3D 座標架的製作
Author: 藍邦偉  老師

正八面體

單位向量

單位點

座標軸

xy平面

顯示作法

x

y

z

α = 0.12217304763960307 rad (slider from 0 to 6.283185307179586, step 0.1*°)
β = 3.162536604613725 rad (slider from 0 to 6.283185307179586, step 0.1*°)
L = 8 (slider from 1 to 10, step 1)
O = (25.436735430238524, 12.873189461541301)
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})
x_{Axis} = Vector(O - L * u, O + L * u)
y_{Axis} = Vector(O - L * v, O + L * v)
z_{Axis} = Vector(O - L * w, O + L * w)
多邊形1, d, e, f, g = Polygon(O + L * u + L * v, O - L * u + L * v, O - L * u - L * v, O + L * u - L * v)
h = false
i = false
j = false
k = false
l = true
A_1: O + 3 * w
A_2: O - 3 * w
A_3: O + 2 * u - 2 * v
A_4: O - 2 * u - 2 * v
A_5: O - 2 * u + 2 * v
A_6: O + 2 * u + 2 * v
a = Segment(A_1, A_4)
b = Segment(A_3, A_4)
c = Segment(A_4, A_5)
m = Segment(A_3, A_6)
n = Segment(A_5, A_6)
p = Segment(A_1, A_3)
q = Segment(A_1, A_5)
r = Segment(A_1, A_6)
s = Segment(A_6, A_2)
t = Segment(A_5, A_2)
a_1 = Segment(A_3, A_2)
b_1 = Segment(A_4, A_2)
poly1, a_6, a_2, a_3 = Polygon(A_1, A_3, A_6)
poly2, a_4, a_5, a_7 = Polygon(A_1, A_4, A_3)
poly3, a_8, a_9, a_{10} = Polygon(A_1, A_5, A_4)
poly4, a_{11}, a_{12}, a_{13} = Polygon(A_1, A_6, A_5)
poly5, a_{14}, a_{15}, a_{16} = Polygon(A_4, A_2, A_3)
poly6, a_{17}, a_{18}, a_{19} = Polygon(A_3, A_6, A_2)
poly7, a_{20}, a_{21}, a_{22} = Polygon(A_6, A_5, A_2)
poly8, a_{23}, a_{24}, a_{25} = Polygon(A_5, A_2, A_4)