Gnomonic Projection

Author

Eric W. Weisstein
December 29, 2010

This notebook downloaded from http://mathworld.wolfram.com/notebooks/MapProjections/GnomonicProjection.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/GnomonicProjection.html.

©2010 Wolfram Research, Inc. except for portions noted otherwise

Plot

V5

m=MapCoordinates[];
Hemisphere=DeleteCases[DeleteCases[(DeleteCases[#,_?(Abs[Last[#]]>Pi/2&)]&/@m),{}],{{x_,y_}}];
NorthernHemisphere=DeleteCases[DeleteCases[#,_?(First[#]<0&)]&/@m,{}];

Show[Graphics[ProjectionPlot[
Projection[Gnomonic[90.Degree,0.Degree]],NorthernHemisphere,GridSegments->200]],
AspectRatio->Automatic,ImageSize->300]

Show[Graphics[ProjectionPlot[
Projection[Gnomonic[0.Degree,0.Degree]],Hemisphere,GridSegments->500]],
AspectRatio->Automatic,ImageSize->400,PlotRange->{{-1,1},{-1,1}}5]

V6

m=MapCoordinates[];
Hemisphere=DeleteCases[DeleteCases[(DeleteCases[#,_?(Abs[Last[#]]>Pi/2&)]&/@m),{}],{{x_,y_}}];
NorthernHemisphere=DeleteCases[DeleteCases[#,_?(First[#]<0&)]&/@m,{}];

Graphics[MapProjectionPlot[
MapProjection[Gnomonic[90.Degree,0.Degree]],NorthernHemisphere,GridSegments->200],
AspectRatio->Automatic,ImageSize->300,PlotRange->2.5]

Graphics[MapProjectionPlot[
MapProjection[Gnomonic[0.Degree,0.Degree]],Hemisphere,GridSegments->500],AspectRatio->Automatic,ImageSize->400,PlotRange->5]

Inverse

Show[Graphics[{Red,Line/@Hemisphere}],AspectRatio->Automatic,PlotRange->{{-1,1}Pi/2,{-1,1}Pi},ImageSize->100]

proj=Flatten[ProjectionPlot[Projection[Gnomonic[]],Hemisphere,GridLines->None][[-1,-1]]];

Show[Graphics[ProjectionPlot[InverseProjection[Gnomonic[]],Identity@@@proj,GridLines->None]],AspectRatio->Automatic,PlotRange->{{-1,1}Pi/2,{-1,1}Pi},ImageSize->100]