3-Geometry-Projections-Sphere To Plane

conical projection

Projecting sphere onto plane {conical projection, geometry} can have meridians radiating from vertex at equal angles and parallels in concentric circles around vertex.

equatorial projection

Equator can be in map center {equatorial projection}. Equatorial projection can have two forms {semisided} {flat polar quartic}.

line projection

Projecting sphere onto plane {line projection} can keep east-west horizontal latitude constant and vertical longitude lines from pole to pole constant.

orthomorphic projection

Projecting sphere onto plane {orthomorphic projection} can keep shapes similar.

3-Geometry-Projections-Sphere To Plane-Area Constant

equal area projection

Projecting sphere onto plane {homalographic projection} {equal area projection} can keep area ratios constant.

cylindrical projection

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.

elliptical projection

Projecting sphere onto plane {elliptical projection} can place equator, meridians, and parallels to maximally reduce distortion. Elliptical projections preserve areas.

orthographic projection

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.

3-Geometry-Projections-Sphere To Plane-Azimuth Constant

azimuthal projection

Projecting sphere onto plane {azimuthal projection} can keep correct azimuth.

conformal transformation

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.

Mercator projection

Projecting sphere onto plane {Mercator's projection} {Mercator projection} can maintain straight-line loxodrome constant bearings.

Miller projection

Projecting sphere onto plane {Miller projection} can keep straight-line loxodrome constant bearings but reduce area distortion at poles.

3-Geometry-Projections-Sphere To Plane-Zenithal

zenithal projection

Projecting sphere onto plane {zenithal projection} can use plane tangent to sphere.

3-Geometry-Projections-Sphere To Plane-Zenithal-Center

central projection of sphere

Projecting sphere onto plane {central projection, mapping} {gnomic projection} can use zenithal projection with projection center at sphere center.

orthographic projection zenithal

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.

stereographic projection

Projecting sphere onto plane {stereographic projection, map} can use zenithal projection with projection center at opposite end of diameter at tangent.

3-Geometry-Projections-Sphere To Plane-Zenithal-Tangent

normal projection

Projecting sphere onto plane {normal projection} can use plane tangent at equator.

oblique projection zenithal

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.

polar projection

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