// *** Script computing the shortest path between Paris and Tokyo ***
 clf()
// Earth as an ellipsoide :
[a,b,c] = (6378137,6378137,6356752)

// Paris and tokyo coordinates :
// Paris : 48° 51' 44" N 2° 21' 3" E
// Tokyo : 35° 40' N		139° 45' E
lat1 = [48,51,44,1]
lat2 = [35,40,0,1]
lon1 = [2,21,3,-1]
lon2 = [139,45,0,-1]

// Discretisation of theta and phi
[n,m] = (10,5)

// To get a mesh of the earth (one line of A is describing an edge : [node1,node2,length])
A = MaillageEllipsoide(a,b,c,n,m);

// To number all the nodes (line i = node n°1)
S = NumerotationSommets(A,n,m);

// To convert A in a matrix D : dij = length between i and j if (i,j) is an edge or %inf
D = Aretes2MatriceDistance(A,S,n,m);

// To get the edge i near to Paris (idem for tokyo : j)
i = SommetPlusProche(lat1,lon1,S)
j = SommetPlusProche(lat2,lon2,S)

// Shortest Path algorithmes
[FD,FP] = AlgoFloyd(D);
[DD,DP] = AlgoDijkstra(D,i);

// To get the path :
CF = Geodesique(FP(i,:),j); // use Floyd result
CD = Geodesique(DP,j);      // use Dijkstra result

// To draw the shortest path on the graph... What doesn't work well!
TraceChemin(CF,2,5,5);