méridiens

parallèles

pôles

équateur

points A et B sur la sphère

grand cercle passant par A et B

route orthodromique de A à B

cylindre de projection

projections de A et B sur le cylindre

point mobile M sur l'orthodromie de A à B et sa projection sur le cylindre

méridiens mercator

parallèles mercator

Orthodromie - Loxodromie - Projection de Mercator

O: (0, 0, 0)
N: (0, 0, 1)
S: (0, 0, -1)
a = Sphere(O, N)
f = Segment(N, S)
c = IntersectPath(xOyPlane, a)
h = Line(N, S)
liste1 = Sequence(Circle[h, (cos(β), 0, sin(β))], β, -90°, 90°, 10°)
liste2 = Sequence(Circle[N, S, (cos(α), sin(α))], α, 0°, 180°, 10°)
b = false
d = false
e = false
g = false
A = PointIn(a)
B = PointIn(a)
i = false
j = Plane(O, A, B)
k = IntersectPath(j, a)
l = Segment(A, O)
m = Segment(O, B)
o = false
p = CircleArc(O, A, B)
n = false
q, r, s, t = Cylinder(N, S, 1)
u = false
f_1 = Ray(O, A)
g_1 = Ray(O, B)
C = Intersect(f_1, t)
D = Intersect(g_1, t)
M_1 = Point(p)
h_1 = Ray(O, M_1)
F = Intersect(h_1, t)
v = false
w = false
liste3 = Sequence((cos(t), sin(t), 0), t, 0°, 350°, 10°)
L_1 = Sequence(Segment[(cos(t), sin(t), -1), (cos(t), sin(t), 1)], t, 0°, 350°, 10°)
L_2 = Sequence(Circle[(0, 0, tan(t)), 1, xOyPlane], t, -40°, 40°, 10°)
a_1 = false
b_1 = false
M = PointIn(a)
i_1 = Ray(O, M)
M' = Intersect(i_1, t)
j_1 = Segment(M, O)
k_1 = Segment(M', M)
c_1 = Plane(M, O, N)
d_1 = IntersectPath(c_1, q)
E, G, H, I = Corner(d_1)
e_1 = IntersectPath(c_1, a)
l_1 = OrthogonalPlane(M, f)
p_1 = IntersectPath(l_1, a)
m_1 = OrthogonalPlane(M', f)
q_1 = IntersectPath(m_1, q)
L_3 = Sequence((cos(t), sin(t), t), t, 0°, 360°, 0.1°)