A cylindrical projection of points on a unit sphere centered at O consists of extending the line O S for each point S until it intersects a cylinder tangent to the sphere at its equator at a corresponding point C. If the sphere is tangent to the cylinder at longitude λ_0, then a point on the sphere with latitude ϕ and longitude λ is mapped to a point on the cylinder with height tan ϕ. Unwrapping and flattening out the cylinder then gives the Cartesian coordinates x | = | λ - λ_0 y | = | tan ϕ. The cylindrical projection of the Earth is illustrated above.
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