正立方體中的正八面體
Author: 藍邦偉  老師

x

y

z

顯示xy平面

顯示單位向量

顯示座標軸

Reset

A: (x((Corner[3] + 39 * Corner[4]) / 40), y((Corner[1] + 9 * Corner[4]) / 10))
B: (x((4 * Corner[3] + 16 * Corner[4]) / 20), y((Corner[1] + 9 * Corner[4]) / 10))
a = Segment(A, B)
C: (3 * A + B) / 4
D: (3 * B + A) / 4
E = Point(a)
c = Circle(C, E)
c' = Translate(c, Vector[C, D])
A' = Rotate(A, 270*°, C)
B' = Rotate(B, 270*°, C)
a' = Segment(A', B')
c'' = Rotate(c', 270*°, C)
D' = Rotate(D, 270*°, C)
E' = Rotate(Translate[E, Vector[C, D]], 90*°, D)
E'' = Rotate(E', 270*°, C)
F = Point(c'')
G = Point(c')
α = Angle(E'', D', F)
b = Segment(D', F)
d = Segment(D, G)
β = Angle(G, D, E')
I: C + (b * cos(α), b * sin(α) * sin(β))
J: C + (b * cos(α + 90°), b * sin(α + 90°) * sin(β))
K: C + (0, b * cos(β))
e = Segment(C, K)
f = Segment(C, I)
g = Segment(C, J)
O = (0.1495072113418034, -2.0299189092251257)
I' = Translate(I, Vector[C, O])
J' = Translate(J, Vector[C, O])
K' = Translate(K, Vector[C, O])
L = 8 (slider from 1 to 10, step 1)
I'' = Dilate(I', L, O)
J'' = Dilate(J', L, O)
K'' = Dilate(K', L, O)
I''' = Dilate(I'', -1, O)
J''' = Dilate(J'', -1, O)
K''' = Dilate(K'', -1, O)
u' = Vector(I''', I'')
v' = Vector(J''', J'')
w' = Vector(K''', K'')
h = Segment(D', E'')
i = Segment(D, E')
軌跡1 = Locus(I, F)
L_{axis}: L
j = false
w = Vector(O, K')
u = Vector(O, I')
v = Vector(O, J')
k = false
list1 = Sequence(CurveCartesian[x(O + t * u + s * v), y(O + t * u + s * v), t, -L, L], s, -L, L, 1)
list2 = Sequence(CurveCartesian[x(O + t * u + s * v), y(O + t * u + s * v), s, -L, L], t, -L, L, 1)
A_1: O + 4 * u + 4 * v + 4 * w
A_2: O + 4 * u + 4 * v - 4 * w
A_3: O + 4 * u - 4 * v + 4 * w
A_4: O - 4 * u + 4 * v + 4 * w
A_6: O + 4 * u - 4 * v - 4 * w
A_7: O - 4 * u + 4 * v - 4 * w
A_8: O - 4 * u - 4 * v - 4 * w
A_5: O - 4 * u - 4 * v + 4 * w
Q_1: O + 4 * u
Q_2: O - 4 * u
Q_4: O - 4 * v
Q_3: O + 4 * v
Q_5: O + 4 * w
Q_6: O - 4 * w
l = false
m, n = SDLine(A_3, A_6, A_5, A_1)
p, q = SDLine(A_1, A_2, A_3, A_4)
t, a_1 = SDLine(A_5, A_8, A_4, A_3)
r, s = SDLine(A_4, A_7, A_1, A_5)
b_1, c_1 = SDLine(A_1, A_3, A_4, A_2)
d_1, e_1 = SDLine(A_4, A_1, A_5, A_7)
s_1, t_1 = SDLine(A_5, A_4, A_3, A_8)
a_2, b_2 = SDLine(A_3, A_5, A_1, A_6)
c_2, d_2 = SDLine(A_7, A_8, A_2, A_4)
e_2, f_2 = SDLine(A_8, A_6, A_7, A_5)
g_2, h_2 = SDLine(A_2, A_7, A_6, A_1)
i_2, j_2 = SDLine(A_6, A_2, A_8, A_3)
f_1, k_2 = SDLine(Q_5, Q_4, Q_2, Q_1)
g_1, l_2 = SDLine(Q_5, Q_1, Q_4, Q_3)
i_1, m_2 = SDLine(Q_5, Q_3, Q_1, Q_2)
h_1, n_2 = SDLine(Q_5, Q_2, Q_3, Q_4)
k_1, p_2 = SDLine(Q_1, Q_3, Q_6, Q_5)
l_1, q_2 = SDLine(Q_3, Q_2, Q_6, Q_5)
m_1, r_2 = SDLine(Q_2, Q_4, Q_6, Q_5)
j_1, s_2 = SDLine(Q_4, Q_1, Q_6, Q_5)
n_1, t_2 = SDLine(Q_1, Q_6, Q_4, Q_3)
p_1, a_3 = SDLine(Q_3, Q_6, Q_1, Q_2)
r_1, b_3 = SDLine(Q_4, Q_6, Q_2, Q_1)
q_1, c_3 = SDLine(Q_2, Q_6, Q_3, Q_4)

Tool: SDLine
Input: A, B, C, D
Output: g, h

b: sgn(sin(Angle[D, B, A]))
a: sgn(sin(Angle[A, B, C]))
c: sgn(a + b + 0.5)
d: sqrt(c)
e: sqrt(-c)
E = Midpoint(A, B)
A' = Dilate(A, d, E)
B' = Dilate(B, d, E)
g = Segment(A', B')
A'_1 = Dilate(A, e, E)
B'_1 = Dilate(B, e, E)
h = Segment(A'_1, B'_1)