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Craters which are circles on the sphere appear circular in this projection, regardless of whether they are close to the pole or the edge of the map. The stereographic is the only projection that maps all circles on a sphere to circles on a plane. This property is valuable in planetary mapping where craters are typical features.
For example, a small circle of fixed radius (e.g., 15 degrees angular radius). [14] Sometimes spherical triangles are used. [citation needed] In the first half of the 20th century, projecting a human head onto different projections was common to show how distortion varies across one projection as compared to another. [15]
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 ...
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
For example, lines traced from the eye point at 45° to the picture plane intersect the latter along a circle whose radius is the distance of the eye point from the plane, thus tracing that circle aids the construction of all the vanishing points of 45° lines; in particular, the intersection of that circle with the horizon line consists of two ...
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
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.
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]