Conic Projection


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


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


Letting phi^'=pi/2-phi be the colatitude of a point S on a sphere, the length of the vector OC along OS is


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 (phi,lambda) to a point on the flattened cone are


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).

See also

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

Explore with Wolfram|Alpha


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.

Referenced on Wolfram|Alpha

Conic Projection

Cite this as:

Weisstein, Eric W. "Conic Projection." From MathWorld--A Wolfram Web Resource.

Subject classifications