x_2

x_1

x_2

x_3

Haftendorn

Ha 2020

gl1: (7 * x^(2)) - ((4 * x) * y) - ((2 * x) * z) - ((2 * y) * z) + (7 * y^(2)) + (4 * z^(2)) - (70 * x) + (38 * y) + (28 * z) + 202 = 0
A1: 7
B2: 7
C3: 4
B1: -2
A2: -2
C1: -1
A3: -1
C2: -1
B3: -1
E1: -70
E2: 38
E3: 28
G3: 202
A: {{A1, B1, C1}, {A2, B2, C2}, {A3, B3, C3}}
d: G3
A5: 1
A6: -1
A7: 0
B5: 1
B6: 1
B7: -1
C5: 1
C6: 1
C7: 2
A9: 1 / sqrt(2)
A10: -0.70711
A11: 0
B9: 1 / sqrt(3)
B10: 0.57735
B11: -0.57735
C9: 1 / sqrt(6)
C10: 0.408248290463864
C11: (0.40825 * 2)
P: {{A9, B9, C9}, {A10, B10, C10}, {A11, B11, C11}}
P' = Transpose(P)
F1: E1 / 2
F2: E2 / 2
F3: E3 / 2
a: {{F1}, {F2}, {F3}}
A13(x) = x^(2)
B: ((P' * A) * P)
p: {{C13}, {C14}, {C15}}
p' = Transpose(p)
b(x, y, z) = (9 * x^(2)) + (6 * y^(2)) + (3 * z^(2))
a' = Transpose(a)
c(x, y, z) = (9 * x^(2)) + (6 * y^(2)) + (3 * z^(2)) + 2
a_p: (a' * P)
gl2: (9 * x^(2)) + (6 * y^(2)) + (3 * z^(2)) + (2 * ((-38.18 * x) - (17.32 * y) + (4.9 * z))) + 202 = 0
xm: 38.18 / 9
ym: 17.32 / 6
zm: -4.9 / 3
d': (-9 * xm^(2)) - (6 * ym^(2)) - (3 * zm^(2)) + 202
gl3: (9 * (x - xm)^(2)) + (6 * (y - ym)^(2)) + (3 * (z - zm)^(2)) + d' = 0
M: (xm, ym, zm)
gl4: (9 * x^(2)) + (6 * y^(2)) + (3 * z^(2)) - 18 = 0
E5: xm
E6: ym
E7: zm
mv: {{E5}, {E6}, {E7}}
mur: (P * mv)
u = Vector((4, -2, -3))
v = Vector(M)
O: (0, 0, 0)
M_{ur}: (4, -2, -3)
C = Point(p')
e = CircleArc(C, M_{ur}, M)
α = Angle(M_{ur}, O, M)
D = Center(gl2)
E = Center(gl4)
F = Center(gl1)
A17: 2020