Author: 李季樵

x

y

z

單位向量

座標軸

xy平面

$ 三角測量 $

K = 2.1 (slider from 0 to 10, step 0.1)
O = (-0.3693790145244174, -1.0319977055542495)
β = 1.2217304763960306 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
Z_{unit}: O + (0, sin(β))
w = Vector(O, Z_{unit})
α = 5.323254218582705 rad (slider from 0*° to 6.283185307179586, step 0.017453292519943295)
Y_{unit}: O + (-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})
l = 6 (slider from 0 to 10, step 0.1)
L = 1 (slider from 1 to 10, step 1)
c = Vector(O - L * w, O + L * w)
poly1, d, e, f, g = Polygon(O + L * u + L * v, O - L * u + L * v, O - L * u - L * v, O + L * u - L * v)
h_1 = false
i = false
list_1 = Sequence(O + 0.2 * l * u + 0.2 * l * v + 0.4 * K * k * w, k, 0, 10)
j = true
list_2 = Sequence(O - 0.2 * l * u + 0.2 * l * v + 0.4 * K * k * w, k, 0, 10)
list_3 = Sequence(O - 0.2 * l * u - 0.2 * l * v + 0.4 * K * k * w, k, 0, 10)
list_4 = Sequence(O + 0.2 * l * u - 0.2 * l * v + 0.4 * K * k * w, k, 0, 10)
list_5 = Sequence(Segment[Element[list_1, k], Element[list_1, k + 1]], k, 0, 10)
list_6 = Sequence(Segment[Element[list_2, k], Element[list_2, k + 1]], k, 0, 10)
list_7 = Sequence(Segment[Element[list_3, k], Element[list_3, k + 1]], k, 0, 10)
list_8 = Sequence(Segment[Element[list_4, k], Element[list_4, k + 1]], k, 0, 10)
list_a = Sequence(Segment[Element[list_1, k], Element[list_2, k]], k, 0, 11)
list_b = Sequence(Segment[Element[list_3, k], Element[list_2, k]], k, 0, 11)
list_c = Sequence(Segment[Element[list_3, k], Element[list_4, k]], k, 0, 11)
list_d = Sequence(Segment[Element[list_1, k], Element[list_4, k]], k, 0, 11)
list = Sequence(Translate[poly1, Vector[k * u]], k, 1, 10)
list_A = Sequence(Polygon[Element[list_1, k], Element[list_2, k], Element[list_2, k + 1], Element[list_1, k + 1]], k, 1, 10)
list_B = Sequence(Polygon[Element[list_2, k], Element[list_3, k], Element[list_3, k + 1], Element[list_2, k + 1]], k, 0, 10)
list_C = Sequence(Polygon[Element[list_3, k], Element[list_4, k], Element[list_4, k + 1], Element[list_3, k + 1]], k, 0, 10)
list_D = Sequence(Polygon[Element[list_4, k], Element[list_1, k], Element[list_1, k + 1], Element[list_4, k + 1]], k, 0, 10)
n = 3 (slider from 0 to floor(l), step 1)
list_{01} = Sequence(Element[list_1, 1] + k / n * Vector[Element[list_1, 1], Element[list_2, 1]], k, 1, n)
list_{02} = Sequence(Element[list_1, 11] + k / n * Vector[Element[list_1, 11], Element[list_2, 11]], k, 1, n)
list_{03} = Sequence(Element[list_2, 1] + k / n * Vector[Element[list_2, 1], Element[list_3, 1]], k, 1, n)
list_{04} = Sequence(Element[list_2, 11] + k / n * Vector[Element[list_2, 11], Element[list_3, 11]], k, 1, n)
list_{05} = Sequence(Element[list_3, 1] + k / n * Vector[Element[list_3, 1], Element[list_4, 1]], k, 1, n)
list_{06} = Sequence(Element[list_3, 11] + k / n * Vector[Element[list_3, 11], Element[list_4, 11]], k, 1, n)
list_{07} = Sequence(Element[list_4, 1] + k / n * Vector[Element[list_4, 1], Element[list_1, 1]], k, 1, n)
list_{08} = Sequence(Element[list_4, 11] + k / n * Vector[Element[list_4, 11], Element[list_1, 11]], k, 1, n)
list_{12} = Sequence(Segment[Element[list_{07}, n], Element[list_{08}, n]], n, 0, floor(l))
list_{11} = Sequence(Segment[Element[list_{05}, n], Element[list_{06}, n]], n, 0, floor(l))
list_{10} = Sequence(Segment[Element[list_{03}, n], Element[list_{04}, n]], n, 0, floor(l))
list_{09} = Sequence(Segment[Element[list_{01}, n], Element[list_{02}, n]], n, 0, floor(l))
list_E = Sequence(Polygon[Element[list_1, k], Element[list_2, k], Element[list_3, k], Element[list_4, k]], k, 0, 11)
P_1, h, k, m, p = Polygon(Element[list_1, 11], Element[list_2, 11], Element[list_3, 11], Element[list_4, 11])
poly2, q, r, s, t = Polygon(O + 8 * u + 8 * v, O - 8 * u + 8 * v, O - 8 * u - 8 * v, O + 8 * u - 8 * v)
a = 6 (slider from 2 to 8, step 0.1)
b = 5.2 (slider from 2 to 8, step 0.1)
P: O + a * u + b * v
S_1 = Segment(P, Element[list_1, 1])
S_2 = Segment(P, Element[list_1, 11])
P_2, a_1, p_1, b_1 = Polygon(P, Element[list_1, 1], Element[list_1, 11])