旋轉體的體積(1)
Author: 藍邦偉　老師

單位向量

座標軸

x

y

z

$ 旋轉體的體積(1) $

O = (7.092970622815234, 4.037582824474442)
β = 1.5707963267948966 rad (slider from 0 to 6.283185307179586, step 0.1*°)
Z_{unit}: O + (0, sin(β))
w = Vector(O, Z_{unit})
α = 0.17453292519943295 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 = 11 (slider from 1 to 12, step 1)
y_{axis} = Vector(O - L * v, O + L * v)
z_{axis} = Vector(O - L * w, O + L * w)
x_{axis} = Vector(O - L * u, O + L * u)
c = false
d = true
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])
n = 0 (slider from 0 to L - 1, step 1)
c_3 = CurveCartesian(x(O + sqrt(n) * cos(s) * w + sqrt(n) * sin(s) * v + n * u), y(O + sqrt(n) * cos(s) * w + sqrt(n) * sin(s) * v + n * u), s, 0, 6.28)
c_1 = CurveCartesian(x(O + t * w + t^(2) * u), y(O + t * w + t^(2) * u), t, 0, sqrt(n))
c_2 = CurveCartesian(x(O - t * w + t^(2) * u), y(O - t * w + t^(2) * u), t, 0, sqrt(n))
c_{ini} = CurveCartesian(x(O + t * w + t^(2) * u), y(O + t * w + t^(2) * u), t, 0, 10)
c_{sec} = CurveCartesian(x(O - t * w + t^(2) * u), y(O - t * w + t^(2) * u), t, 0, 10)
Step = 1 (slider from 0 to 2, step 1)
list_{rev} = Sequence(CurveCartesian[x(O + sqrt(n) * cos(t) * cos(i * π / 12) * u + sqrt(n) * cos(t) * sin(i * π / 12) * v + sqrt(n) * sin(t) * w), y(O + sqrt(n) * cos(t) * cos(i * π / 12) * u + sqrt(n) * cos(t) * sin(i * π / 12) * v + sqrt(n) * sin(t) * w), t, -1.5708, 1.5708], i, 1, n)
m = 0 (slider from 0 to 24, step 1)
list1 = Sequence(CurveCartesian[x(O + t * u + sqrt(t) * cos(s) * v + sqrt(t) * sin(s) * w), y(O + t * u + sqrt(t) * cos(s) * v + sqrt(t) * sin(s) * w), t, 0, 10], s, 1.5707963267948966, π / 2 + π / 12 * m, 0.2618)
list2 = Sequence(CurveCartesian[x(O + t * u + sqrt(t) * cos(s) * v + sqrt(t) * sin(s) * w), y(O + t * u + sqrt(t) * cos(s) * v + sqrt(t) * sin(s) * w), s, 1.5708, π / 2 + π / 12 * m], t, 0, 10, 0.25)
list_1 = Sequence(CurveCartesian[x(O + sqrt(t) * cos(s) * w + sqrt(t) * sin(s) * v + t * u), y(O + sqrt(t) * cos(s) * w + sqrt(t) * sin(s) * v + t * u), s, 0, 6.28], t, 0, n, 0.25)
list_2 = Sequence(CurveCartesian[x(O + sqrt(t) * cos(s) * w + sqrt(t) * sin(s) * v + t * u), y(O + sqrt(t) * cos(s) * w + sqrt(t) * sin(s) * v + t * u), t, 0, n], s, 0, 6.28, 0.25)