Merak sur ciel

Megrez sur le ciel

Dubhe sur ciel

Alioth sur ciel

Benetnash sur le ciel

α

δ

UMA

Dubhe

Merak

Phekda

Megrez

Alioth

Mizar

Benetnash

Sphère des fixes de rayon 1

y

x

z

Lignes

Constellations sur la voute celleste

ORI

Betelgeuse

Rigel

Bellatrix

Mintaka

Alnilam

Alnitak

Saïph

dist en al

Mizar sur le ciel

Observateur hors projection sur le plan

Pour réduire les al

Alioth

Benetnash

Dubhe

Megrez

Merak

Mizar

Phekda

Constellation "réelle"

Sphère, plan et points de base

B5 = 178.5
C5 = 53.7
PheSp: (1; B5°; C5°)
S = (0, 0, -1)
B4 = 165.5
C4 = 56.4
MerSp: (1; B4°; C4°)
B6 = 183.9
C6 = 57
MegSp: (1; B6°; C6°)
B3 = 165.9
C3 = 61.8
DubSp: (1; B3°; C3°)
C7 = 56
B7 = 193.5
AliSp: (1; B7°; C7°)
B9 = 206.9
C9 = 49.3
BenSp: (1; B9°; C9°)
D5: 83.18
D8: 78.16
C8 = 54.9
B8 = 201
D4: 79.74
D7: 82.55
D9: 103.94
D3: 123.64
D6: 80.51
G7: sin(C7°)
F7: (sin(B7°) * cos(C7°))
E7: (cos(B7°) * cos(C7°))
N: (0, 0, 1)
SphCel = Sphere((0, 0, 0), 1)
E3: (cos(B3°) * cos(C3°))
F3: (sin(B3°) * cos(C3°))
G3: sin(C3°)
E4: (cos(B4°) * cos(C4°))
F4: (sin(B4°) * cos(C4°))
G4: sin(C4°)
E5: (cos(B5°) * cos(C5°))
F5: (sin(B5°) * cos(C5°))
G5: sin(C5°)
E6: (cos(B6°) * cos(C6°))
F6: (sin(B6°) * cos(C6°))
G6: sin(C6°)
E8: (cos(B8°) * cos(C8°))
F8: (sin(B8°) * cos(C8°))
G8: sin(C8°)
E9: (cos(B9°) * cos(C9°))
F9: (sin(B9°) * cos(C9°))
G9: sin(C9°)
affLigne = true
affCons = true
B11 = 88.8
C11: 7.4
E11 = 7.91
F11 = 8.26
B12 = 78.6
C12 = -8.2
E12 = 10.39
F12 = 9.82
B13 = 81.3
C13 = 6.3
E13 = 8.06
F13 = 8.37
B14 = 83
C14 = -0.3
E14 = 9.05
F14 = 9.03
B15 = 84.1
C15 = -1.2
E15 = 9.19
F15 = 9.12
B16 = 85.2
C16 = -1.9
E16 = 9.3
F16 = 9.19
B17 = 86.9
C17 = -9.7
E17 = 10.67
F17 = 9.97
G11: sin(C11°)
G12: sin(C12°)
G13: sin(C13°)
G14: sin(C14°)
G15: sin(C15°)
G16: sin(C16°)
G17: sin(C17°)
d = Line(N, S)
D7_{1}: 82.55
MizSp: (1; B8°; C8°)
T: (0, 0, 0)
ddMiz = Ray(T, MizSp)
ddBen = Ray(T, BenSp)
ddAli = Ray(T, AliSp)
ddDub = Ray(T, DubSp)
ddMeg = Ray(T, MegSp)
ddMer = Ray(T, MerSp)
ddPhe = Ray(T, PheSp)
e = 10.4 (slider from -5 to 20)
Ali = Intersect(ddAli, Sphere[T, D7 / e])
Ben = Intersect(ddBen, Sphere[T, D9 / e])
Dub = Intersect(ddDub, Sphere[T, D3 / e])
Meg = Intersect(ddMeg, Sphere[T, D6 / e])
Mer = Intersect(ddMer, Sphere[T, D4 / e])
Miz = Intersect(ddMiz, Sphere[T, D8 / e])
Phe = Intersect(ddPhe, Sphere[T, D5 / e])
affReelle = true
affSphere = true

Tool: Projection stereographique (command ProjSte)
Le point à projeter, le centre de projection, le plan de projection
Input: A, S, pe
Output: B

B = (0.06410702672133516, 1.1837023313521506, 0)

Tool: StereoCercle
Input: P, O, pe
Output: c

S: (x(O), y(O), z(O) - 1)
n = (0.3272612614568508, 0.02728630202435406, 0)
A_1 = (-0.8738910890424567, 0.25667327370967985, 0.41283555449518244)
A_2 = (0.8193184849937485, 0.39784924920402176, 0.41283555449518244)
B_1 = (0.027955611642380203, -0.33528869990215343, 0.9417005742249625)
B_2 = (-0.08252821569108834, 0.9898112228158551, -0.11602946523459762)
A = (-0.6185370167547242, 0.18167243377548725, 0)
B = (0.5799107209518787, 0.28159628906435363, 0)
C = (0.014397488476583882, -0.17267785999187094, 0)

Tool: Projection stereographique (command ProjSte1)
Le point à projeter, le centre de projection, le plan de projection
Input: A, S, pe
Output: B

B = (0.06410702672133516, 1.1837023313521506, 0)

Tool: StereoCercle (command StereoCercle1)
Input: P, O, pe
Output: c

S: (x(O), y(O), z(O) - 1)
n = (0.3272612614568508, 0.02728630202435406, 0)
A_1 = (-0.8738910890424567, 0.25667327370967985, 0.41283555449518244)
A_2 = (0.8193184849937485, 0.39784924920402176, 0.41283555449518244)
B_1 = (0.027955611642380203, -0.33528869990215343, 0.9417005742249625)
B_2 = (-0.08252821569108834, 0.9898112228158551, -0.11602946523459762)
A = (-0.6185370167547242, 0.18167243377548725, 0)
B = (0.5799107209518787, 0.28159628906435363, 0)
C = (0.014397488476583882, -0.17267785999187094, 0)

Tool: Projection stereographique (command ProjSte2)
Le point à projeter, le centre de projection, le plan de projection
Input: A, S, pe
Output: B

B = (0.06410702672133516, 1.1837023313521506, 0)

Tool: StereoCercle (command StereoCercle2)
Input: P, O, pe
Output: c

S: (x(O), y(O), z(O) - 1)
n = (0.3272612614568508, 0.02728630202435406, 0)
A_1 = (-0.8738910890424567, 0.25667327370967985, 0.41283555449518244)
A_2 = (0.8193184849937485, 0.39784924920402176, 0.41283555449518244)
B_1 = (0.027955611642380203, -0.33528869990215343, 0.9417005742249625)
B_2 = (-0.08252821569108834, 0.9898112228158551, -0.11602946523459762)
A = (-0.6185370167547242, 0.18167243377548725, 0)
B = (0.5799107209518787, 0.28159628906435363, 0)
C = (0.014397488476583882, -0.17267785999187094, 0)

Tool: Projection stereographique (command ProjSte11)
Le point à projeter, le centre de projection, le plan de projection
Input: A, S, pe
Output: B

B = (0.06410702672133516, 1.1837023313521506, 0)

Tool: StereoCercle (command StereoCercle11)
Input: P, O, pe
Output: c

S: (x(O), y(O), z(O) - 1)
n = (0.3272612614568508, 0.02728630202435406, 0)
A_1 = (-0.8738910890424567, 0.25667327370967985, 0.41283555449518244)
A_2 = (0.8193184849937485, 0.39784924920402176, 0.41283555449518244)
B_1 = (0.027955611642380203, -0.33528869990215343, 0.9417005742249625)
B_2 = (-0.08252821569108834, 0.9898112228158551, -0.11602946523459762)
A = (-0.6185370167547242, 0.18167243377548725, 0)
B = (0.5799107209518787, 0.28159628906435363, 0)
C = (0.014397488476583882, -0.17267785999187094, 0)

Tool: Projection stereographique (command ProjSte3)
Le point à projeter, le centre de projection, le plan de projection
Input: A, S, pe
Output: B

B = (0.06410702672133516, 1.1837023313521506, 0)

Tool: StereoCercle (command StereoCercle3)
Input: P, O, pe
Output: c

S: (x(O), y(O), z(O) - 1)
n = (0.3272612614568508, 0.02728630202435406, 0)
A_1 = (-0.8738910890424567, 0.25667327370967985, 0.41283555449518244)
A_2 = (0.8193184849937485, 0.39784924920402176, 0.41283555449518244)
B_1 = (0.027955611642380203, -0.33528869990215343, 0.9417005742249625)
B_2 = (-0.08252821569108834, 0.9898112228158551, -0.11602946523459762)
A = (-0.6185370167547242, 0.18167243377548725, 0)
B = (0.5799107209518787, 0.28159628906435363, 0)
C = (0.014397488476583882, -0.17267785999187094, 0)

Tool: Projection stereographique (command ProjSte12)
Le point à projeter, le centre de projection, le plan de projection
Input: A, S, pe
Output: B

B = (0.06410702672133516, 1.1837023313521506, 0)

Tool: StereoCercle (command StereoCercle12)
Input: P, O, pe
Output: c

S: (x(O), y(O), z(O) - 1)
n = (0.3272612614568508, 0.02728630202435406, 0)
A_1 = (-0.8738910890424567, 0.25667327370967985, 0.41283555449518244)
A_2 = (0.8193184849937485, 0.39784924920402176, 0.41283555449518244)
B_1 = (0.027955611642380203, -0.33528869990215343, 0.9417005742249625)
B_2 = (-0.08252821569108834, 0.9898112228158551, -0.11602946523459762)
A = (-0.6185370167547242, 0.18167243377548725, 0)
B = (0.5799107209518787, 0.28159628906435363, 0)
C = (0.014397488476583882, -0.17267785999187094, 0)

Tool: Projection stereographique (command ProjSte21)
Le point à projeter, le centre de projection, le plan de projection
Input: A, S, pe
Output: B

B = (0.06410702672133516, 1.1837023313521506, 0)

Tool: StereoCercle (command StereoCercle21)
Input: P, O, pe
Output: c

S: (x(O), y(O), z(O) - 1)
n = (0.3272612614568508, 0.02728630202435406, 0)
A_1 = (-0.8738910890424567, 0.25667327370967985, 0.41283555449518244)
A_2 = (0.8193184849937485, 0.39784924920402176, 0.41283555449518244)
B_1 = (0.027955611642380203, -0.33528869990215343, 0.9417005742249625)
B_2 = (-0.08252821569108834, 0.9898112228158551, -0.11602946523459762)
A = (-0.6185370167547242, 0.18167243377548725, 0)
B = (0.5799107209518787, 0.28159628906435363, 0)
C = (0.014397488476583882, -0.17267785999187094, 0)

Tool: Projection stereographique (command ProjSte111)
Le point à projeter, le centre de projection, le plan de projection
Input: A, S, pe
Output: B

B = (0.06410702672133516, 1.1837023313521506, 0)

Tool: StereoCercle (command StereoCercle111)
Input: P, O, pe
Output: c

S: (x(O), y(O), z(O) - 1)
n = (0.3272612614568508, 0.02728630202435406, 0)
A_1 = (-0.8738910890424567, 0.25667327370967985, 0.41283555449518244)
A_2 = (0.8193184849937485, 0.39784924920402176, 0.41283555449518244)
B_1 = (0.027955611642380203, -0.33528869990215343, 0.9417005742249625)
B_2 = (-0.08252821569108834, 0.9898112228158551, -0.11602946523459762)
A = (-0.6185370167547242, 0.18167243377548725, 0)
B = (0.5799107209518787, 0.28159628906435363, 0)
C = (0.014397488476583882, -0.17267785999187094, 0)