立體測量 (18)
Author: 藍邦偉  老師

A

C

x

y

z

顯示xy平面

顯示單位向量

顯示座標軸

立體測量(18)

立體測量(18)

B

分解三角形

O_1

A_1

H_1

B_1

O_2

H_2

O_3

C_1

H_3

O

A

C

B

θ

180°-θ

 \frac{ h}{ \sqrt{ 3 }  } 

h

h

h

h

 \sqrt{ 3 } h

h

 \sqrt{ 3 } h

 \frac{ h }{  \sqrt{ 3 } } 

h

 \frac{ h }{ \sqrt{ 3 }  } 

 \sqrt{ 3 } h

h

O = (-1.3949652394728496, -4.265272009268816)
B: (x((4.0 * Corner[3.0] + 16.0 * Corner[4.0]) / 20.0), y((Corner[1.0] + 9.0 * Corner[4.0]) / 10.0))
A: (x((Corner[3.0] + 39.0 * Corner[4.0]) / 40.0), y((Corner[1.0] + 9.0 * Corner[4.0]) / 10.0))
a = Segment(A, B)
E = Point(a)
D: (3.0 * B + A) / 4.0
h = 11.26 (slider from 0 to 20, step 0.02)
C: (3.0 * A + B) / 4.0
c = Circle(C, E)
c' = Translate(c, Vector[Vector[C, D]])
c'' = Rotate(c', 270.0*°, C)
F = Point(c'')
G = Point(c')
E' = Rotate(Translate[E, Vector[C, D]], 90.0*°, D)
A' = Rotate(A, 270.0*°, C)
B' = Rotate(B, 270.0*°, C)
a' = Segment(A', B')
D' = Rotate(D, 270.0*°, C)
b = Segment(D', F)
E'' = Rotate(E', 270.0*°, C)
α = Angle(E'', D', F)
d = Segment(D, G)
β = Angle(G, D, E')
J: C + (b * cos(α + 90.0°), b * sin(α + 90.0°) * sin(β))
J' = Translate(J, Vector[Vector[C, O]])
v = Vector(O, J')
I: C + (b * cos(α), b * sin(α) * sin(β))
I' = Translate(I, Vector[Vector[C, O]])
u = Vector(O, I')
P_1: O + 7.0 * u
R_1: P_1 - 10.0 * v
R_2: P_1 + 11.0 * v
y_y = Segment(R_1, R_2)
K: C + (0.0, b * cos(β))
K' = Translate(K, Vector[Vector[C, O]])
w = Vector(O, K')
e = Segment(C, K)
f = Segment(C, I)
g = Segment(C, J)
L = 13 (slider from 1 to 15, step 1)
I'' = Dilate(I', L, O)
J'' = Dilate(J', L, O)
K'' = Dilate(K', L, O)
I''' = Dilate(I'', -1.0, O)
J''' = Dilate(J'', -1.0, O)
K''' = Dilate(K'', -1.0, O)
u' = Vector(I''', I'')
v' = Vector(J''', J'')
h_1 = Segment(D', E'')
i = Segment(D, E')
軌跡1 = Locus(I, F)
L_{axis}: L
j = false
k = false
l = false
list1 = Sequence(CurveCartesian[x(O + t * u + s * v), y(O + t * u + s * v), t, -(L), L], s, -(L), L, 1.0)
list2 = Sequence(CurveCartesian[x(O + t * u + s * v), y(O + t * u + s * v), s, -(L), L], t, -(L), L, 1.0)
C_a: C + (b * cos(α + 10.0°), b * sin(α + 10.0°) * sin(β))
C_b: C + (b * cos(α + 20.0°), b * sin(α + 20.0°) * sin(β))
C_c: C + (b * cos(α + 30.0°), b * sin(α + 30.0°) * sin(β))
C_d: C + (b * cos(α + 40.0°), b * sin(α + 40.0°) * sin(β))
C_e: C + (b * cos(α + 50.0°), b * sin(α + 50.0°) * sin(β))
p = Conic(C_a, C_b, C_c, C_d, C_e)
n = 3 (slider from 0 to 5, step 1)
m = Line(P_1, v)
t = 0.426 (slider from 0 to 1, step 0.0010)
x_1: x = x(Corner[1.0])
x_2: x = x(Corner[2.0])
P_a = Intersect(x_1, m)
P_b = Intersect(x_2, m)
P: P_b + t * Vector[P_b, P_a]
H: O + h * w
q = Segment(H, P)
r = Segment(P, O)
s = Segment(O, H)
P_3: P + (-(2.34), -(0.05))
P_4: P + (2.37, 0.02)
Tire_F = Circle(P_3, 0.65)
Tire_R = Circle(P_4, 0.65)
γ = 2.3364722696448093 rad (slider from 0 to 6.283185307179586, step 1.7453292519943296E-4)
Q_1: P_3 + (0.55 * cos(γ), 0.55 * sin(γ))
Q_2: P_3 + (0.55 * cos(γ + 72.0°), 0.55 * sin(γ + 72.0°))
Q_3: P_3 + (0.55 * cos(γ + 144.0°), 0.55 * sin(γ + 144.0°))
Q_4: P_3 + (0.55 * cos(γ + 216.0°), 0.55 * sin(γ + 216.0°))
Q_5: P_3 + (0.55 * cos(γ + 288.0°), 0.55 * sin(γ + 288.0°))
Q_6: P_4 + (0.55 * cos(γ), 0.55 * sin(γ))
Q_7: P_4 + (0.55 * cos(γ + 72.0°), 0.55 * sin(γ + 72.0°))
Q_8: P_4 + (0.55 * cos(γ + 144.0°), 0.55 * sin(γ + 144.0°))
Q_9: P_4 + (0.55 * cos(γ + 216.0°), 0.55 * sin(γ + 216.0°))
Q_0: P_4 + (0.55 * cos(γ + 288.0°), 0.55 * sin(γ + 288.0°))
q_1 = Segment(P_3, Q_1)
q_2 = Segment(P_3, Q_2)
q_3 = Segment(P_3, Q_3)
q_4 = Segment(P_3, Q_4)
q_5 = Segment(P_3, Q_5)
q_6 = Segment(P_4, Q_6)
q_7 = Segment(P_4, Q_7)
q_8 = Segment(P_4, Q_8)
q_9 = Segment(P_4, Q_9)
q_0 = Segment(P_4, Q_0)
Q_a: P_3 + (0.3 * cos(γ), 0.3 * sin(γ))
Q_b: P_3 + (0.3 * cos(γ + 90.0°), 0.3 * sin(γ + 90.0°))
Q_c: P_3 + (0.3 * cos(γ + 180.0°), 0.3 * sin(γ + 180.0°))
Q_d: P_3 + (0.3 * cos(γ + 270.0°), 0.3 * sin(γ + 270.0°))
Q_e: P_4 + (0.3 * cos(γ), 0.3 * sin(γ))
Q_f: P_4 + (0.3 * cos(γ + 90.0°), 0.3 * sin(γ + 90.0°))
Q_g: P_4 + (0.3 * cos(γ + 180.0°), 0.3 * sin(γ + 180.0°))
Q_h: P_4 + (0.3 * cos(γ + 270.0°), 0.3 * sin(γ + 270.0°))
H_F = Circle(P_3, 0.2)
H_R = Circle(P_4, 0.2)
c_1 = Circle(O, 0.5)
M = Intersect(c_1, s)
N = Intersect(c_1, r)
Q: M + N - O
s_1 = Segment(Q, N)
s_2 = Segment(Q, M)
R_3 = Point(y_y)
多邊形1, a_1, b_1, d_1, e_1 = Polygon(Corner[1.0], Corner[2.0], Corner[3.0], Corner[4.0])
f_1 = Segment(R_1, O)
g_1 = Segment(R_3, O)
i_1 = Segment(O, R_2)
j_1 = Segment(R_2, R_1)
k_1 = Segment(R_1, H)
l_1 = Segment(H, R_2)
m_1 = Segment(H, R_3)
p_1 = Circle(O, 0.4)
R = Intersect(p_1, i_1)
S = Intersect(p_1, s)
S_1: R + S - O
U = Intersect(p_1, g_1)
S_3: U + S - O
z_b = Segment(S_1, S)
z_a = Segment(S_1, R)
z_e = Segment(S_3, S)
z_f = Segment(S_3, U)
V = (-5.7448360765504844, -1.0753667287452173)
V_1: V - (sqrt(3.0), 0.0)
V_2: V + (0.0, 3.0)
n_1 = Segment(V_1, V)
r_1 = Segment(V, V_2)
t_1 = Segment(V_2, V_1)
W: V + (1.0, 0.0)
W_1: W + (r_1, 0.0)
W_2: W + (r_1, r_1)
a_2 = Segment(W, W_1)
b_2 = Segment(W_1, W_2)
c_2 = Segment(W_2, W)
Z: W_1 + (1.0, 0.0)
Z_1: Z + (sqrt(3.0) * r_1, 0.0)
Z_2: Z + (0.0, r_1)
d_2 = Segment(Z_2, Z)
e_2 = Segment(Z, Z_1)
f_2 = Segment(Z_1, Z_2)
δ = Angle(V_1, V, V_2)
ε = Angle(W_2, W_1, W)
ζ = Angle(Z_2, Z, Z_1)
η = Angle(V, V_1, V_2)
θ = Angle(W_2, W, W_1)
ι = Angle(Z, Z_1, Z_2)
A_1: V + (0.3, -(1.5))
h_2: y = y(A_1) - 3.0
A_2 = Point(h_2)
A_3 = Point(h_2)
A_4 = Point(h_2)
g_2 = Segment(A_1, A_2)
j_2 = Segment(A_3, A_1)
k_2 = Segment(A_1, A_4)
κ = Angle(A_1, A_4, A_2)
λ = Angle(A_3, A_4, A_1)
i_2 = Segment(A_2, A_4)
l_2 = Segment(A_4, A_3)
文字13: "" + i_2
文字14: "" + l_2
m_2 = Segment(R_1, R_3)
文字19: "" + m_2
n_2 = Segment(R_3, R_2)
文字20: "" + n_2
w' = Vector(O, K'')
T = Intersect(p_1, f_1)
B_1: S + T - O
p_2 = Segment(B_1, S)
r_2 = Segment(B_1, T)