Mathematical Principles for Scientific Computing and Visualization  
http://www.farinhansford.com/books/scv
by Gerald Farin and Dianne Hansford


This notebook illustrates the idea behind UTM coordinates.

A sphere and cylinder are illustrated. The sphere has been subdivided into 60 longitudinal wedges and 20 latitudinal slices. A UTM coordinate section is created with one 3 degree LONG wedge, and this is displayed as a white strip in the plot. This wedge can be mapped to the cylinder fairly accurately. The cylinder can be unfolded to a flat sheet without distortion -- and there we have our map!

See Chapter 3: Coordinate Systems for details.

Updated May 2008

(* Output results to folder that this file lives in *)
(SetDirectory[ToFileName[Extract["FileName"/.NotebookInformation[EvaluationNotebook[]],{1},FrontEnd`FileName]]];) 


(* Create a sphere with 60 LONG section and 20 LAT sections *)

sppic = ParametricPlot3D[{Cos[ϕ]Sin[θ],Sin[ϕ]Sin[θ],Cos[θ]},{ϕ,0,2π},{θ,0,π}, Axes->False, Mesh->{60,20}]

(* Create a cylinder the touches the sphere *)

cpic =Graphics3D[{Opacity[0.5],Cylinder[{{0,-2,0},{0,2,0}},1]}];


(* Contact area is a wedge *)
(* Plot thick line segments along this wedge *)
n=60;
contact=Graphics3D[{Thickness[0.02],RGBColor[1,1,1],
Line[Table[{1*Sin[(i/n)],0,1* Cos[(i/n)]},{i,1,2 n π}]]}];


(* Combine graphics and display *)
pic=Show[sppic,cpic,contact, Boxed->False,PlotRange->All]

(* Output to postscript file *)
(* Export["UTM_coords.eps",pic] *)