拋物面
Author: 藍邦偉  老師

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y

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顯示xy平面

顯示單位向量

顯示座標軸

拋物面

A: (x((Corner[3.0] + 39.0 * Corner[4.0]) / 40.0), y((Corner[1.0] + 9.0 * Corner[4.0]) / 10.0))
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 = Segment(A, B)
C: (3.0 * A + B) / 4.0
D: (3.0 * B + A) / 4.0
E = Point(a)
c = Circle(C, E)
c' = Translate(c, Vector[Vector[C, D]])
A' = Rotate(A, 270.0*°, C)
B' = Rotate(B, 270.0*°, C)
a' = Segment(A', B')
c'' = Rotate(c', 270.0*°, C)
D' = Rotate(D, 270.0*°, C)
E' = Rotate(Translate[E, Vector[C, D]], 90.0*°, D)
E'' = Rotate(E', 270.0*°, 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 + 90.0°), b * sin(α + 90.0°) * sin(β))
K: C + (0.0, b * cos(β))
e = Segment(C, K)
f = Segment(C, I)
g = Segment(C, J)
O = (0.0820175309471018, -1.7287053169966222)
I' = Translate(I, Vector[Vector[C, O]])
J' = Translate(J, Vector[Vector[C, O]])
K' = Translate(K, Vector[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'', -1.0, O)
J''' = Dilate(J'', -1.0, O)
K''' = Dilate(K'', -1.0, 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
l = true
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)
n = 0.71 (slider from 0 to 1, step 0.0010)
m = 0.44 (slider from 0 to 1, step 0.0010)
集合1 = Sequence(CurveCartesian[x(O + sqrt(t) * cos(s) * u + sqrt(t) * sin(s) * v + t * w), y(O + sqrt(t) * cos(s) * u + sqrt(t) * sin(s) * v + t * w), s, 0.0, 6.28], t, 0.0, L - 1.0, n)
集合2 = Sequence(CurveCartesian[x(O + sqrt(t) * cos(s) * u + sqrt(t) * sin(s) * v + t * w), y(O + sqrt(t) * cos(s) * u + sqrt(t) * sin(s) * v + t * w), t, 0.0, L - 1.0], s, 0.0, 6.28, m)