Stereographic Projection

Author

Eric W. Weisstein
January 26, 2011

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

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

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

Figure

Projection

V5

Show[Graphics[ProjectionPlot[Projection[Stereographic[]],GridSegments->200]],AspectRatio->Automatic]//Timing

Graphics[MapProjectionPlot[MapProjection[Stereographic[]],GridSegments->200]]

"StereographicProjection"->,

Inverse

InverseProjection[Stereographic[phi1_:0,l0_:0]]:=Function[{x,y},Module[{rho=Sqrt[x^2+y^2],c},
c=2ArcTan[rho/2];
{ArcSin[Cos[c]Sin[phi1]+y Sin[c]Cos[phi1]/rho],
l0+ArcTan[rho Cos[phi1]Cos[c]-y Sin[phi1]Sin[c],x Sin[c]]}
]
]

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

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

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