薄片法求體積(1)
Author: 藍邦偉　老師

單位向量

座標軸

x

y

z

$ O $

$半徑為%v$

$x=%v$

1

2

$ 正三角形 $

$ 正方形 $

$ 薄片法求體積(1) $

O = (11.029497356599325, 1.0470149530200599)
β = 1.3962634015954636 rad (slider from 0 to 6.283185307179586, step 0.1*°)
Z_{unit}: O + (0, sin(β))
w = Vector(O, Z_{unit})
α = 4.276056667386108 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 = 7 (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)
poly1, h, q_1, q_4, i = Polygon(Corner[1], Q_2, Q_3, Corner[4])
r = 4 (slider from 1 to 5, step 1)
b = 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)
t = 2.72 (slider from -r to r, step 0.01)
A_1: O + t * u + sqrt(r^(2) - t^(2)) * v
A_2: O + t * u - sqrt(r^(2) - t^(2)) * v
A_3: O + sqrt(3) * sqrt(r^(2) - t^(2)) * w + t * u
poly2, a_2, a_3, a_1 = Polygon(A_3, A_1, A_2)
a = CurveCartesian(x(O + sqrt(3) * sqrt(r^(2) - t^(2)) * w + t * u), y(O + sqrt(3) * sqrt(r^(2) - t^(2)) * w + t * u), t, -r, r)
ListA = Sequence(O + t * u + sqrt(r^(2) - t^(2)) * v, t, -r, r, 0.5)
ListB = Sequence(O + t * u - sqrt(r^(2) - t^(2)) * v, t, -r, r, 0.5)
ListC = Sequence(O + sqrt(3) * sqrt(r^(2) - t^(2)) * w + t * u, t, -r, r, 0.5)
ListT = Sequence(Polygon[Element[ListA, k], Element[ListB, k], Element[ListC, k]], k, 1, 16, 1)
e = true
B_1: A_1 + 2 * sqrt(r^(2) - t^(2)) * w
B_2: A_2 + 2 * sqrt(r^(2) - t^(2)) * w
poly3, a_4, a_5, b_1, b_2 = Polygon(A_2, A_1, B_1, B_2)
ListD = Sequence(O + t * u + sqrt(r^(2) - t^(2)) * v + 2 * sqrt(r^(2) - t^(2)) * w, t, -r, r, 0.5)
ListE = Sequence(O + t * u - sqrt(r^(2) - t^(2)) * v + 2 * sqrt(r^(2) - t^(2)) * w, t, -r, r, 0.5)
ListQ = Sequence(Polygon[Element[ListA, k], Element[ListB, k], Element[ListE, k], Element[ListD, k]], k, 1, 16, 1)
f = CurveCartesian(x(O + t * u + sqrt(r^(2) - t^(2)) * v + 2 * sqrt(r^(2) - t^(2)) * w), y(O + t * u + sqrt(r^(2) - t^(2)) * v + 2 * sqrt(r^(2) - t^(2)) * w), t, -r, r)
j = CurveCartesian(x(O + t * u - sqrt(r^(2) - t^(2)) * v + 2 * sqrt(r^(2) - t^(2)) * w), y(O + t * u - sqrt(r^(2) - t^(2)) * v + 2 * sqrt(r^(2) - t^(2)) * w), t, -r, r)
k = false