橢球面
Author: 藍邦偉  老師

經度為θ，緯度為φ的橢球面
x=acosθcosφ,y=bcosθsinφ,z=csinφ
-π/2≤θ≤π/2,-π≤φ≤π

x

y

z

顯示xy平面

顯示單位向量

顯示座標軸

雙曲面

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_1 = Segment(A, B)
C: (3.0 * A + B) / 4.0
D: (3.0 * B + A) / 4.0
E = Point(a_1)
c_1 = Circle(C, E)
c' = Translate(c_1, 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_1 = Segment(D', F)
d = Segment(D, G)
β = Angle(G, D, E')
I: C + (b_1 * cos(α), b_1 * sin(α) * sin(β))
J: C + (b_1 * cos(α + 90.0°), b_1 * sin(α + 90.0°) * sin(β))
K: C + (0.0, b_1 * 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 = 9 (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)
a = 3 (slider from 1 to 10, step 1)
b = 5 (slider from 1 to 10, step 1)
c = 7 (slider from 1 to 10, step 1)
m = 0.71 (slider from 0.0010 to 1, step 0.0010)
n = 0.081 (slider from 0.0010 to 1, step 0.0010)
集合1 = Sequence(CurveCartesian[x(O + a * cos(t) * cos(s) * u + b * cos(t) * sin(s) * v + c * sin(t) * w), y(O + a * cos(t) * cos(s) * u + b * cos(t) * sin(s) * v + c * sin(t) * w), s, -3.14, 3.14], t, -1.57, 1.57, n)
集合2 = Sequence(CurveCartesian[x(O + a * cos(t) * cos(s) * u + b * cos(t) * sin(s) * v + c * sin(t) * w), y(O + a * cos(t) * cos(s) * u + b * cos(t) * sin(s) * v + c * sin(t) * w), t, -1.57, 1.57], s, 0.0, 6.28, m)
文字2: "\frac{ x² }{" + (a^(2.0)) + " }+ \frac{ y² }{" + (b^(2.0)) + " }+ \frac{ z² }{" + (c^(2.0)) + " }=1"
c_0: (c * (1.0 + sgn(c)) + 0.0 * (1.0 - sgn(c))) / 2.0