Y

z

RMX1

RMX2

RMX3

 \vec{i } 

 \vec{j  } 

 \vec{ k } 

Source: http://dmentrard.free.fr/GEOGEBRA/Maths/Espace/3Dcoordonnees.ggb

z_M = 5 (slider from -10 to 10, step 0.1)
y_M = -2.3999999999999995 (slider from -10 to 10, step 0.1)
x_M = 6.800000000000001 (slider from -10 to 10, step 0.1)
B14 = 1
Yrotation = 0 (slider from 0 to 5, step 0.1)
E2: sin(Yrotation)
F7 = 0
E3: cos(Yrotation)
Zrotation = 5.300000000000001 (slider from 0 to 7, step 0.1)
F3: cos(Zrotation)
D7: E3 * F3
F2: sin(Zrotation)
E7: -(F2) * E3
A14 = 1
C14 = -1
A24 = -1
B24 = 1
C24 = -1
Xrotation = 1.2000000000000002 (slider from 0 to 5, step 0.1)
Xsin: sin(Xrotation)
D3: cos(Xrotation)
C2: sin(Xrotation)
D2: sin(Xrotation)
D8: F3 * (-(E2)) * (-(D2)) + F2 * D3
E8: -(F2) * (-(E2)) * (-(D2)) + F3 * D3
E9: -(F2) * (-(E2)) * D3 + F3 * D2
F8: E3 * (-(D2))
F9: E3 * D3
D9: F3 * (-(E2)) * D3 + F2 * D2
A13 = 1
B13 = -1
C13 = -1
A15 = -1
B15 = 1
C15 = -1
A16 = -1
B16 = -1
C16 = -1
A17 = -1
B17 = -1
C17 = 1
A18 = 1
B18 = -1
C18 = 1
A19 = 1
B19 = 1
C19 = 1
A20 = -1
B20 = 1
C20 = 1
A21 = -1
B21 = -1
C21 = 1
A23 = -1
B23 = 1
C23 = 1
A26 = 1
B26 = 1
C26 = -1
A27 = 1
B27 = 1
C27 = 1
A29 = 1
B29 = -1
C29 = 1
A30 = 1
B30 = -1
C30 = -1
A12 = 2.5
B12 = 3
C12: -(z_M)
F12: A12 * D7 + B12 * E7 + C12 * F7
G12: A12 * D8 + B12 * E8 + C12 * F8
F13: A13 * D7 + B13 * E7 + C13 * F7
G13: A13 * D8 + B13 * E8 + C13 * F8
G14: A14 * D8 + B14 * E8 + C14 * F8
F15: A15 * D7 + B15 * E7 + C15 * F7
G15: A15 * D8 + B15 * E8 + C15 * F8
F16: A16 * D7 + B16 * E7 + C16 * F7
G16: A16 * D8 + B16 * E8 + C16 * F8
F17: A17 * D7 + B17 * E7 + C17 * F7
G17: A17 * D8 + B17 * E8 + C17 * F8
F18: A18 * D7 + B18 * E7 + C18 * F7
G18: A18 * D8 + B18 * E8 + C18 * F8
F19: A19 * D7 + B19 * E7 + C19 * F7
G19: A19 * D8 + B19 * E8 + C19 * F8
F20: A20 * D7 + B20 * E7 + C20 * F7
G20: A20 * D8 + B20 * E8 + C20 * F8
F21: A21 * D8 + B21 * E8 + C21 * F8
G21: A21 * D8 + B21 * E8 + C21 * F8
F23: A23 * 0.0 + B23 * 0.0 + C23 * 0.0
G23: A23 * 0.0 + B23 * 0.0 + C23 * 0.0
F26 = -1.004193116
G26 = -1.32746102
F27 = 0.678748853
G27 = -1.479955952
F29 = 1.58804628
G29 = -0.210318842
F30 = -0.09489569
G30 = -0.05782391
A22 = 0
B22 = 0
C22 = 0
F22: A22 * D9 + B22 * E9 + C22 * F9
F14: A14 * D7 + B14 * E7 + C14 * F7
I12 = -1
J12 = 0
K12 = 0
I13 = 1
J13 = 0
K13 = 0
I15 = 0
J15 = -1
K15 = 0
I16 = 0
J16 = 1
K16 = 0
I18 = 0
J18 = 0
K18 = -1
I19 = 0
J19 = 0
K19 = 1
M12: I12 * D7 + J12 * E7 + K12 * F7
G7 = 0
N12: I12 * D8 + J12 * E8 + K12 * F8
M13: I13 * D7 + J13 * E7 + K13 * F7
N13: I13 * D8 + J13 * E8 + K13 * F8
I14 = 0
J14 = 0
K14 = 0
M14: I14 * D7 + J14 * E7 + K14 * 7.0
D10 = 0
E10 = 0
F10 = 0
N14: I14 * D8 + J14 * E8 + K14 * F8
M15: I15 * D7 + J15 * E7 + K15 * F7
D11 = 0
E11 = 0
F11 = 0
N15: I15 * D8 + J15 * E8 + K15 * F8
M16: I16 * D7 + J16 * E7 + K16 * F7
N16: I16 * D8 + J16 * E8 + K16 * F8
I17 = 0
J17 = 0
K17 = 0
M17: I17 * D8 + J17 * E8 + K17 * F8
N17: I17 * D9 + J17 * E9 + K17 * F9
M18: I18 * D7 + J18 * E7 + K18 * F7
N18: I18 * D8 + J18 * E8 + K18 * F8
M19: I19 * D7 + J19 * E7 + K19 * F7
N19: I19 * D8 + J19 * E8 + K19 * F8
P_9: (M12, N12)
P_{10}: (M13, N13)
P_{11}: (M14, N14)
P_{12}: (M15, N15)
P_{13}: (M16, N16)
P_{14}: (M17, N17)
P_{15}: (M18, N18)
P_{16}: (M19, N19)
L_3: {(M12, N12), (M13, N13), (M14, N14), (M15, N15), (M16, N16), (M17, N17), (M18, N18), (M19, N19)}
c = Segment(P_{13}, P_{14})
d = Line(P_{12}, P_{13})
e = Line(P_{15}, P_{16})
f = Line(P_9, P_{10})
u = Vector(P_{14}, P_{10})
v = Vector(P_{14}, P_{13})
w = Vector(P_{14}, P_{15})
B = Translate(P_{14}, u)
A = Translate(P_{14}, u)
C = Point(Circle[P_{14}, abs(x_M)])
g = Segment(P_{14}, C)
b = Segment(P_{14}, A)
h = Circle(P_{14}, abs(x_M) * b)
D, E = Intersect(h, f)
k = Circle(P_{14}, abs(y_M) * c)
F, G = Intersect(k, d)
a = Segment(P_{14}, P_{15})
p = Circle(P_{14}, abs(z_M) * a)
H, I = Intersect(p, e)
i = Line(If[x_M ≥ 0.0, E, D], d)
q = Line(If[x_M ≥ 0.0, E, D], e)
i_1 = Segment(P_{14}, If[x_M ≥ 0.0, E, D])
k_1 = Segment(P_{14}, If[z_M ≥ 0.0, H, I])
l_1 = Segment(P_{14}, If[y_M ≥ 0.0, G, F])
text7: "(" + x_M + " ; " + y_M + " ; " + z_M + " )"
text8: "" + x_M
text9: "" + y_M
text10: "" + z_M
j = Line(If[x_M ≥ 0.0, E, D], e)
l = Line(If[y_M ≥ 0.0, G, F], f)
m = Line(If[y_M ≥ 0.0, G, F], e)
n = Line(If[z_M ≥ 0.0, H, I], f)
J = Intersect(n, j)
r = Segment(J, If[x_M ≥ 0.0, E, D])
s = Segment(If[z_M ≥ 0.0, H, I], J)
t = Line(If[z_M ≥ 0.0, H, I], d)
K = Intersect(m, t)
a1 = Segment(If[z_M ≥ 0.0, H, I], K)
b1 = Line(K, s)
c1 = Line(J, d)
M = Intersect(c1, b1)
d1 = Segment(M, P_{11})
e1 = Segment(K, M)
L = Intersect(i, l)
f1 = Segment(M, L)
g1 = Segment(If[y_M ≥ 0.0, G, F], L)
h1 = Segment(If[x_M ≥ 0.0, E, D], L)
i1 = Segment(K, If[y_M ≥ 0.0, G, F])
j1 = Segment(J, M)
T1: "" + x_M
T2: "" + y_M
T3: "" + z_M