101指考數學甲多選第9題
Author: 藍邦偉　老師

單位向量

座標軸

x

y

z

$A$

$B$

$C$

$D$

$E$

$F$

$G$

$H$

$第%v步$

$ 101數甲多選9 $

O = (10.452452622254713, 0.48618365973915423)
β = 1.3962634015954636 rad (slider from 0 to 6.283185307179586, step 0.1*°)
Z_{unit}: O + (0, sin(β))
w = Vector(O, Z_{unit})
α = 4.276056667386108 rad (slider from 0 to 6.283185307179586, step 0.1*°)
X_{unit}: O + (cos(α), sin(α) * cos(β))
u = Vector(O, X_{unit})
Y_{unit}: O + (-1 * sin(α), cos(α) * cos(β))
v = Vector(O, Y_{unit})
L = 3 (slider from 1 to 10, step 1)
c = false
d = false
Q_2: 0.2 * Corner[2] + 0.8 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
poly1, h, q_1, q_4, i = Polygon(Corner[1], Q_2, Q_3, Corner[4])
A: O - u - v + w
B: O + u - v + w
C: O + u + v + w
D: O - u + v + w
E: O - u - v - w
F: O + u - v - w
G: O + u + v - w
H: O - u + v - w
a_1, a_2 = SDLine(C, G, B, D)
a_3, a_4 = SDLine(D, H, C, A)
a_5, a_6 = SDLine(B, F, A, C)
a_7, a_8 = SDLine(A, E, D, B)
b_1, b_2 = SDLine(D, C, A, H)
b_3, b_4 = SDLine(B, C, F, A)
b_5, b_6 = SDLine(A, D, B, E)
b_7, b_8 = SDLine(B, A, C, F)
c_1, c_2 = SDLine(F, E, B, G)
c_3, c_4 = SDLine(G, F, C, H)
c_5, c_6 = SDLine(E, H, A, F)
c_7, c_8 = SDLine(H, G, D, E)
d_0, d_1 = SDLine(B, C, F, A)
d_2, d_3 = SDLine(C, G, B, D)
d_4, d_5 = SDLine(D, C, A, H)
e_1, e_2 = SDLine(B, F, A, C)
e_3, e_4 = SDLine(A, B, E, D)
d_8, d_9 = SDLine(D, B, E, C)
e_9, e_a = SDLine(A, C, B, E)
J: O + u
K: O + w
poly4_1 = Poly_B3(C, B, J)
poly4_2 = Poly_B3(K, B, C)
poly4_3 = Poly_B3(K, C, J)
poly4_4 = Poly_B3(B, K, J)
e_c, e_b = SDLine(A, F, C, B)
e_5, e_6 = SDLine(B, C, F, A)
e_7, e_8 = SDLine(C, F, B, A)
d_a, d_b = SDLine(D, G, C, B)
d_6, d_7 = SDLine(B, G, D, C)
n = 0 (slider from 0 to 4, step 1)
a = Vector(E - L * v, E + L * v)
z = Vector(E - L * u, E + L * u)
b = Vector(E - L * w, E + L * w)
Poly2_1 = Poly_B3(A, B, C)
Poly2_2 = Poly_B3(C, B, F)
Poly2_3 = Poly_B3(B, A, F)
Poly2_4 = Poly_B3(A, C, F)
Poly3_1 = Poly_B3(D, C, G)
Poly3_2 = Poly_B3(C, B, G)
Poly3_3 = Poly_B3(B, C, D)
Poly3_4 = Poly_B3(B, D, G)

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)

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')