Projection {projection, geometry} can project object onto plane or planes or project sphere onto plane.
Pictures of scenes can use linear perspective {perspective projection}.
Objects can project {geometric projection} onto planes. Plane figures {plane of projection} {projection plane} {image-plane} can transform to objects {image-picture} by one-to-one correspondence. Lines {projection ray} can join corresponding points from figures to images.
Projections {axonometric projection} can keep vertical lines vertical, have main horizontal axis at angle 45 or 30 degrees to verticals, and have third dimension at angle of 45 or 60 degrees to main horizontal axis.
Projections {isometric projection} can have all vertical lines stay vertical, and both other axes at angle 60 degrees to verticals.
Projections {oblique projection, object} can keep all vertical lines vertical, have main horizontal axis at right angle to right of verticals, and have third axis at angle 45 degrees to left of verticals. Oblique projection has projection rays not perpendicular to the plane.
Parallel projection {orthogonal projection, geometry} {orthographic projection, orthogonal} can have projection rays perpendicular to the plane. Orthogonal projection can be on horizontal plane {horizontal projection} {plan, projection}, vertical plane {elevation, projection}, or other planes {section, projection}. Plans {figured plan} can mark vertical distances from plane to figure.
Orthogonal projection {first angle projection} can be on bottom horizontal plane {plan projection, first angle}, back left vertical plane {front elevation, first angle}, and back right vertical plane {side elevation, first angle} {end elevation, first angle}. Front and plan are like looking into far lower corner from outside room.
Orthogonal projection {third angle projection} can be on top horizontal plane {plan projection, third angle}, front right vertical plane {front elevation, third angle}, and front left vertical plane {side elevation, third angle} {end elevation, third angle}. Front and plan projections are like looking into top front corner from outside room. This projection makes common edges closer and is usually better.
All three dimensions can be in one picture {pictorial projection}.
Pictorial projection {metric projection} can be to scale.
Projection rays can be parallel {cylindrical projection, rays} {parallel projection, rays}, so projection center is at infinity. Parallel projection can have projection rays perpendicular to plane {orthogonal projection, parallel} or not perpendicular to plane {oblique projection, parallel}.
Projection rays can pass through fixed point {central projection, rays} {radial projection} {conical projection, rays}.
Three-dimensional object can project onto two orthogonal planes {descriptive geometry} in central projection, point projection, parallel projection, perspectivity, or projectivity.
Three-dimensional object can project onto two orthogonal planes from center {central projection, geometry}.
Three-dimensional object can project onto two orthogonal planes using parallel lines {parallel projection, descriptive geometry}.
Three-dimensional object can project onto two orthogonal planes using section through object and projection onto plane {perspectivity}.
Three-dimensional object can project onto two orthogonal planes from point {point projection}.
Three-dimensional objects can project onto two orthogonal planes using projection and section sequences {projectivity}.
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.
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0225