Quartic Authalic Projection

Classification

Pseudocylindrical

Identifier

quartic

Graticule

Central Meridian: Straight line 0.45 as long as the Equator.

Other Meridians: Equally spaced quartic (fourth-order equation) curves concave toward the central meridian.

Parallels: Unequally spaced straight parallel lines, perpendicular to the central meridian. Spacing changes gradually and is greatest near the Equator.

Poles: Points.

Symmetry: About the central meridian or the Equator.

Features

This is an equal-area projection. Scale is true along the Equator and is constant along any parallel and between any pair of parallels equidistant from the Equator. Distortion is severe near the outer meridians at high latitudes, but less so than on the Sinusoidal projection. It is free of distortion along the Equator. This projection is not conformal or equidistant.

Parallels

This projection has one standard parallel, which is by definition fixed at 0º.

Remarks

This projection was presented by Karl Siemon in 1937 and independently by Oscar Sherman Adams in 1945.

Example

landareas = shaperead('landareas.shp','UseGeoCoords',true);
axesm ('quartic', 'Frame', 'on', 'Grid', 'on');
geoshow(landareas,'FaceColor',[1 1 .5],'EdgeColor',[.6 .6 .6]);
tissot;

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