地球的經線與緯線
Author: 藍邦偉　老師

顯示:座標軸

地球的經度與緯度

O = (7.894685559762031, 4.371366576527852)
α = 1.2740903539558606 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
β = 1.4486232791552935 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, sin(β))
u = Vector(O, X_{unit})
v = Vector(O, Y_{unit})
w = Vector(O, Z_{unit})
L = 8 (slider from 1 to 10, step 1)
z = Vector(O - L * u, O + L * u)
a = Vector(O - L * v, O + L * v)
b = Vector(O - L * w, O + L * w)
c = false
r = 5 (slider from 1 to 5, step 1)
N: O + r * w
S: O - r * w
n = 0.311 (slider from 0.0010 to 1, step 0.0010)
m = 0.311 (slider from 0.0010 to 1, step 0.0010)
list2 = Sequence(CurveCartesian[x(O + r * cos(t) * cos(s) * u + r * cos(t) * sin(s) * v + r * sin(t) * w), y(O + r * cos(t) * cos(s) * u + r * cos(t) * sin(s) * v + r * sin(t) * w), s, 0, 6.28], t, -1.57, 1.57, n)
list1 = Sequence(CurveCartesian[x(O + r * cos(t) * cos(s) * u + r * cos(t) * sin(s) * v + r * sin(t) * w), y(O + r * cos(t) * cos(s) * u + r * cos(t) * sin(s) * v + r * sin(t) * w), t, -1.57, 1.57], s, 0, 6.28, m)
φ = 2.7576202181510405 rad (slider from 1.5707963267948966 to 4.71238898038469, step 0.017453292519943295)
θ = 4.71238898038469 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
A: O + r * (-cos(θ) * cos(φ)) * u - r * sin(θ) * cos(φ) * v + r * sin(φ) * w
d = Segment(O, A)
φ_1: φ - 180°
文字1: "南緯" + φ_1 + "度"
φ_2: abs(φ - 180°)
文字2: "北緯" + φ_2 + "度"
A_B: O + r * (-cos(θ) * cos(φ)) * u - r * sin(θ) * cos(φ) * v
e = Segment(A, A_B)
f = Segment(O, A_B)
equator = CurveCartesian(x(O + r * cos(s) * u + r * sin(s) * v), y(O + r * cos(s) * u + r * sin(s) * v), s, 0, 6.283185307179586)
g = CurveCartesian(x(O + r * cos(φ) * cos(s) * u + r * cos(φ) * sin(s) * v + r * sin(φ) * w), y(O + r * cos(φ) * cos(s) * u + r * cos(φ) * sin(s) * v + r * sin(φ) * w), s, 0, 6.28319)
latitude_1 = CurveCartesian(x(O + r * cos(t) * cos(θ) * u + r * cos(t) * sin(θ) * v + r * sin(t) * w), y(O + r * cos(t) * cos(θ) * u + r * cos(t) * sin(θ) * v + r * sin(t) * w), t, -1.5707963267948966, 1.5707963267948966)
Meridian_1 = CurveCartesian(x(O + r * cos(t) * u + r * sin(t) * w), y(O + r * cos(t) * u + r * sin(t) * w), t, -1.5707963267948966, 1.5707963267948966)
Meridian_2 = CurveCartesian(x(O - r * cos(t) * u + r * sin(t) * w), y(O - r * cos(t) * u + r * sin(t) * w), t, -1.5707963267948966, 1.5707963267948966)
文字3: "西經" + θ + "度"
文字4: "東經" + (360° - θ) + "度"