Re: "Traveling salesman on a hemisphere" problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg121569] Re: "Traveling salesman on a hemisphere" problem*From*: Dana DeLouis <dana01 at me.com>*Date*: Tue, 20 Sep 2011 06:09:19 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Hi. Don't know if this could be of help. In Version #8, I don't know of a way to customize the datum's used in the Geodesy section. The old version has a package to manipulate Datums. Needs["Miscellaneous`Geodesy`"]//Quiet; ArcLen2[{_,Pt1_List},{_,Pt2_List}]:=SphericalDistance[Pt1,Pt2,Radius->1] (* Yours *) arclen[{"M51",{21,44.7`}},{"Comet",{57.3,7}}] 0.7945159 (* From Above *) ArcLen2[{"M51",{21,44.7}},{"Comet",{57.3,7}}] 0.7945159 If one wanted to be close, but not highly accurate, here's an approximate way in Ver 8. ArcLen3[{_,Pt1_List},{_,Pt2_List}]:= GeoDistance[Pt1,Pt2]/6367449 ArcLen3[{"M51",{21,44.7}},{"Comet",{57.3,7}}] 0.7948832 I used an Approximate conversion factor from the following: Solve[Pi / 2 - GeoDistance[{0,0},{90,0}]/x==0,x][[1,1,2]] //Round 6367449 = = = = = Dana DeLouis $Version 8.0 for Mac OS X x86 (64-bit) (November 6, 2010) On Sep 16, 5:55 am, Olaf <olaf.rogal... at googlemail.com> wrote: > Hi Peter, > > with the arclen from http://en.wikipedia.org/wiki/Great-circle_distance, > the following code will give you the shortest route. > > stars = { > {"M51", {21, 44.7}}, > {"NGC2721", {4, -17}}, > {"a funny comet", {57.3, 7}}, > {"absolutely must see", {23, -176.3}}}; > > arclen[{_, {F1_, L1_}}, {_, {F2_, L2_}}] := > Module[{f1 = F1 Degree, l1 = L1 Degree, f2 = F2 Degree, l2 = L2 > Degree, dl = (L1 - L2) Degree}, > ArcTan[Sin[f1] Sin[f2] + Cos[f1] Cos[f2] Cos[dl], > Sqrt[(Cos[f2] Sin[dl])^2 + (Cos[f1] Sin[f2] - Sin[f1] > Cos[f2] Cos[dl])^2]]] > > tour = FindShortestTour[stars, DistanceFunction -> arclen] > > sortedStars = starlist[[tour[[2]]]] > > And here some eye-candy: > > p2c[{_, {f_, l_}}] := {Cos[f Degree] Cos[l Degree], > Sin[f Degree] Cos[l Degree], Sin[l Degree]} > greatCircleArc[{q_, p_}] := > Module[{u = p2c[q], v = p2c[p], a}, a = VectorAngle[u, v]; > Table[Evaluate[RotationTransform[t, {u, v}][u]], {t, 0, a, > a/Ceiling[10 a]}]] > > Graphics3D[ > {Sphere[{0, 0, 0}, 0.97], > {Black, Thick, Arrow[{{0, 0, -1.3}, {0, 0, 1.3}}]}, > {Red, PointSize[Medium], Point[Map[p2c, sortedStars]]}, > {Blue, Thick, > Map[Line, Map[greatCircleArc, Partition[sortedStars, 2, 1]]]} > }, SphericalRegion -> True] > > Regards, Olaf