Date: 22 janeiro 2016

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Blue

Cyan

Green

Orange

Yellow

Red

Graph of deviation angle

Deviation angles

todas = false
viol = false
azul = false
ciano = false
verd = false
lar = false
amar = false
verm = true
k = 1 (slider from 1 to 10, step 0.1)
C = (0.14448147107635323, 3.980523622867139)
D: (x(C), y(C) - 9)
k_3 = Line(C, D)
c = Segment(C, D)
F = Point(c)
d = Ray(F, C)
F_2 = Point(d)
A = (6.8977282243231075, 3.305198947542463)
B: (x(A), y(A) - 5)
β = 1.53588974175501 rad (slider from 0 to 180*°, step 0.017453292519943295)
F' = Rotate(F_2, (-β), F)
f = Ray(F, F')
α = 0.5235987755982988 rad (slider from 5*° to 60*°, step 0.017453292519943295)
B'_1 = Rotate(B, (-α), A)
a = Ray(A, B'_1)
H = Intersect(a, f)
e = OrthogonalLine(H, a)
nverm = 1.33
B' = Rotate(B, α, A)
γ = Angle(B, A, B')
δ = Angle(B'_1, A, B)
b = Ray(A, B')
ε = Angle(F', F, F_2)
u = Vector(F, H)
G = Intersect(e, k_3)
ζ = Angle(F, H, G)
angverm: asin(sin(ζ) / nverm)
I = Point(e)
I' = Rotate(I, (-angverm), H)
η = Angle(I', H, I)
g = Ray(H, I')
J = Intersect(b, g)
j = Segment(H, J)
l = OrthogonalLine(J, b)
K = Intersect(l, k_3)
θ = Angle(H, J, K)
angverm2: asin((sin(θ) * nverm))
L = Point(l)
L' = Rotate(L, (-angverm2), J)
ι = Angle(L', J, L)
m = Ray(J, L')
M = Point(m)
n = Segment(J, M)
nlar: 1.33 + (0.001 * k)
N, p, O, q = Raio(A, C, F, α, β, nlar)
namar: 1.33 + (0.003 * k)
nverd: 1.33 + (0.005 * k)
R, t, S, a_1 = Raio(A, C, F, α, β, nverd)
nciano: 1.33 + (0.007 * k)
T, b_1, U, c_1 = Raio(A, C, F, α, β, nciano)
nazul: 1.33 + (0.009 * k)
V, d_1, W, e_1 = Raio(A, C, F, α, β, nazul)
nviol: 1.33 + (0.011 * k)
Z, f_1, A_1, g_1 = Raio(A, C, F, α, β, nviol)
v = Vector(F, H)
H' = Mirror(H, l)
J' = Mirror(J, l)
j' = Segment(H', J')
H'_1 = Mirror(H, l)
J'_1 = Mirror(J, l)
j'_1 = Segment(H'_1, J'_1)
h = OrthogonalLine(O, b)
B_1 = Intersect(h, k_3)
κ = Angle(H, O, B_1)
q' = Mirror(q, h)
h_1 = OrthogonalLine(S, b)
D_1 = Intersect(h_1, k_3)
μ = Angle(H, S, D_1)
i_1 = Mirror(a_1, h_1)
j_1 = OrthogonalLine(U, b)
E_1 = Intersect(j_1, k_3)
k_1 = Mirror(c_1, j_1)
ν = Angle(H, U, E_1)
l_1 = OrthogonalLine(W, b)
F_1 = Intersect(l_1, k_3)
ξ = Angle(H, W, F_1)
m_1 = Mirror(e_1, l_1)
n_1 = OrthogonalLine(A_1, b)
G_1 = Intersect(n_1, k_3)
H_1 = Mirror(G_1, g_1)
p_1 = Mirror(g_1, n_1)
bol: {If[verm, 1, 0], If[lar, 1, 0], If[amar, 1, 0], If[verd, 1, 0], If[ciano, 1, 0], If[azul, 1, 0], If[viol, 1, 0]}
ο = Angle(H, A_1, G_1)
nbol = Sum(bol)
rgb = If(nbol ≟ 0, {1, 1, 1}, {(Element[bol, 1] + Element[bol, 2] + Element[bol, 3] + (0.5 * Element[bol, 7])) / nbol, ((0.5 * Element[bol, 2]) + Element[bol, 3] + Element[bol, 4] + Element[bol, 5]) / nbol, (Element[bol, 5] + Element[bol, 6] + Element[bol, 7]) / nbol})
max = Max(rgb)
E = Point(n)
q_1 = Ray(J, E)
r = 10 (slider from -5 to 10, step 1)
s = Circle(J, r)
P = Intersect(s, q_1, 1)
i = Segment(J, P)
Q = Point(p)
r_1 = Ray(O, Q)
s_1 = Circle(O, r)
C_1 = Intersect(s_1, r_1, 1)
t_1 = Segment(O, C_1)
I_1, a_2, J_1, b_2 = Raio(A, C, F, α, β, namar)
c_2 = Ray(J_1, I_1)
d_2 = Circle(J_1, r)
K_1 = Intersect(d_2, c_2, 1)
e_2 = Segment(J_1, K_1)
f_2 = OrthogonalLine(J_1, b)
L_1 = Intersect(f_2, k_3)
λ = Angle(H, J_1, L_1)
g_2 = Mirror(b_2, f_2)
h_2 = Ray(S, R)
k_2 = Circle(S, r)
M_1 = Intersect(k_2, h_2, 1)
i_2 = Segment(S, M_1)
j_2 = Ray(U, T)
p_2 = Circle(U, r)
N_1 = Intersect(p_2, j_2, 1)
l_2 = Segment(U, N_1)
m_2 = Ray(W, V)
q_2 = Circle(W, r)
O_1 = Intersect(q_2, m_2, 1)
n_2 = Segment(W, O_1)
r_2 = Ray(A_1, Z)
s_2 = Circle(A_1, r)
P_1 = Intersect(s_2, r_2, 1)
t_2 = Segment(A_1, P_1)
incpar: (asin((sin(α) * nverm)) * 180 / π)
betapar: 90° - incpar° + α
Q_1: (x(A), y(A) - 5)
a_3 = Ray(A, Q_1)
ρ = Angle(H, A, B)
o = If(abs(β - betapar)  <  2, β = betapar, β = β)
R_1 = Point(a_3)
b_3 = Segment(A, R_1)
w = Vector(J, M)
σ = Angle(w, u)
S_1 = (4.3349576615525445, -3.725104082760564)
T_1: (x(S_1) + 1, y(S_1))
c_3 = Line(S_1, T_1)
z = If(abs(β - betapar)  <  2, β = betapar, β = β)
U_1: (x(S_1) + (0.09 * β / °), y(S_1))
o_1 = If(abs(β - betapar)  <  2, β = betapar, β = β)
V_1: (x(U_1), σ / ° - 20)
Lugar_Geométrico1 = Locus(V_1, β)
u_1 = If(abs(β - betapar)  <  2, β = betapar, β = β)
W_1: (x(S_1) + (0.15 * β / °), y(S_1))
Z_1: (x(W_1), σ / ° - 25)
Lugar_Geométrico2 = Locus(Z_1, β)
v_1 = If(abs(β - betapar)  <  2, β = betapar, β = β)
A_2: J + u
d_3 = Segment(J, A_2)
texto1: "" + σ + ""
B_2: O + u
e_3 = Segment(O, B_2)
τ = Angle(C_1, O, B_2)
C_2: J_1 + u
f_3 = Segment(J_1, C_2)
υ = Angle(K_1, J_1, C_2)
D_2: S + u
g_3 = Segment(S, D_2)
ϕ = Angle(M_1, S, D_2)
E_2: U + u
h_3 = Segment(U, E_2)
χ = Angle(N_1, U, E_2)
G_2: W + u
i_3 = Segment(W, G_2)
ψ = Angle(O_1, W, G_2)
H_2: A_1 + u
j_3 = Segment(A_1, H_2)
ω = Angle(P_1, A_1, H_2)
w_1 = If(abs(β - betapar)  <  2, β = betapar, β = β)
z_1 = If(abs(β - betapar)  <  2, β = betapar, β = β)
o_2 = If(abs(β - betapar)  <  2, β = betapar, β = β)
u_2 = If(abs(β - betapar)  <  2, β = betapar, β = β)
v_2 = If(abs(β - betapar)  <  2, β = betapar, β = β)
w_2 = If(abs(β - betapar)  <  2, β = betapar, β = β)
z_2 = If(abs(β - betapar)  <  2, β = betapar, β = β)
I_2: (x(W_1), σ / ° - (0.9 * α / °))
Lugar_Geométrico3 = Locus(I_2, β)
l_3 = If(abs(β - betapar)  <  2, β = betapar, β = β)
J_2: (x(W_1), τ / ° - (0.9 * α / °))
Lugar_Geométrico4 = Locus(J_2, β)
m_3 = If(abs(β - betapar)  <  2, β = betapar, β = β)
texto3: "" + τ + ""
K_2: (x(W_1), υ / ° - (0.9 * α / °))
Lugar_Geométrico5 = Locus(K_2, β)
n_3 = If(abs(β - betapar)  <  2, β = betapar, β = β)
texto4: "" + υ + ""
L_2: (x(W_1), ϕ / ° - (0.9 * α / °))
Lugar_Geométrico6 = Locus(L_2, β)
o_3 = If(abs(β - betapar)  <  2, β = betapar, β = β)
texto5: "" + ϕ + ""
M_2: (x(W_1), χ / ° - (0.9 * α / °))
Lugar_Geométrico7 = Locus(M_2, β)
p_3 = If(abs(β - betapar)  <  2, β = betapar, β = β)
texto6: "" + χ + ""
N_2: (x(W_1), ψ / ° - (0.9 * α / °))
Lugar_Geométrico8 = Locus(N_2, β)
q_3 = If(abs(β - betapar)  <  2, β = betapar, β = β)
texto7: "" + ψ + ""
O_2: (x(W_1), ω / ° - (0.9 * α / °))
Lugar_Geométrico9 = Locus(O_2, β)
r_3 = If(abs(β - betapar)  <  2, β = betapar, β = β)
texto8: "" + ω + ""
s_3 = If(abs(β - betapar)  <  2, β = betapar, β = β)
t_3 = true
u_3 = If(abs(β - betapar)  <  2, β = betapar, β = β)
v_3 = If(abs(β - betapar)  <  2, β = betapar, β = β)
w_3 = If(abs(β - betapar)  <  2, β = betapar, β = β)
z_3 = If(abs(β - betapar)  <  2, β = betapar, β = β)
a_4 = If(abs(β - betapar)  <  2, β = betapar, β = β)
b_4 = If(abs(β - betapar)  <  2, β = betapar, β = β)
c_4 = If(abs(β - betapar)  <  2, β = betapar, β = β)
d_4 = If(abs(β - betapar)  <  2, β = betapar, β = β)
e_4 = If(abs(β - betapar)  <  2, β = betapar, β = β)
f_4 = If(abs(β - betapar)  <  2, β = betapar, β = β)
g_4 = If(abs(β - betapar)  <  2, β = betapar, β = β)
h_4 = If(abs(β - betapar)  <  2, β = betapar, β = β)
i_4 = If(abs(β - betapar)  <  2, β = betapar, β = β)
j_4 = If(abs(β - betapar)  <  2, β = betapar, β = β)
k_4 = If(abs(β - betapar)  <  2, β = betapar, β = β)
l_4 = If(abs(β - betapar)  <  2, β = betapar, β = β)

Tool: Raio
Input: A, C, E, α, β, nverm
Output: M, n, J, j

D: (x(C), y(C) - 9)
k = Line(C, D)
c = Segment(C, D)
d = Ray(E, C)
F = Point(d)
B: (x(A), y(A) - 5)
F' = Rotate(F, (-β), E)
f = Ray(E, F')
B'_1 = Rotate(B, (-α), A)
a = Ray(A, B'_1)
H = Intersect(a, f)
e = OrthogonalLine(H, a)
B' = Rotate(B, α, A)
b = Ray(A, B')
G = Intersect(e, k)
ζ = Angle(E, H, G)
angverm: asin(sin(ζ) / nverm)
I = Point(e)
I' = Rotate(I, (-angverm), H)
g = Ray(H, I')
J = Intersect(b, g)
j = Segment(H, J)
l = OrthogonalLine(J, b)
K = Intersect(l, k)
θ = Angle(H, J, K)
angverm2: asin((sin(θ) * nverm))
L = Point(l)
L' = Rotate(L, (-angverm2), J)
m = Ray(J, L')
M = Point(m)
n = Segment(J, M)