# Projecting a Circle on a Sphere to an Enclosing Cylinder

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A cylindrical projection maps points on a sphere to a cylinder wrapped around the sphere at its equator.

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Contributed by: Erik Mahieu (February 2016)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The transformation formulas used in this Demonstration are based on the Mathematica built-in function ToSphericalCoordinates and the conversion formulas in [1, 2].

For the equidistant projection, the following mapping is used to convert the Cartesian coordinates of a point on the unit sphere to the corresponding point on the cylinder wrapped around it: .

The equidistant projection to a plane uses the following mapping to convert the Cartesian coordinates of a point on the unit sphere to the corresponding point on the 2D plane: .

For the equal area projection, the following mapping is used to convert the Cartesian coordinates of a point on the unit sphere to the corresponding point on the cylinder wrapped around it: .

The equal-area projection to a plane uses the following mapping to convert the Cartesian coordinates of a point on the unit sphere to the corresponding point on the 2D plane: .

References

[1] E. W. Weisstein. "Cylindrical Equidistant Projection" from MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/CylindricalEquidistantProjection.html (Wolfram *MathWorld*).

[2] E. W. Weisstein. "Cylindrical Equal-Area Projection" from MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/CylindricalEqual-AreaProjection.html (Wolfram *MathWorld*).

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