圓錐的形成
Author: 藍邦偉  老師

x

y

z

單位向量

座標軸

圓錐的形成

α = 3.3929200658769765 rad (slider from 0*° to 6.283185307179586, step 0.1*°)
β = 1.3264502315156905 rad (slider from 0*° to 6.283185307179586, step 0.1*°)
O = (8.957686644524928, 2.6477706488784443)
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 = false
r = 2.8 (slider from 1 to 5, step 0.1)
n = 35 (slider from 1 to 50, step 1)
h = 6.6 (slider from 1 to 7, step 0.1)
s = 0 rad (slider from 0*° to 6.283185307179586, step 0.1*°)
V_2: O - h * w
f = CurveCartesian(x(O + r * cos(t) * u + r * sin(t) * v), y(O + r * cos(t) * u + r * sin(t) * v), t, 0, 6.28319)
集合1 = Sequence(Segment[O + h * w, O + r * cos(i * 2 * 3.141592653589793 / n) * u + r * sin(i * 2 * 3.141592653589793 / n) * v], i, 1, n)
U_1: O + r * cos(s) * u + r * sin(s) * v
V_1: O + h * w
多邊形1, v_1, o, u_1 = Polygon(O, U_1, V_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')

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')