三角測量
Author: 藍邦偉 老師

於A,B,C三點測量艾菲爾鐵塔塔頂的仰角

x

y

z

單位向量

座標軸

C

B

A

三角測量

O = (7.176106550425464, 0.8661905547789785)
P_2 = Corner(2.0)
β = 1.5009831567151233 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
α = 3.5255650890285457 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
Y_{unit}: O + (-1.0 * sin(α), cos(α) * cos(β))
v = Vector(O, Y_{unit})
X_{unit}: O + (cos(α), sin(α) * cos(β))
u = Vector(O, X_{unit})
n = CurveCartesian(x(O + 9.0 * cos(θ) * u + 9.0 * sin(θ) * v), y(O + 9.0 * cos(θ) * u + 9.0 * sin(θ) * v), θ, 0.0, 2.1362830044410597)
Z_{unit}: O + (0.0, sin(β))
w = Vector(O, Z_{unit})
L = 10 (slider from 1 to 10, step 1)
a = Vector(O - L * v, O + L * v)
b = Vector(O - L * w, O + L * w)
z = Vector(O - L * u, O + L * u)
A_1: O + L * u
B_1: O + L * v
Z: O + L * w
c = false
d = false
Q_1 = Corner(1.0)
Q_2: Q_1 + (4.7, 0.0)
A = (5.416521272302538, 0.998159450638198)
Q_3 = (3.480977466367319, 0.9541698186851248)
e = Ray(A, Q_3)
Q_4 = Point(e)
多邊形1, q_1, q_2, q_3, q_4 = Polygon(Q_1, Q_2, Q_3, Q_4)
B = (5.284552376443319, 1.8119676417700512)
Q_5 = (3.480977466367319, 2.5597913849722946)
f = Ray(B, Q_5)
Q_6 = Point(f)
多邊形2, q_6, q_5, q_7, q_8 = Polygon(Q_6, Q_5, Q_3, Q_4)
C = (8.605769588900342, 1.0201542666147345)
P_4 = (10.849240818507072, 0.8441957388024419)
g = Ray(C, P_4)
P_3 = Point(g)
P_1: P_2 - (4.8, 0.0)
多邊形3, p_1, p_2, p_3, p_4 = Polygon(P_1, P_2, P_3, P_4)
D = (7.176106550425464, 1.3720713222393197)
P_5 = (10.849240818507072, 2.031915801535417)
h = Ray(D, P_5)
P_6 = Point(h)
多邊形4, p_5, p_6, p_7, p_8 = Polygon(P_5, P_6, P_3, P_4)
P_7 = Corner(3.0)
P_8 = (10.783256370577464, 9.312199889769023)
多邊形5, p_9, p_{10}, p_{11}, p_{12} = Polygon(P_5, P_6, P_7, P_8)
Q_7 = Corner(4.0)
Q_8 = (3.5469619142969293, 9.312199889769023)
多邊形6, q_9, q_{10}, q_{11}, q_{12} = Polygon(Q_5, Q_6, Q_7, Q_8)
K_2 = Point(n)
j = Segment(O, K_2)
E = Point(b)
k = Segment(O, E)
m = Segment(E, K_2)
F = Point(n)
G = Point(n)
i = Segment(O, F)
l = Segment(O, G)
p = Segment(E, F)
q = Segment(E, G)

Tool: Poly_B3
Input: A, B, C
Output: poly1'

α = Angle(C, B, A)
d: sqrt(sgn(sin(α)))
A' = Dilate(A, d, A)
B' = Dilate(B, d, A)
C' = Dilate(C, d, A)
poly1', c', a', b' = Polygon(A', B', C')

Tool: Poly_B5
Input: A, B, C, D, E
Output: poly1'

poly1, a, b, c, d, e = Polygon(A, B, C, D, E)
F = Midpoint(b)
G = Midpoint(d)
α = Angle(G, F, A)
f: sqrt(sgn(sin(α)))
A' = Dilate(A, f, A)
B' = Dilate(B, f, A)
C' = Dilate(C, f, A)
D' = Dilate(D, f, A)
E' = Dilate(E, f, A)
poly1', a', b', c', d', e' = Polygon(A', B', C', D', E')