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# Conic Projection

A conic projection of points on a unit sphere centered at consists of extending the line for each point until it intersects a cone with apex which tangent to the sphere along a circle passing through a point in a point . For a cone with apex a height above , the angle from the z-axis at which the cone is tangent is given by

 (1)

and the radius of the circle of tangency and height above at which it is located are given by

 (2) (3)

Letting be the colatitude of a point on a sphere, the length of the vector along is

 (4)

The left figure above shows the result of re-projecting onto a plane perpendicular to the z-axis (equivalent to looking at the cone from above the apex), while the figure on the right shows the cone cut along the solid line and flattened out. The equations transforming a point on a sphere to a point on the flattened cone are

 (5) (6)

This form of the projection, however, is seldom used in practice, and the term "conic projection" is used instead to refer to any projection in which lines of longitude are mapped to equally spaced radial lines and lines of latitude (parallels) are mapped to circumferential lines with arbitrary mathematically spaced separations (Snyder 1987, p. 5).

Albers Equal-Area Conic Projection, Conic Equidistant Projection, Cylindrical Projection, Lambert Azimuthal Equal-Area Projection, Polyconic Projection

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## References

Lee, L. P. "The Nomenclature and Classification of Map Projections." Empire Survey Rev. 7, 190-200, 1944.Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, p. 5, 1987.

Conic Projection

## Cite this as:

Weisstein, Eric W. "Conic Projection." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ConicProjection.html