Paramètres de la perspective

Afficher M

Parallèles seulement

Méridiens seulement

Parallèles et méridiens

0°

-45° 0° 45°

-60° 30° 0° 30° 60°

-67,5° 45° -22,5° 0° 22,5° 45° 67,5°

-72° -54° -36° -18° 0° 18° 36° 54° 72°

-75° -60° -45° -30° -15° 0° 15° 30° 45° 60° 75°

-78,75° -67,5° -56,25° -45° -33,75° -22,5° -11,25°
0°
11,25° 22,5° 33,75° 45° 56,25° 67,5° 78,75°

-80° -70° -60° -50° -40° -30° -20° -10°
0°
10° 20° 30° 40° 50° 60° 70° 80°

-81° -72° -63° -54° -45° -36° -27° -18° -9°
0°
9° 18° 27° 36° 45° 54° 63° 72° 81°

0° 90°

0° 45° 90° 135°

0° 30° 60° 90° 120° 150°

0° 22,5° 45° 67,5° 90° 112,5° 135° 157,5°

0° 18° 36° 54° 72° 90° 108° 126° 144° 162°

0° 15° 30° 45° 60° 75°
90° 105° 120° 135° 150° 165°

-77,14° -64,29° -51,43° -38,57° -25,72° -12,86° 
0°
12,86° 25,72° 38,57° 51,43° 64,29° 77,14°

0° 12,86° 25,74° 38,57° 51,53° 64,29° 77,14°
90° 102,86° 115,71° 128,57° 141,43° 154,29° 167,14°

0° 11,25° 22,5° 33,75° 45° 56,25° 67,5° 78,75°
90° 101,25° 112,5° 123,75° 135° 146,25° 157,5° 168,75°

0° 10° 20° 30° 40° 50° 60° 70° 80°
90° 100° 110° 120° 130° 140° 150° 160° 170°

0° 9° 18° 27° 36° 45° 54° 63° 72° 81°
90° 99° 108° 117° 126° 135° 144° 153° 162° 171°

φ = 0.6283185307179586 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
θ = 0.6632251157578453 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
O_3: {0, 0, 0}
O: (Element[O_3, 1], Element[O_3, 2])
i_3: {1, 0, 0}
i = Vector(O, (Element[i_3, 1], Element[i_3, 2]))
j_3: {0, 1, 0}
j = Vector(O, (Element[j_3, 1], Element[j_3, 2]))
k_3: {0, 0, 1}
P: {-sin(θ), cos(θ), 0, -cos(θ) sin(φ), -sin(θ) sin(φ), cos(φ), cos(θ) cos(φ), sin(θ) cos(φ), sin(φ)}
U: (Element[P, 1] Element[i_3, 1] + Element[P, 2] Element[i_3, 2] + Element[P, 3] Element[i_3, 3], Element[P, 4] Element[i_3, 1] + Element[P, 5] Element[i_3, 2] + Element[P, 6] Element[i_3, 3])
V: (Element[P, 1] Element[j_3, 1] + Element[P, 2] Element[j_3, 2] + Element[P, 3] Element[j_3, 3], Element[P, 4] Element[j_3, 1] + Element[P, 5] Element[j_3, 2] + Element[P, 6] Element[j_3, 3])
W: (Element[P, 1] Element[k_3, 1] + Element[P, 2] Element[k_3, 2] + Element[P, 3] Element[j_3, 3], Element[P, 4] Element[k_3, 1] + Element[P, 5] Element[k_3, 2] + Element[P, 6] Element[k_3, 3])
u = Vector(O, U)
v = Vector(O, V)
w = Vector(O, W)
horiz_1 = Translate(xAxis, Vector[9 / 2 j])
horiz_2 = Translate(xAxis, Vector[7 / 2 j])
horiz_3 = Translate(xAxis, Vector[5 / 2 j])
horiz_4 = Translate(xAxis, Vector[3 / 2 j])
vert_1 = Translate(yAxis, Vector[-7 / 2 i])
vert_2 = Translate(yAxis, Vector[7 / 2 i])
Φ = 1.0995574287564276 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
R_Φ: {cos(Φ), -sin(Φ), 0, sin(Φ), cos(Φ), 0, 0, 0, 1}
Ψ = 0.47123889803846897 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
Coordsph: {cos(Φ) cos(Ψ), sin(Φ) cos(Ψ), sin(Ψ)}
AffM = false
M: (Element[P, 1] Element[Coordsph, 1] + Element[P, 2] Element[Coordsph, 2] + Element[P, 3] Element[Coordsph, 3], Element[P, 4] Element[Coordsph, 1] + Element[P, 5] Element[Coordsph, 2] + Element[P, 6] Element[Coordsph, 3])
coefΓ_0: {1, 0, 1 / sin(φ)^(2)}
Γ_0: Element[coefΓ_0, 1] x^(2) + Element[coefΓ_0, 2] x y + Element[coefΓ_0, 3] y^(2) = 1
den_Φ: cos(Φ) * (Element[P, 1] Element[P, 6] - Element[P, 4] Element[P, 3]) + sin(Φ) * (Element[P, 2] Element[P, 6] - Element[P, 5] Element[P, 3])
coefMer_0: {(Element[P, 6]^(2) + Element[P, 4]^(2)) / (Element[P, 1] Element[P, 6] - Element[P, 4] Element[P, 3])^(2), -2 * (Element[P, 3] Element[P, 6] + Element[P, 4] Element[P, 1]) / (Element[P, 1] Element[P, 6] - Element[P, 4] Element[P, 3])^(2), (Element[P, 3]^(2) + Element[P, 1]^(2)) / (Element[P, 1] Element[P, 6] - Element[P, 4] Element[P, 3])^(2)}
Mer_0: Element[coefMer_0, 1] x^(2) + Element[coefMer_0, 2] x y + Element[coefMer_0, 3] y^(2) = 1
coefMer_{90}: {(Element[P, 6]^(2) + Element[P, 5]^(2)) / (Element[P, 2] Element[P, 6] - Element[P, 5] Element[P, 3])^(2), -2 * (Element[P, 3] Element[P, 6] + Element[P, 5] Element[P, 2]) / (Element[P, 2] Element[P, 6] - Element[P, 5] Element[P, 3])^(2), (Element[P, 3]^(2) + Element[P, 2]^(2)) / (Element[P, 2] Element[P, 6] - Element[P, 5] Element[P, 3])^(2)}
Mer_{90}: Element[coefMer_{90}, 1] x^(2) + Element[coefMer_{90}, 2] x y + Element[coefMer_{90}, 3] y^(2) = 1
coefMer_Φ: {(Element[P, 6]^(2) + (cos(Φ) Element[P, 4] + sin(Φ) Element[P, 5])^(2)) / den_Φ^(2), -2 * (Element[P, 3] Element[P, 6] + (cos(Φ) Element[P, 4] + sin(Φ) Element[P, 5]) * (cos(Φ) Element[P, 1] + sin(Φ) Element[P, 2])) / den_Φ^(2), (Element[P, 3]^(2) + (cos(Φ) Element[P, 1] + sin(Φ) Element[P, 2])^(2)) / den_Φ^(2)}
Mer_{Phi}: Element[coefMer_Φ, 1] x^(2) + Element[coefMer_Φ, 2] x y + Element[coefMer_Φ, 3] y^(2) = 1
X_Ψ(x) = Element[P, 1] cos(x) cos(Ψ) + Element[P, 2] sin(x) cos(Ψ) + Element[P, 3] sin(Ψ)
Y_Ψ(x) = Element[P, 4] cos(x) cos(Ψ) + Element[P, 5] sin(x) cos(Ψ) + Element[P, 6] sin(Ψ)
Γ_Ψ = CurveCartesian(X_Ψ(t), Y_Ψ(t), t, 0, 6.283185307179586)
X_Φ(x) = Element[P, 1] cos(Φ) cos(x) + Element[P, 2] sin(Φ) cos(x) + Element[P, 3] sin(x)
Y_Φ(x) = Element[P, 4] cos(Φ) cos(x) + Element[P, 5] sin(Φ) cos(x) + Element[P, 6] sin(x)
Mer_Φ = CurveCartesian(X_Φ(t), Y_Φ(t), t, 0, 6.283185307179586)
AffPar = false
n_Γ = 3 (slider from 1 to 10, step 1)
k_Γ = CurveCartesian(t / (2 * 3.14), floor(t / (2 * 3.14)) - n_Γ + 1, t, 0, (2 n_Γ - 1) 2 * 3.14)
Psi(x) = (floor(x / (2 * 3.14)) - n_Γ + 1) 3.14 / (2 n_Γ)
X_Γ(x) = Element[P, 1] cos(x) cos(Psi(x)) + Element[P, 2] sin(x) cos(Psi(x)) + Element[P, 3] sin(Psi(x))
Y_Γ(x) = Element[P, 4] cos(x) cos(Psi(x)) + Element[P, 5] sin(x) cos(Psi(x)) + Element[P, 6] sin(Psi(x))
Γ = CurveCartesian(X_Γ(t), Y_Γ(t), t, 0, (2 n_Γ - 1) 2 * 3.14)
AffMer = false
n_M = 3 (slider from 1 to 10, step 1)
k_M = CurveCartesian(t / (2 * 3.14), floor(t / (2 * 3.14)), t, 0, 2 n_M 2 * 3.14)
Phi(x) = floor(x / (2 * 3.14)) 3.14 / (2 n_M)
X_M(x) = Element[P, 1] cos(Phi(x)) cos(x) + Element[P, 2] sin(Phi(x)) cos(x) + Element[P, 3] sin(x)
Y_M(x) = Element[P, 4] cos(Phi(x)) cos(x) + Element[P, 5] sin(Phi(x)) cos(x) + Element[P, 6] sin(x)
Mer = CurveCartesian(X_M(t), Y_M(t), t, 0, 2 n_M 2 * 3.14)
AffPM = true
n = 5 (slider from 1 to 10, step 1)
δ(x) = floor(x / (2 * 3.14 * 2 n))
Δ = CurveCartesian(t / (2 * 3.14), δ(t), t, 0, (4 n - 1) 2 * 3.14)
Φ_{M,Γ}(x) = floor(x / (2 * 3.141592653589793)) 3.141592653589793 / (2 n)
Ψ_{M,Γ}(x) = (floor(x / (2 * 3.141592653589793)) - 3 n + 1) 3.141592653589793 / (2 n)
Sph_1(x) = (1 - δ(x)) cos(Φ_{M,Γ}(x)) cos(x) + δ(x) cos(x) cos(Ψ_{M,Γ}(x))
Sph_2(x) = (1 - δ(x)) sin(Φ_{M,Γ}(x)) cos(x) + δ(x) sin(x) cos(Ψ_{M,Γ}(x))
Sph_3(x) = (1 - δ(x)) sin(x) + δ(x) sin(Ψ_{M,Γ}(x))
X_{M,Γ}(x) = Element[P, 1] Sph_1(x) + Element[P, 2] Sph_2(x) + Element[P, 3] Sph_3(x)
Y_{M,Γ}(x) = Element[P, 4] Sph_1(x) + Element[P, 5] Sph_2(x) + Element[P, 6] Sph_3(x)
MerΓ = CurveCartesian(X_{M,Γ}(t), Y_{M,Γ}(t), t, 0, (4 n - 1) 2 * 3.141592653589793)