與三座標平面相切的球面
Author: 藍邦偉  老師

x

y

z

單位向量

座標軸

座標平面

與三座標平面
相切的球面

α = 4.101523742186674 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
β = 1.3089969389957472 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
O = (8.656357665646375, 2.361838041183465)
X_{unit}: O + (cos(α), sin(α) * cos(β))
Y_{unit}: O + (-1 * 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 = 7 (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 = true
Q_2: 0.2 * Corner[2] + 0.8 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
多邊形1, e, q_2, q_3, f = Polygon(Corner[1], Q_2, Q_3, Corner[4])
g = Segment(Q_2, Q_3)
r = 2.9 (slider from 1 to 5, step 0.1)
Q: O + r * u + r * v + r * w
h = Circle(Q, r)
i = CurveCartesian(x(Q + r * cos(θ) * u + r * sin(θ) * v), y(Q + r * cos(θ) * u + r * sin(θ) * v), θ, 0, 6.28319)
P_a: O + r * u + r * v
P_b: O + r * w + r * v
P_c: O + r * w + r * u
j = Segment(P_c, Q)
k = Segment(Q, P_a)
l = Segment(Q, P_b)
t: L - 1
P_1: O + t * u
P_2: O + t * v
P_3: O + t * w
P_4: O + t * w + t * u
P_5: O + t * v + t * u
P_6: O + t * v + t * w
多邊形2, o, p_1, p_5, p_2 = Polygon(O, P_1, P_5, P_2)
多邊形3, p_4, p_3, o_1, p_6 = Polygon(P_4, P_1, O, P_3)
多邊形4, p_7, p_8, p_9, o_2 = Polygon(P_3, P_6, P_2, O)
m = true

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')