空間中的直線(2)
Author: 藍邦偉  老師

x

y

z

顯示xy平面

顯示單位向量

x

y

z

顯示座標軸

顯示座標軸

點P(

方向向量

1

2

3

4

5

6

,

,

$  )$

\overrightarrow{L}=(

,

,

$ ) $

P(

x

y

z

A: (x((Corner[3] + 39 * Corner[4]) / 40), y((Corner[1] + 9 * Corner[4]) / 10))
B: (x((4 * Corner[3] + 16 * Corner[4]) / 20), y((Corner[1] + 9 * Corner[4]) / 10))
a_2 = Segment(A, B)
C: (3 * A + B) / 4
D: (3 * B + A) / 4
E = Point(a_2)
c_2 = Circle(C, E)
c' = Translate(c_2, Vector[C, D])
A' = Rotate(A, 270*°, C)
B' = Rotate(B, 270*°, C)
a' = Segment(A', B')
c'' = Rotate(c', 270*°, C)
D' = Rotate(D, 270*°, C)
E' = Rotate(Translate[E, Vector[C, D]], 90*°, D)
E'' = Rotate(E', 270*°, C)
F = Point(c'')
G = Point(c')
α = Angle(E'', D', F)
b_2 = Segment(D', F)
d = Segment(D, G)
β = Angle(G, D, E')
I: C + (b_2 * cos(α), b_2 * sin(α) * sin(β))
J: C + (b_2 * cos(α + 90°), b_2 * sin(α + 90°) * sin(β))
K: C + (0, b_2 * cos(β))
e = Segment(C, K)
f = Segment(C, I)
g = Segment(C, J)
O = (-5.610009412555331, -1.4633466057041935)
I' = Translate(I, Vector[C, O])
J' = Translate(J, Vector[C, O])
K' = Translate(K, Vector[C, O])
L = 8 (slider from 1 to 10, step 1)
I'' = Dilate(I', L, O)
J'' = Dilate(J', L, O)
K'' = Dilate(K', L, O)
I''' = Dilate(I'', -1, O)
J''' = Dilate(J'', -1, O)
K''' = Dilate(K'', -1, O)
u' = Vector(I''', I'')
v' = Vector(J''', J'')
w' = Vector(K''', K'')
h = Segment(D', E'')
i = Segment(D, E')
軌跡1 = Locus(I, F)
L_{axis}: L
j = false
w = Vector(O, K')
u = Vector(O, I')
v = Vector(O, J')
k = false
list1 = Sequence(CurveCartesian[x(O + t * u + s * v), y(O + t * u + s * v), t, -L, L], s, -L, L, 1)
list2 = Sequence(CurveCartesian[x(O + t * u + s * v), y(O + t * u + s * v), s, -L, L], t, -L, L, 1)
x1 = 4 (slider from -5 to 5, step 1)
y1 = 3 (slider from -5 to 5, step 1)
z1 = 2 (slider from -5 to 5, step 1)
P: O + x1 * u + y1 * v + z1 * w
P_1: O + x1 * u
P_2: O + y1 * v
P_3: O + z1 * w
P_4: O + x1 * u + y1 * v
P_5: O + y1 * v + z1 * w
P_6: O + x1 * u + z1 * w
p = Segment(P, P_4)
q = Segment(P, P_5)
r = Segment(P, P_6)
s = Segment(P_6, P_3)
t_5 = Segment(P_5, P_3)
a_1 = Segment(P_5, P_2)
b_1 = Segment(P_6, P_1)
c_1 = Segment(P_4, P_2)
d_1 = Segment(P_4, P_1)
e_1 = Segment(P_1, O)
g_1 = Segment(P_3, O)
a = 1 (slider from -5 to 5, step 1)
b = 2 (slider from -5 to 5, step 1)
c = -3 (slider from -5 to 5, step 1)
l: O + a * u + b * v + c * w
h_1 = Line(P, l)
z = true
T_1 = Corner(1)
T_4 = Corner(4)
f_1 = Segment(O, P_2)
n = 1 (slider from 1 to 2, step 1)
T_2: (7.5 * Corner[1] + 2.5 * Corner[2]) / 10
T_3: (7.5 * Corner[4] + 2.5 * Corner[3]) / 10
多邊形1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
i_1 = Segment(T_2, T_3)
inputBox1 = Textfield(x1)
inputBox2 = Textfield(y1)
inputBox3 = Textfield(z1)
inputBox4 = Textfield(a)
inputBox5 = Textfield(b)
inputBox6 = Textfield(c)
m, j_1 = SDLine(P_6, P_1, P_3, P)
k_1, l_1 = SDLine(P_6, P, P_1, P_3)
m_1, n_1 = SDLine(P, P_4, P_6, P_5)
p_1, q_1 = SDLine(P_5, P_2, P, P_3)
r_1, s_1 = SDLine(P, P_5, P_4, P_6)
d_2, e_2 = SDLine(P_5, P_3, P_2, P)
f_2, g_2 = SDLine(P_3, P_6, P_1, P)
h_2, i_2 = SDLine(P_3, O, P_2, P_1)
j_2, k_2 = SDLine(P_2, P_4, P_5, O)
l_2, m_2 = SDLine(P_1, P_4, O, P_6)
n_2, p_2 = SDLine(P_1, O, P_6, P_4)
q_2, r_2 = SDLine(P_2, O, P_4, P_5)
if: i * f
X1 = 0
text12: "P(" + x1 + "," + y1 + "," + z1 + ")"
t_{sym}: "L:\frac{x" + (LaTeX[If[x1 < 0, "+", If[x1 > 0, "-", ""]]]) + "" + (LaTeX[If[x1 ≠ 0, abs(x1), ""]]) + "}{" + (LaTeX[a]) + "}=\frac{y" + (LaTeX[If[y1 < 0, "+", If[y1 > 0, "-", ""]]]) + "" + (LaTeX[If[y1 ≠ 0, abs(y1), ""]]) + "}{" + (LaTeX[b]) + "}=\frac{z" + (LaTeX[If[z1 < 0, "+", If[z1 > 0, "-", ""]]]) + "" + (LaTeX[If[z1 ≠ 0, abs(z1), ""]]) + "}{" + (LaTeX[c]) + "}"
t_{Par}: "L:\left\lbrace \begin{array}{ll} x=" + (LaTeX[If[x1 ≠ 0, x1, ""]]) + "" + (LaTeX[If[x1 ≟ 0 ∧ a ≟ 0, "0", ""]]) + "" + (LaTeX[If[a < 0, "-", If[a > 0, "+", ""]]]) + "" + (LaTeX[If[a ≟ 1, "", If[a ≠ 0, abs(a), ""]]]) + "" + (LaTeX[If[a ≠ 0, "t", ""]]) + " \\ y=" + (LaTeX[If[y1 ≠ 0, y1, ""]]) + "" + (LaTeX[If[y1 ≟ 0 ∧ b ≟ 0, "0", ""]]) + "" + (LaTeX[If[b < 0, "-", If[b > 0, "+", ""]]]) + "" + (LaTeX[If[b ≟ 1, "", If[b ≠ 0, abs(b), ""]]]) + "" + (LaTeX[If[b ≠ 0, "t", ""]]) + "\\ z=" + (LaTeX[If[z1 ≠ 0, z1, ""]]) + "" + (LaTeX[If[z1 ≟ 0 ∧ c ≟ 0, "0", ""]]) + "" + (LaTeX[If[c < 0, "-", If[c > 0, "+", ""]]]) + "" + (LaTeX[If[c ≟ 1, "", If[c ≠ 0, abs(c), ""]]]) + "" + (LaTeX[If[c ≠ 0, "t", ""]]) + " \end{array}  \right.\ ,t∈\mathbb{R}"
H = (-12.307311351104943, 3.5649116320712246)

Tool: SDLine
Input: A, B, C, D
Output: g, h

b: sgn(sin(Angle[D, B, A]))
a: sgn(sin(Angle[A, B, C]))
c: sgn(a + b + 0.5)
d: sqrt(c)
e: sqrt(-c)
E = Midpoint(A, B)
A' = Dilate(A, d, E)
B' = Dilate(B, d, E)
g = Segment(A', B')
A'_1 = Dilate(A, e, E)
B'_1 = Dilate(B, e, E)
h = Segment(A'_1, B'_1)