三角測量概念
Author: 藍邦偉  老師

N

E

1. 方向與方位

2. 仰角與俯角

Eye

3. 立體測量

東北

東南

西南

西北

N

E

P

東北

西北

西南

東南

8

16

東北東

北北東

西南西

南南西

北北西

西北西

南南東

東南東

開始縮小

4. 縮小燈

y_1 = 0.36400000000000093 (slider from 0 to 2, step 0.1)
x_1 = 0.8732000000000016 (slider from 0 to 4, step 0.1)
O: (x(0.4 * Corner[1.0] + 0.6 * Corner[2.0]), y(0.5 * (Corner[1.0] + Corner[3.0])))
v = Vector((x(O), y(Corner[1.0])), (x(O), y(Corner[3.0])))
A_1 = Corner(1.0)
A_4 = Corner(4.0)
A_3: 1.0 / 5.0 * Corner[3.0] + 4.0 / 5.0 * A_4
A_2: 1.0 / 5.0 * Corner[2.0] + 4.0 / 5.0 * A_1
多邊形1, a_1, a_2, a_3, a_4 = Polygon(A_1, A_2, A_3, A_4)
g = Segment(A_2, A_3)
c = Circle(O, 3.0)
A = Point(c)
a = Ray(O, A)
P_a: O + (3.0, 0.0)
P_b: O + (0.0, 3.0)
P_c: O - (3.0, 0.0)
P_d: O - (0.0, 3.0)
α_1 = Angle(P_a, O, A)
文字4: "東" + α_1 + "北"
文字5: "北" + (90.0° - α_1) + "東"
β_1 = Angle(A, O, P_c)
文字6: "西" + β_1 + "北"
文字7: "北" + (90.0° - β_1) + "西"
γ = Angle(P_c, O, A)
文字8: "西" + γ + "南"
文字9: "南" + (90.0° - γ) + "西"
δ = Angle(A, O, P_a)
文字10: "東" + δ + "南"
文字11: "南" + (90.0° - δ) + "東"
B = (-3.52, 4.28)
C: B + (0.0, 0.4)
n = 0 (slider from 0 to 6, step 1)
J: (x_1, y_1)
E_2: J + (1.7, 1.9)
L_1: y = y(E_2)
E = Point(L_1)
L_2: x = x(E)
F = Point(L_2)
G = Point(L_2)
e = Segment(E_2, F)
f = Segment(E_2, G)
ε = Angle(E, E_2, F)
ζ = Angle(G, E_2, E)
文字13: "仰角" + ε
文字14: "俯角" + ζ
α = 5.323254218582705 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
β = 1.7453292519943295 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
X_{unit}: O + (cos(α), sin(α) * cos(β))
Y_{unit}: O + (-sin(α), cos(α) * cos(β))
Z_{unit}: O + (0.0, sin(β))
u' = Vector(O, X_{unit})
v' = Vector(O, Y_{unit})
w' = Vector(O, Z_{unit})
L = 4 (slider from 1 to 10, step 1)
w = Vector(O - L * u', O + L * u')
z = Vector(O - L * v', O + L * v')
b = Vector(O, O + L * w')
Q_a: O + L * u' + L * v'
Q_b: O - L * u' + L * v'
Q_c: O - L * u' - L * v'
Q_d: O + L * u' - L * v'
多邊形2, q_a, q_b, q_c, q_d = Polygon(Q_a, Q_b, Q_c, Q_d)
u = Vector((x(Corner[1.0]), y(O)), (x(Corner[3.0]), y(O)))
h = CurveCartesian(x(O + (L - 1.0) * cos(t) * u' + (L - 1.0) * sin(t) * v'), y(O + (L - 1.0) * cos(t) * u' + (L - 1.0) * sin(t) * v'), t, 0.0, 6.28319)
P_1 = Point(h)
D = (-3.9, 5.404)
NE: O + (3.0 * cos(45.0°), 3.0 * sin(45.0°))
NW: O + (3.0 * cos(135.0°), 3.0 * sin(135.0°))
SW: O + (3.0 * cos(225.0°), 3.0 * sin(225.0°))
SE: O + (3.0 * cos(315.0°), 3.0 * sin(315.0°))
i = Vector(O, NE)
j = Vector(O, NW)
k = Vector(O, SW)
l = Vector(O, SE)
m = false
d = Vector(O, P_1)
p = Vector(O, Q_a)
q = Vector(O, Q_d)
r = Vector(O, Q_c)
s = Vector(O, Q_b)
o = false
ENE: O + (3.0 * cos(22.5°), 3.0 * sin(22.5°))
NNE: O + (3.0 * cos(67.5°), 3.0 * sin(67.5°))
WSW = Mirror(ENE, O)
SSW = Mirror(NNE, O)
NNW: O + (3.0 * cos(112.5°), 3.0 * sin(112.5°))
WNW: O + (3.0 * cos(157.5°), 3.0 * sin(157.5°))
NNW' = Mirror(NNW, O)
WNW' = Mirror(WNW, O)
t_1 = Vector(O, NNE)
u_1 = Vector(O, ENE)
v_1 = Vector(O, WNW')
w_1 = Vector(O, NNW')
z_1 = Vector(O, SSW)
b_1 = Vector(O, WSW)
c_1 = Vector(O, WNW)
d_1 = Vector(O, NNW)
e_1 = false
t = 0 (slider from 0 to 0.5, step 0.05)
H = (4.54, -1.48)
g_1: x = x(H)
I = Point(g_1)
h_1: y = y(H)
P = Point(h_1)
i_1 = Segment(I, P)
j_1 = Segment(I, H)
k_1 = Segment(H, P)
Q_2 = Corner(2.0)
B_2: Q_2 - t * Vector[A_2, Q_2]
K = (1.78, -1.92)
f_1: y = y(K)
l_1: x = x(K)
M = Point(l_1)
H_1: H + 2.0 * t * Vector[H, K]
I_1: I + 2.0 * t * Vector[I, M]
J_1: K + Distance[M, K] / Distance[I, H] * (Distance[H, P], 0.0)
m_1 = Segment(I_1, H_1)
J_2: P + 2.0 * t * Vector[P, J_1]
n_1 = Segment(H_1, J_2)
p_1 = Segment(I_1, J_2)
多邊形3, a_5, q_1, r_1, a_6 = Polygon(A_2, Corner[2.0], Corner[3.0], A_3)
多邊形4, s_1, b_2, c_2, d_2 = Polygon(A_2, A_3, Corner[3.0], Corner[2.0])