球的極平面
Author: 藍邦偉  老師

P

顯示座標軸

x

y

z

顯示單位向量

顯示xy平面

o = 5.6 (slider from 3 to 10, step 0.1)
r = 3.1 (slider from 3 to 5, step 0.1)
O = (2.0477502250278685, -3.8355160524830896)
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))
D: (3 * B + A) / 4
a = Segment(A, B)
E = Point(a)
t = 2.3736477827122884 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
C: (3 * A + B) / 4
E' = Rotate(Translate[E, Vector[C, D]], 90*°, D)
c = Circle(C, E)
c' = Translate(c, Vector[C, D])
G = Point(c')
c'' = Rotate(c', 270*°, C)
F = Point(c'')
A' = Rotate(A, 270*°, C)
B' = Rotate(B, 270*°, C)
a' = Segment(A', B')
D' = Rotate(D, 270*°, C)
b = Segment(D', F)
E'' = Rotate(E', 270*°, C)
α = Angle(E'', D', F)
d_1 = Segment(D, G)
β = Angle(G, D, E')
K: C + (0, b * cos(β))
K' = Translate(K, Vector[C, O])
w = Vector(O, K')
P_0: O + o * w
A_0: O + r * w
p = Circle(O, A_0)
s, c_1 = Tangent(P_0, p)
N = Intersect(p, c_1)
M = Intersect(p, s)
P = Midpoint(M, N)
l = Segment(P, M)
J: C + (b * cos(α + 90°), b * sin(α + 90°) * sin(β))
J' = Translate(J, Vector[C, O])
v = Vector(O, J')
I: C + (b * cos(α), b * sin(α) * sin(β))
I' = Translate(I, Vector[C, O])
u = Vector(O, I')
e = Segment(C, K)
f = Segment(C, I)
g = Segment(C, J)
L = 10 (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
k = false
P_1: O + L * u + L * v
P_2: O + L * u - L * v
P_3: O - L * u - L * v
P_4: O - L * u + L * v
多邊形1, p_1, p_2, p_3, p_4 = Polygon(P_1, P_2, P_3, P_4)
j = false
Q_4: O + L * v - L * w
R_1: O + L * u + L * w
R_2: O - L * u + L * w
R_3: O - L * u - L * w
R_4: O + L * u - L * w
P_b: P + l * cos(120°) * u + l * sin(120°) * v
P_c: P + l * cos(240°) * u + l * sin(240°) * v
P_d: P + l * cos(300°) * u + l * sin(300°) * v
P_e: P + l * cos(340°) * u + l * sin(340°) * v
P_a: P + l * cos(0°) * u + l * sin(0°) * v
e_1 = Conic(P_d, P_e, P_a, P_b, P_c)
d = Ray(P_0, M)
m = Ray(P_0, N)
Q_0: P + (r + 2) * u + (r + 2) * v
Q_1: P - (r + 2) * u + (r + 2) * v
Q_2: P - (r + 2) * u - (r + 2) * v
Q_3: P + (r + 2) * u - (r + 2) * v
多邊形2, q_0, q_1, q_2, q_3 = Polygon(Q_0, Q_1, Q_2, Q_3)