四面體的體積
Author: 藍邦偉  老師

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y

z

單位向量

單位點

座標軸

xy平面

Length=

Width=

Height=

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y

z

$ 四面體的體積 $

α = 0 rad (slider from 0 to 6.283185307179586, step 0.3*°)
β = 4.799655442984406 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
L = 6 (slider from 1 to 10, step 1)
O = (30.1, 11.26)
X_{unit}: O + (cos(α), sin(α) * cos(β))
Y_{unit}: O + (-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})
x_a = Vector(O - L * u, O + L * u)
y_b = Vector(O - L * v, O + L * v)
z_c = Vector(O - L * w, O + L * w)
多邊形1, d_1, e, f, g = Polygon(O + L * u + L * v, O - L * u + L * v, O - L * u - L * v, O + L * u - L * v)
X_{x}: O + L * u
Y_{y}: O + L * v
Z_{z}: O + L * w
A = (20.64, 16.56)
h = false
i = false
j = true
k = false
a = 0
b = 0
c = 0
inputBox1 = Textfield(a)
inputBox2 = Textfield(b)
inputBox3 = Textfield(c)
d = 0 (slider from 0 to 3, step 0.1)
A_1: O + a * u
A_2: O + a * u + b * v
A_3: O + b * v
A_4: O
A_5: O + a * u + c * w
A_6: O + a * u + b * v + c * w
A_7: O + b * v + c * w
A_8: O + c * w
P_1: O + a * u + d * u
P_5: O + (a + d) * u + c * w
P_6: O + (a + d) * u + b * v + c * w
Q_1: O + (a - d) * u
Q_2: O + (a - d) * u + b * v
Q_3: O + b * v - d * u
Q_7: O + b * v + c * w - d * u
poly4, q_2, q_7, q_3 = Polygon(Q_7, Q_3, Q_2)
poly5, q_1, q_4, q_5 = Polygon(Q_3, Q_1, Q_2)
poly6, q_6, q_8, q_9 = Polygon(Q_7, Q_1, Q_2)
P_7: O + b * v + c * w + d * u
poly1, p_1, p_5, p_6 = Polygon(P_5, P_6, P_1)
poly2, p_2, p_3, p_7 = Polygon(P_5, P_7, P_6)
poly3, p_4, p_8, p_9 = Polygon(P_7, P_1, P_6)
poly7, a_6, a_7, a_2 = Polygon(A_7, A_2, A_6)
poly8, a_1, a_3, a_4 = Polygon(A_6, A_2, A_1)
poly9, a_5, a_8, a_9 = Polygon(A_7, A_1, A_2)
l = Segment(A_7, A_8)
m = Segment(A_8, A_5)
n = Segment(A_5, A_6)
p = Segment(A_7, A_3)
q = Segment(A_8, A_4)
r = Segment(A_5, A_1)
s = Segment(A_1, A_4)
t = Segment(A_4, A_3)
b_1 = Segment(A_3, A_2)