微分的應用(9)
Author: 藍邦偉　老師

單位向量

座標軸

x

y

z

$ 微分的應用(9) $

t = 0.6 (slider from 0.1 to 1.4, step 0.1)
r_1: sqrt(2) * (3 + t) / 2
α = 0.7853981633974483 rad (slider from 0 to 6.283185307179586, step 0.1*°)
β = 0 rad (slider from 0 to 6.283185307179586, step 0.1*°)
O = (5.280125170468116, 2.6868102829732563)
Y_{unit}: O + (-1 * sin(α), cos(α) * cos(β))
v = Vector(O, Y_{unit})
C_4: O - 3 * sqrt(2) * v
C_2: O + 3 * sqrt(2) * v
X_{unit}: O + (cos(α), sin(α) * cos(β))
u = Vector(O, X_{unit})
C_3: O - 3 * sqrt(2) * u
M_7 = Midpoint(C_3, C_4)
D_6: M_7 + t * sqrt(2) / 2 * u - t * sqrt(2) / 2 * v
D_5: M_7 - t * sqrt(2) / 2 * u + t * sqrt(2) / 2 * v
M_6 = Midpoint(C_3, C_2)
D_3: M_6 + t * sqrt(2) / 2 * u + t * sqrt(2) / 2 * v
a_g = Segment(D_6, D_3)
C_1: O + 3 * sqrt(2) * u
M_8 = Midpoint(C_1, C_4)
D_8: M_8 - t * sqrt(2) / 2 * u - t * sqrt(2) / 2 * v
D_7: M_8 + t * sqrt(2) / 2 * u + t * sqrt(2) / 2 * v
a_e = Segment(D_5, D_7)
D_c = Intersect(a_e, a_g)
M_5 = Midpoint(C_1, C_2)
D_2: M_5 - t * sqrt(2) / 2 * u + t * sqrt(2) / 2 * v
a_c = Segment(D_2, D_8)
D_b = Intersect(a_c, a_e)
M_b = Midpoint(D_c, D_b)
Z_{unit}: O + (0, sin(β))
w = Vector(O, Z_{unit})
L = 10 (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)
c = false
d = false
Q_2: 0.6 * Corner[2] + 0.4 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
g = Segment(Q_2, Q_3)
poly1, e, f, h, i = Polygon(Corner[2], Q_2, Q_3, Corner[3])
A_0 = (11.058763186121807, -0.11252993222230499)
A_2: A_0 + (6, 0)
A_3: A_0 + (6, 6)
A_4: A_0 + (0, 6)
j = Segment(A_0, A_2)
k = Segment(A_3, A_2)
l = Segment(A_3, A_4)
m = Segment(A_0, A_4)
M_1 = Midpoint(A_0, A_2)
M_2 = Midpoint(A_3, A_2)
M_3 = Midpoint(A_3, A_4)
M_4 = Midpoint(A_0, A_4)
B_1: M_1 + (-t, 0)
B_2: M_1 + (t, 0)
B_3: M_2 - (0, t)
B_4: M_2 + (0, t)
B_6: M_3 + (t, 0)
B_5: M_3 - (t, 0)
B_7: M_4 - (0, t)
B_8: M_4 + (0, t)
n_1 = Segment(B_7, B_1)
p = Segment(B_8, B_2)
q = Segment(B_4, B_1)
r = Segment(B_3, B_2)
a_1 = Segment(B_5, B_3)
b_1 = Segment(B_5, B_8)
c_1 = Segment(B_6, B_7)
A_a = Intersect(a_1, c_1)
A_b = Intersect(p, c_1)
A_c = Intersect(p, q)
A_d = Intersect(q, a_1)
poly2, c_2, b_2, b_3 = Polygon(B_1, B_2, A_c)
poly3, d_1, b_4, b_5 = Polygon(B_3, B_4, A_d)
poly4, a_2, b_6, b_7 = Polygon(B_6, B_5, A_a)
poly5, b_8, b_9, b_{10} = Polygon(B_8, B_7, A_b)
poly6, a_3, b_{11}, b_{12} = Polygon(B_6, B_5, A_a)
poly7, b_{13}, b_{14}, b_{15} = Polygon(B_8, B_7, A_b)
poly8, c_3, b_{16}, b_{17} = Polygon(B_1, B_2, A_c)
poly9, d_2, b_{18}, b_{19} = Polygon(B_3, B_4, A_d)
l_1 = Segment(C_1, C_2)
l_2 = Segment(C_3, C_2)
l_3 = Segment(C_3, C_4)
l_4 = Segment(C_1, C_4)
D_1: M_5 + t * sqrt(2) / 2 * u - t * sqrt(2) / 2 * v
D_4: M_6 - t * sqrt(2) / 2 * u - t * sqrt(2) / 2 * v
a_a = Segment(D_1, D_4)
a_b = Segment(D_2, D_3)
a_d = Segment(D_1, D_7)
a_f = Segment(D_6, D_8)
a_h = Segment(D_4, D_5)
D_a = Intersect(a_a, a_c)
D_d = Intersect(a_a, a_g)
Tri1, d_3, d_4, d_a = Polygon(D_1, D_a, D_2)
Tri5, d_5, d_6, d_7 = Polygon(D_1, D_a, D_2)
Tri2, d_b, d_8, d_9 = Polygon(D_7, D_8, D_b)
Tri6, d_{10}, d_{11}, d_{12} = Polygon(D_7, D_8, D_b)
Tri3, d_c, d_{13}, d_{14} = Polygon(D_6, D_5, D_c)
Tri7, d_{15}, d_{16}, d_{17} = Polygon(D_6, D_5, D_c)
Tri4, d_d, d_{18}, d_{19} = Polygon(D_3, D_4, D_d)
Tri8, d_{20}, d_{21}, d_{22} = Polygon(D_3, D_4, D_d)
n = 0 (slider from 0 to 4, step 1)
b_a = Segment(C_1, D_1)
b_b = Segment(C_1, D_7)
b_c = Segment(C_4, D_8)
b_d = Segment(C_4, D_6)
b_e = Segment(C_3, D_5)
b_f = Segment(C_3, D_4)
b_g = Segment(C_2, D_3)
b_h = Segment(C_2, D_2)
M_a = Midpoint(D_a, D_b)
M_c = Midpoint(D_c, D_d)
M_d = Midpoint(D_a, D_d)
γ = 0 rad (slider from 0 to 90*°, step 0.01*°)
D_{61}: D_c - sqrt(2) * t * cos(γ) * v + sqrt(2) * t * sin(γ) * w
D_{81}: D_b - sqrt(2) * t * cos(γ) * v + sqrt(2) * t * sin(γ) * w
D_{21}: D_a + sqrt(2) * t * cos(γ) * v + sqrt(2) * t * sin(γ) * w
D_{31}: D_d + sqrt(2) * t * cos(γ) * v + sqrt(2) * t * sin(γ) * w
D_{11}: D_a + sqrt(2) * t * cos(γ) * u + sqrt(2) * t * sin(γ) * w
D_{71}: D_b + sqrt(2) * t * cos(γ) * u + sqrt(2) * t * sin(γ) * w
D_{41}: D_d - sqrt(2) * t * cos(γ) * u + sqrt(2) * t * sin(γ) * w
D_{51}: D_c - sqrt(2) * t * cos(γ) * u + sqrt(2) * t * sin(γ) * w
e_1 = Segment(D_c, D_{61})
e_2 = Segment(D_b, D_{81})
C_{41}: M_b - r_1 * cos(γ) * v + r_1 * sin(γ) * w
e_3 = Segment(C_{41}, D_{81})
e_4 = Segment(C_{41}, D_{61})
e_5 = Segment(D_c, D_{51})
e_6 = Segment(D_d, D_{41})
e_7 = Segment(D_d, D_{31})
e_8 = Segment(D_a, D_{21})
e_9 = Segment(D_a, D_{11})
e_0 = Segment(D_b, D_{71})
C_{31}: M_c - r_1 * cos(γ) * u + r_1 * sin(γ) * w
C_{21}: M_d + r_1 * cos(γ) * v + r_1 * sin(γ) * w
C_{11}: M_a + r_1 * cos(γ) * u + r_1 * sin(γ) * w
e_a = Segment(C_{31}, D_{51})
e_b = Segment(C_{31}, D_{41})
e_c = Segment(C_{21}, D_{31})
e_d = Segment(C_{21}, D_{21})
e_e = Segment(C_{11}, D_{11})
e_f = Segment(C_{11}, D_{71})
e_g = Segment(D_a, D_b)
e_h = Segment(D_c, D_b)
e_i = Segment(D_c, D_d)
e_j = Segment(D_a, D_d)
r_2: (3 - t) / sqrt(2)
M_e = Midpoint(D_{41}, D_{51})
M_f = Midpoint(D_{21}, D_{31})
M_g = Midpoint(D_{61}, D_{81})
M_h = Midpoint(D_{11}, D_{71})
δ = 0 rad (slider from 0 to 90*°, step 0.01*°)
C_{111}: M_h - r_2 * sin(δ) * u + r_2 * cos(δ) * w
C_{311}: M_e + r_2 * sin(δ) * u + r_2 * cos(δ) * w
C_{211}: M_f - r_2 * sin(δ) * v + r_2 * cos(δ) * w
C_{411}: M_g + r_2 * sin(δ) * v + r_2 * cos(δ) * w
f_1 = Segment(D_{21}, C_{211})
f_2 = Segment(D_{31}, C_{211})
f_3 = Segment(D_{41}, C_{311})
f_4 = Segment(D_{51}, C_{311})
f_5 = Segment(D_{61}, C_{411})
f_6 = Segment(D_{81}, C_{411})
f_7 = Segment(D_{71}, C_{111})
f_8 = Segment(D_{11}, C_{111})
f_a = Segment(D_{11}, D_{71})
f_b = Segment(D_{21}, D_{31})
f_c = Segment(D_{41}, D_{51})
f_d = Segment(D_{61}, D_{81})
s = Segment(B_4, B_6)
g_1 = Segment(A_2, A_3)