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They are written in terms of longitude (λ) and latitude (φ) on the sphere. Define the radius of the sphere R and the center point (and origin) of the projection (λ 0, φ 0). The equations for the orthographic projection onto the (x, y) tangent plane reduce to the following: [1]
Stereographic projection of the unit sphere from the north pole onto the plane z = 0, shown here in cross section. The unit sphere S 2 in three-dimensional space R 3 is the set of points (x, y, z) such that x 2 + y 2 + z 2 = 1.
The maturation of complex analysis led to general techniques for conformal mapping, where points of a flat surface are handled as numbers on the complex plane.While working at the United States Coast and Geodetic Survey, the American philosopher Charles Sanders Peirce published his projection in 1879, [2] having been inspired by H. A. Schwarz's 1869 conformal transformation of a circle onto a ...
A medieval depiction of the Ecumene (1482, Johannes Schnitzer, engraver), constructed after the coordinates in Ptolemy's Geography and using his second map projection. In cartography, a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane.
A circle with non-zero geodesic curvature is called a small circle, and is analogous to a circle in the plane. A small circle separates the sphere into two spherical disks or spherical caps, each with the circle as its boundary. For any triple of distinct non-antipodal points a unique small circle passes through all three.
Projects the globe onto eight octants (Reuleaux triangles) with no meridians and no parallels. 1909 Cahill's butterfly map: Polyhedral Compromise Bernard Joseph Stanislaus Cahill: Projects the globe onto an octahedron with symmetrical components and contiguous landmasses that may be displayed in various arrangements. 1975 Cahill–Keyes projection
A cross sectional view of the sphere and a plane tangent to it at S. Each point on the sphere (except the antipode) is projected to the plane along a circular arc centered at the point of tangency between the sphere and plane. To define the Lambert azimuthal projection, imagine a plane set tangent to the sphere at some point S on the
The Gauss map provides a mapping from every point on a curve or a surface to a corresponding point on a unit sphere. In this example, the curvature of a 2D-surface is mapped onto a 1D unit circle. In differential geometry , the Gauss map of a surface is a function that maps each point in the surface to a unit vector that is orthogonal to the ...