空間向量的正射影
Author: 藍邦偉  老師

x

y

z

顯示xy平面

顯示單位向量

u

v

顯示座標軸

x1

y1

z1

x2

y2

z2

 )上的正射影

$ \overrightarrow{u}=( $

,

,

)在

$ \overrightarrow{v} =($

,

,

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 = Segment(A, B)
C: (3 * A + B) / 4
D: (3 * B + A) / 4
E = Point(a)
c = Circle(C, E)
c' = Translate(c, 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 = Segment(D', F)
d = Segment(D, G)
β = Angle(G, D, E')
I: C + (b * cos(α), b * sin(α) * sin(β))
J: C + (b * cos(α + 90°), b * sin(α + 90°) * sin(β))
K: C + (0, b * cos(β))
e = Segment(C, K)
f = Segment(C, I)
g = Segment(C, J)
O = (1.0868069332107235, -1.69925969505996)
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)
x_1 = 5 (slider from -5 to 5, step 1)
y_1 = -4 (slider from -5 to 5, step 1)
z_1 = 3 (slider from -5 to 5, step 1)
x_2 = -4 (slider from -5 to 5, step 1)
y_2 = -1 (slider from -5 to 5, step 1)
z_2 = 2 (slider from -5 to 5, step 1)
P: O + x_1 * u + y_1 * v + z_1 * w
Q: O + x_2 * u + y_2 * v + z_2 * w
z = Vector(O, P)
m = Vector(O, Q)
n = Line(Q, O)
p = OrthogonalLine(P, n)
H = Intersect(p, n)
q = Vector(O, H)
T_1 = Corner(1)
T_4 = Corner(4)
T_2: (3 * Corner[1] + 2 * Corner[2]) / 5
T_3: (3 * Corner[4] + 2 * Corner[3]) / 5
多邊形1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
r = Segment(T_2, T_3)
l = true
inputBox1 = Textfield(x_1)
inputBox2 = Textfield(y_1)
inputBox3 = Textfield(z_1)
inputBox4 = Textfield(x_2)
inputBox5 = Textfield(y_2)
inputBox6 = Textfield(z_2)