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projections panotools org wiki projections from panotools org wiki jump to navigation jump to search representing a spherical view of the world on a flat computer monitor or print requires some manner of mapping from the 3d spherical scene in which the camera and viewer are embedded to the 2d medium on which they are rendered the techniques used for mapping are of exactly the same type long used by map makers to project the entire globe or portions of it onto two dimensional maps there is no single unique projection for representing sections of the sphere on the globe instead all projections have various attributes and limitations there are many classes of projections used for various purposes e g mathworld s projection page but only a few are traditionally used for panoramic imaging first a word of warning if you are looking for a single projection that will map a spherical even partial panorama on a flat surface without bending lines this won t work this link explains well why it is impossible http www progonos com furuti mapproj normal cartdef mapdef mapdef html some of the most common projections when working with panoramic imaging are contents 1 cylindrical projections 1 1 cylindrical projection 1 2 mercator projection 1 3 miller projection 1 4 equirectangular projection 1 5 lambert cylindrical equal area 2 azimuthal projections 2 1 rectilinear projection 2 2 stereographic projection 2 3 fisheye projection 2 4 equisolid projection 2 5 orthographic projection 3 other projections 3 1 cubic projection 3 2 sinusoidal projection 3 3 transverse mercator projection 3 4 pannini projection 3 5 architectural projection 4 external links cylindrical projections cylindrical projections resemble classic rectangular world maps the horizontal field of view is anything up to 360 degrees horizontal distance is proportional to pan or yaw angle vertical distance is related to the angle above or below the horizon cylindrical projection cylindrical projection h360 v120 this is the projection most commonly used for printed panoramas with a large range of longitude 120 degrees it can be envisioned by imagining wrapping a flat piece of paper around the sphere tangent to the equator and projecting a light out from the center of the sphere a full range of longitude up to 360 degrees can be represented with a cylindrical projection but near the poles the images become very distorted so a full range of latitude cannot be used see cylindrical projection for more mercator projection mercator projection h360 v140 mercator projection is a conformal projection this shows less pronounced distortion than either cylindrical or equirectangular projection which otherwise look very similar see mathworld s page for details miller projection h360 v147 miller is similar to mercator projection but with slightly more compression at the top and bottom of the image this distortion is less pronounced than equirectangular projection making it a good format for printing equirectangular projection equirectangular projection h360 v180 also called the non projection this is a representation of the sphere which maps longitude directly to the horizontal coordinate and latitude to the vertical coordinate this projection is often used for the source images in panoramic viewers like ptviewer see definition for equirectangular projection for more lambert cylindrical equal area h360 v180 this projection is equal area making it very compact and suitable for purposes where distortion isn t important similar to sinusoidal projection azimuthal projections azimuthal projections have rotational symmetry around the centre of the image these are the kind of images that are produced by the various kinds of camera lens rectilinear projection rectilinear projection h110 v110 this is a fundamental projection which can be envisioned by imagining placing a flat piece of paper tangent to a sphere and projecting a light out from its center obviously only less than 180 degrees of longitude can be represented with this projection exactly 180 degrees would require an image of infinite width and in practice far less most non fisheye cameras produce a nearly rectilinear image over their field of view albeit with varying amounts of unavoidable distortion the rectilinear projection is often used for prints of panoramas which cover less than 120 degrees of longitude since straight lines are preserved see rectilinear projection for more stereographic projection stereographic projection h180 v180 stereographic projection is a conformal form of fisheye projection where the distance from the centre is not equivalent to the spatial angle this is much easier on the eye for printing and display purposes stereographic is limited to a maximum horizontal and vertical angle of 360 degrees images over 330 degrees are pretty but not very usable fisheye projection fisheye projection h180 v180 in a fisheye projection the distance from the centre of the image to a point is proportional to the equivalent spatial angle equisolid projection h360 v360 this closely resembles a photograph of a mirrorball features are equal area making it suitable for applications where distortion isn t critical equisolid is apparently the same as lambert equal area azimuthal cartographic projection orthographic projection h180 v180 this is the view of a sphere with a panorama mapped to the outside seen from a far distance other projections cubic projection cubic projection h90 v90 per cubeface technically a sub case of the rectilinear projection the cubic projection is used as the source projection for fully spherical quicktime vr panoramas see cubic projection for more sinusoidal projection sinusoidal projection h360 v180 sinusoidal projection is an equal area projection which makes it suitable for transmission of spherical images as supported by the devalvr viewer transverse mercator projection transverse mercator projection h147 v360 this is a mercator projection rotated 90 degrees suitable for a long vertical image transverse mercator is limited to a maximum horizontal angle of 180 degrees though in practice images over 150 degrees are not very usable pannini projection h180 v110 the pannini projection also known as recti perspective panini or vedutismo keeps verticals vertical and radial lines straight this can impart a strong sense of correct perspective to wide angle views that have a single central vanishing point however this projection renders horizontal straight lines as curves so called squeezed variants reduce or eliminate that curvature at the expense of bending the ends of long radial lines the general panini projection is an adjustable version that can zoom continuously from rectilinear through the standard pannini projection to the even more compressed orthographic cylindrical projection it was introduced in early 2009 in the panini panorama viewer the version implemented in the panotools library in early 2010 also offers two generally useful flavors of squeeze there were two earlier implementations in the panotools library panini which is actually not the pannini projection but a very similar compressed cylindrical projection and equirectangular panini which is the standard pannini or stereographic cylindrical projection architectural projection h360 v152 this is miller projection above the horizon and lambert equal area projection below suitable for scenes where the the ground isn t very interesting external links description of panoramic image projections http www cambridgeincolour com tutorials image projections htm two talks from the 2009 panotools meeting by the panotwins with a comparison of projection types xkcd discusses what your favorite map projection says about you http xkcd com 977 retrieved from https wiki panotools org index php title projections oldid 16609 categories glossary projections navigation menu personal tools log in namespaces page discussion variants views read view source view history more search navigation main page site map community portal mailinglist tools all pages recent changes random page help tools what links here related changes special pages printable version permanent link page information this page was last edited on 2 august 2021 at 14 58 content is available under gnu free documentation license 1 2 unless otherwise noted privacy policy about panotools org wiki disclaimers