空間中的點座標
Author: 藍邦偉 老師

x

y

z

單位向量

座標軸

x

y

z

空間中的點座標

P(

,

,

)

x0

y0

z0

z_0 = 0 (slider from -5 to 5, step 1)
O = (8.825717748665715, 4.231397399189074)
β = 1.4486232791552935 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
α = 4.014257279586958 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
Y_{unit}: O + (-1 * sin(α), cos(α) * cos(β))
L = 5 (slider from -5 to 5, step 1)
v = Vector(O, Y_{unit})
X_{unit}: O + (cos(α), sin(α) * cos(β))
Z_{unit}: O + (0, sin(β))
u = Vector(O, X_{unit})
w = Vector(O, Z_{unit})
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)
A_x: O + L * u
A_y: O + L * v
A_z: O + L * w
c = false
d = true
Q_2: 0.2 * Corner[2] + 0.8 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
多邊形1, e, q_2, q_3, f = Polygon(Corner[1], Q_2, Q_3, Corner[4])
g = Segment(Q_2, Q_3)
t = 0 (slider from 0 to 4, step 0.01)
B_1: O + L * t * u
B_2: O - t * L * u
B_4: O - L * (t - 1) * v
x_{Axis} = Vector(B_2, B_1)
B_3: O + L * (t - 1) * v
y_{Axis} = Vector(B_4, B_3)
B_5: O + L * (t - 2) * w
B_6: O - L * (t - 2) * w
z_{Axis} = Vector(B_6, B_5)
t1_1 = 0
t2 = 0
t3 = 0
C_1: O + (t - 3) * L * u + (t - 3) * L * v
C_2: O - (t - 3) * L * u + (t - 3) * L * v
C_3: O - (t - 3) * L * u - (t - 3) * L * v
C_4: O + (t - 3) * L * u - (t - 3) * L * v
poly1, c_1, c_2, c_3, c_4 = Polygon(C_1, C_2, C_3, C_4)
t1 = 0 (slider from 0 to 5, step 0.01)
x_0 = 0 (slider from -5 to 5, step 1)
y_0 = 0 (slider from -5 to 5, step 1)
D_1: O + x_0 * u
D_2: O + y_0 * v
D_4: O + z_0 * w
P: O + x_0 * u + y_0 * v + z_0 * w
D_5: O + x_0 * u + z_0 * w
D_6: O + y_0 * v + z_0 * w
D_3: O + x_0 * u + y_0 * v
P_1: O + t1 * Vector[O, D_1]
P_2: O + t1 * Vector[O, D_2]
l_2 = Segment(O, P_2)
l_1 = Segment(O, P_1)
l_a = Segment(O, D_1)
l_b = Segment(O, D_2)
P_3: D_1 + (t1 - 1) * Vector[O, D_2]
P_4: D_2 + (t1 - 1) * Vector[O, D_1]
l_c = Segment(D_3, D_1)
l_d = Segment(D_3, D_2)
l_3 = Segment(D_1, P_3)
l_4 = Segment(D_2, P_4)
P_5: O + (t1 - 2) * Vector[O, D_4]
P_6: D_1 + (t1 - 2) * Vector[O, D_4]
P_7: D_2 + (t1 - 2) * Vector[O, D_4]
P_8: D_3 + (t1 - 2) * Vector[O, D_4]
l_5 = Segment(O, P_5)
l_6 = Segment(D_1, P_6)
l_7 = Segment(D_2, P_7)
l_8 = Segment(D_3, P_8)
l_e = Segment(D_2, D_6)
l_f = Segment(D_3, P)
l_g = Segment(D_1, D_5)
l_h = Segment(O, D_4)
E_1: P + (t1 - 3) * Vector[P, D_5]
E_2: P + (t1 - 3) * Vector[P, D_6]
l_9 = Segment(P, E_1)
l_{10} = Segment(P, E_2)
l_i = Segment(D_5, P)
l_j = Segment(D_6, P)
l_k = Segment(D_6, D_4)
l_l = Segment(D_5, D_4)
E_3: D_5 + (t1 - 4) * Vector[D_5, D_4]
E_4: D_6 + (t1 - 4) * Vector[D_6, D_4]
l_{11} = Segment(D_5, E_3)
l_{12} = Segment(D_6, E_4)
inputBox1 = Textfield(x_0)
inputBox2 = Textfield(y_0)
inputBox3 = Textfield(z_0)
text9: "P(" + (LaTeX[x_0]) + "," + (LaTeX[y_0]) + "," + (LaTeX[z_0]) + ")"