圓柱體的截面
Author: 藍邦偉　老師

單位向量

座標軸

Start

x

y

z

$ O $

$r=%v$

$h=%v$

$x=%v$

$P$

$Q$

$R$

$ 截圓柱的體積 $

O = (10.164973845984383, 1.0928223383596263)
β = 1.3089969389957472 rad (slider from 0 to 6.283185307179586, step 0.1*°)
Z_{unit}: O + (0, sin(β))
w = Vector(O, Z_{unit})
α = 4.014257279586958 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 = 6 (slider from 1 to 10, step 1)
yy = Vector(O - L * v, O + L * v)
zz = Vector(O - L * w, O + L * w)
xx = Vector(O - L * u, O + L * u)
c = false
d = false
Q_2: 0.2 * Corner[2] + 0.8 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
g = Segment(Q_2, Q_3)
r = 2 (slider from 1 to 5, step 0.1)
h = 6.3 (slider from 1 to 8, step 0.1)
c_1 = CurveCartesian(x(O + r * cos(t) * u + r * sin(t) * v + h * w), y(O + r * cos(t) * u + r * sin(t) * v + h * w), t, 0, 6.283185307179586)
c_2 = CurveCartesian(x(O + r * cos(t) * u + r * sin(t) * v), y(O + r * cos(t) * u + r * sin(t) * v), t, 0, 6.283185307179586)
H: O + h * w
U_a: H + (r, 0)
U_b = Mirror(U_a, H)
B_1 = Midpoint(H, O)
C = Mirror(U_a, B_1)
L_a = Mirror(U_b, B_1)
a_1 = Segment(U_b, C)
a_2 = Segment(U_a, L_a)
A: O + r * u
B: O - r * u
a = Segment(A, B)
θ = 1.0471975511965976 rad (slider from 30*° to 60*°, step 15*°)
t = 0 (slider from -r to r, step 0.1)
P: O + t * u
Q: O + sqrt(r^(2) - t^(2)) * v + t * u
b = Segment(O, Q)
m = Segment(P, Q)
R: Q + m * tan(θ) * w
e = Segment(R, Q)
f = Segment(R, P)
loc1 = Locus(R, t)
poly1, i, q_2, q_3, j = Polygon(Corner[1], Q_2, Q_3, Corner[4])
poly2, b_1, r_1, a_3 = Polygon(R, A, B)