Projecting sphere onto plane {conical projection, geometry} can have meridians radiating from vertex at equal angles and parallels in concentric circles around vertex.
Equator can be in map center {equatorial projection}. Equatorial projection can have two forms {semisided} {flat polar quartic}.
Projecting sphere onto plane {line projection} can keep east-west horizontal latitude constant and vertical longitude lines from pole to pole constant.
Projecting sphere onto plane {orthomorphic projection} can keep shapes similar.
Projecting sphere onto plane {homalographic projection} {equal area projection} can keep area ratios constant.
Projecting sphere onto plane {cylindrical projection, geometry} can make equator horizontal, make meridians perpendicular to equator and equidistant from each other, and place parallels at distances that maximally reduce distortion. Cylindrical projections preserve areas.
Projecting sphere onto plane {elliptical projection} can place equator, meridians, and parallels to maximally reduce distortion. Elliptical projections preserve areas.
Projecting sphere onto plane {orthographic projection, area} can use parallel rays to place one hemisphere on its equatorial plane, making circle edges highly distorted. Orthographic projection preserves either equivalent angles or areas. Mapmaker can choose to keep equivalent areas or equivalent directions but cannot choose both.
Projecting sphere onto plane {azimuthal projection} can keep correct azimuth.
Projecting sphere onto plane {conformal transformation}, such as stereographic, Mercator, and Miller projections, can preserve directions and angles. Gnomic, cylindrical, and elliptical projections do not preserve directions and angles.
Projecting sphere onto plane {Mercator's projection} {Mercator projection} can maintain straight-line loxodrome constant bearings.
Projecting sphere onto plane {Miller projection} can keep straight-line loxodrome constant bearings but reduce area distortion at poles.
Projecting sphere onto plane {zenithal projection} can use plane tangent to sphere.
Projecting sphere onto plane {central projection, mapping} {gnomic projection} can use zenithal projection with projection center at sphere center.
Projecting sphere onto plane {orthographic projection, zenithal} can use zenithal projection with projection center at infinite distance. Orthographic projection preserves either equivalent angles or areas. Mapmaker can choose to keep equivalent areas or equivalent directions but cannot choose both.
Projecting sphere onto plane {stereographic projection, map} can use zenithal projection with projection center at opposite end of diameter at tangent.
Projecting sphere onto plane {normal projection} can use plane tangent at equator.
Projecting sphere onto plane {oblique projection, zenithal} can use plane tangent to sphere at point that is neither at pole nor on equator. Pole can be not at map center.
Projecting sphere onto plane {polar projection} can use plane tangent at pole. Pole can be at map center {transverse projection} or offset from center.
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Date Modified: 2022.0225