0))
i = Segment((0, -1), (0, 1))
j = Segment((-1, -1), (1, -1))
k = Segment((-1, 1), (1, 1))
l = Segment((-1, -1), (-1, 1))
m = Segment((1, -1), (1, 1))
n = true
delta: Δφ * 180 / π
AA: (sin(ω_x * t), sin(ω_y * t + Δφ * π / 180))
E = (2.2, 0)
p = Circle(E, 1)
B: (2.2 + cos(ω_y * t + Δφ * π / 180), sin(ω_y * t + Δφ * π / 180))
q = Segment(AA, B)
u = Vector(E, B)
H = (0, -2.2)
r = Circle(H, 1)
A: (sin(ω_x * t), -2.2 - cos(ω_x * t))
s = Segment(C, A)
v = Vector(H, A)
a = CurveCartesian(sin(ω_x * t), sin(ω_y * t + Δφ * π / 180), t, 0, 12.56637)
e = CurveCartesian(0.35 * sin(ω_x * t) + x(D), 0.35 * sin(ω_y * t + Δφ * π / 180) + y(D), t, 0, 12.56637)
J: (x(E) + 1, 0)
J' = Rotate(J, 15*°, E)
J'_1 = Rotate(J, 30*°, E)
J'_2 = Rotate(J, 45*°, E)
J'_3 = Rotate(J, 60*°, E)
J'_4 = Rotate(J, 75*°, E)
J'_5 = Rotate(J, 90*°, E)
J'_6 = Rotate(J, 105*°, E)
J'_7 = Rotate(J, 120*°, E)
J'_8 = Rotate(J, 135*°, E)
J'_9 = Rotate(J, 150*°, E)
J'_{10} = Rotate(J, 165*°, E)
J'_{11} = Rotate(J, 180*°, E)
J'_{12} = Rotate(J, 195*°, E)
J'_{13} = Rotate(J, 210*°, E)
J'_{14} = Rotate(J, 225*°, E)
J'_{15} = Rotate(J, 240*°, E)
J'_{16} = Rotate(J, 255*°, E)
J'_{17} = Rotate(J, 270*°, E)
J'_{18} = Rotate(J, 285*°, E)
J'_{19} = Rotate(J, 300*°, E)
J'_{20} = Rotate(J, 315*°, E)
J'_{21} = Rotate(J, 330*°, E)
J'_{22} = Rotate(J, 345*°, E)
t_1 = Segment(J'_{11}, J)
a_1 = Segment(J'_5, J'_{17})
K = (0, -3.2)
K' = Rotate(K, 90*°, H)
K'_1 = Rotate(K, 180*°, H)
K'_2 = Rotate(K, 270*°, H)
w = Vector(E, Rotate[J, Δφ°, E])
b_1 = Segment(K'_2, K')
c_1 = Segment(K'_1, K)
time = 0
ma = 0
G: (20, ω_x + ω_y + Δφ + n + ma)
on = 0
anim = 0.52 (slider from 0.01 to 1.5, step 0.01)
text2: " \frac{ ω_x }{ω_y }\;=   " + (LaTeX[text1]) + ""
F = (1.2589833460111597, -1.8164098743634511)
f_1(x) = 0.25 * sin(4 * ω_y * (x - x(F)) + Δφ * π / 180) + y(F) - 0.65
f_2(x) = 0.25 * sin(4 * ω_x * (x - x(F))) + y(F)
g_1 = Function(f_1, x(F), x(F) + 2)
h_1 = Function(f_2, x(F), x(F) + 2)
I: F + (0, 0.3)
L: I + (2, 0)
M: F + (0, -0.95)
N: M + (2, 0)
mnohoúhelník1, m_1, n_1, l_1, i_1 = Polygon(M, N, L, I)
text4: "t=" + (LaTeX[t * 12 / π]) + ""
K5 = Rotate(K, 15*°, H)
K'_3 = Rotate(K, 30*°, H)
K'_4 = Rotate(K, 45*°, H)
K'_5 = Rotate(K, 60*°, H)
K'_6 = Rotate(K, 75*°, H)
K'_7 = Rotate(K, 105*°, H)
K'_8 = Rotate(K, 120*°, H)
K'_9 = Rotate(K, 135*°, H)
K'_{10} = Rotate(K, 150*°, H)
K'_{11} = Rotate(K, 165*°, H)
K'_{12} = Rotate(K, 195*°, H)
K'_{13} = Rotate(K, 210*°, H)
K'_{14} = Rotate(K, 225*°, H)
K'_{15} = Rotate(K, 240*°, H)
K'_{16} = Rotate(K, 255*°, H)
K'_{17} = Rotate(K, 285*°, H)
K'_{18} = Rotate(K, 300*°, H)
K'_{19} = Rotate(K, 315*°, H)
K'_{20} = Rotate(K, 330*°, H)
K'_{21} = Rotate(K, 345*°, H)
d_1 = Line(J'_4, J'_6)
e_1 = Line(J'_3, J'_7)
j_1 = Line(J'_2, J'_8)
O = Intersect(l, d_1)
P = Intersect(l, e_1)
Q = Intersect(l, j_1)
k_1 = Segment(J'_4, O)
p_1 = Segment(P, J'_3)
q_1 = Segment(Q, J'_2)
r_1 = Line(J'_1, J'_9)
s_1 = Line(J', J'_{10})
R = Point(t_1)
a_2 = Line(R, J'_{11})
b_2 = Line(J'_{22}, J'_{12})
c_2 = Line(J'_{21}, J'_{13})
d_2 = Line(J'_{20}, J'_{14})
e_2 = Line(J'_{19}, J'_{15})
g_2 = Line(J'_{18}, J'_{16})
S = Intersect(r_1, l)
T = Intersect(s_1, l)
U = Intersect(a_2, l)
V = Intersect(b_2, l)
W = Intersect(c_2, l)
Z = Intersect(d_2, l)
C_1 = Intersect(e_2, l)
D_1 = Intersect(g_2, l)
h_2 = Segment(J'_1, S)
i_2 = Segment(J', T)
j_2 = Segment(J'_{21}, W)
k_2 = Segment(J'_{20}, Z)
l_2 = Segment(C_1, J'_{19})
m_2 = Segment(J'_{18}, D_1)
n_2 = Segment(J'_{22}, V)
p_2 = OrthogonalLine(J'_{17}, m)
E_1 = Intersect(m, p_2)
q_2 = Segment(E_1, J'_{17})
r_2 = OrthogonalLine(J'_5, m)
F_1 = Intersect(r_2, m)
s_2 = Segment(F_1, J'_5)
t_2 = OrthogonalLine(K'_2, j)
a_3 = OrthogonalLine(K', q_2)
G_1 = Intersect(t_2, j)
H_1 = Intersect(j, a_3)
b_3 = Segment(K'_2, G_1)
c_3 = Segment(H_1, K')
d_3 = Line(K'_{17}, K'_{16})
e_3 = Line(K'_{18}, K'_{15})
f_3 = Line(K'_{19}, K'_{14})
g_3 = Line(K'_{21}, K'_{12})
h_3 = Line(K5, K'_{11})
i_3 = Line(K'_3, K'_{10})
j_3 = Line(K'_4, K'_9)
k_3 = Line(K'_5, K'_8)
l_3 = Line(K'_6, K'_7)
m_3 = Line(K'_{13}, K'_{20})
I_1 = Intersect(d_3, k)
J_1 = Intersect(e_3, k)
K_1 = Intersect(f_3, k)
L_1 = Intersect(m_3, k)
M_1 = Intersect(g_3, k)
N_1 = Intersect(h_3, k)
O_1 = Intersect(i_3, k)
P_1 = Intersect(j_3, k)
Q_1 = Intersect(k_3, k)
R_1 = Intersect(l_3, k)
n_3 = Segment(I_1, K'_{17})
p_3 = Segment(J_1, K'_{18})
q_3 = Segment(K_1, K'_{19})
r_3 = Segment(L_1, K'_{20})
s_3 = Segment(M_1, K'_{21})
t_3 = Segment(N_1, K5)
a_4 = Segment(O_1, K'_3)
b_4 = Segment(P_1, K'_4)
c_4 = Segment(Q_1, K'_5)
d_4 = Segment(R_1, K'_6)
S_1 = Intersect(k, l)
T_1 = Intersect(m, k)
U_1 = Intersect(j, m)
V_1 = Intersect(j, l)
mnohoúhelník2, s_4, t_4, u_1, v_1 = Polygon(S_1, T_1, U_1, V_1)
text6: "Δφ=" + (LaTeX[Δφ]) + "°"