投影的面積
Author: 藍邦偉  老師

x

y

z

單位向量

座標軸

θ

投影的面積

A'=A×|cosθ|

a_3 = 3.5 (slider from 1 to 5, step 0.1)
θ = 1.0471975511965976 rad (slider from 0*° to 180*°, step 0.1*°)
O = (7.606577069852329, -1.4541347270615526)
β = 1.4835298641951802 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
Z_{unit}: O + (0, sin(β))
w = Vector(O, Z_{unit})
α = 4.014257279586958 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
Y_{unit}: O + (-1 * sin(α), cos(α) * cos(β))
v = Vector(O, Y_{unit})
X_{unit}: O + (cos(α), sin(α) * cos(β))
u = Vector(O, X_{unit})
a_2 = 2.1 (slider from 1 to 5, step 0.1)
a_1 = 2 (slider from 1 to 5, step 0.1)
L = 6 (slider from 1 to 10, step 1)
C_1: O + (L - 1) * u + (L - 1) * v
C_2: O + (L - 1) * v
C_8 = Mirror(C_2, O)
C_4: O + (L - 1) * u
C_7 = Mirror(C_1, C_4)
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 = false
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)
C_3: O
poly1, i, j, k, l = Polygon(C_7, C_1, C_2, C_8)
h = Segment(C_4, C_3)
C_5: O + (L - 1) * u + (L - 1) * v * cos(θ) + (L - 1) * sin(θ) * w
C_6: O + (L - 1) * cos(θ) * v + (L - 1) * sin(θ) * w
poly2, c_5, c_6, c_7, c_8 = Polygon(C_5, C_4, C_3, C_6)
m = Segment(C_4, C_5)
n = Segment(C_4, C_1)
γ = Angle(C_1, C_4, C_5)
H_a: O + a_1 * v * cos(θ) + u
H_b: O + a_2 * v * cos(θ) + 4 * u
H_c: O + a_3 * v * cos(θ) + 3 * u
A_b: O + a_2 * v * cos(θ) + a_2 * sin(θ) * w + 4 * u
p_1 = Segment(A_b, H_b)
A_a: O + a_1 * v * cos(θ) + a_1 * sin(θ) * w + u
p_2 = Segment(A_a, H_a)
A_c: O + a_3 * v * cos(θ) + a_3 * sin(θ) * w + 3 * u
p_3 = Segment(A_c, H_c)
Tri1, a_c, a_a, a_b = Polygon(A_a, A_b, A_c)
Tri2, h_c, h_a, h_b = Polygon(H_a, H_b, H_c)
text1: "目前兩平面夾角為" + (LaTeX[θ]) + ""
text3: "" + (LaTeX[Tri1 * abs(cos(θ))]) + "=" + (LaTeX[Tri1]) + "×|cos" + (LaTeX[θ]) + "|=" + (LaTeX[Tri1]) + "×" + (LaTeX[abs(cos(θ))]) + ""