Murdoch III Minimum Error Conic Projection

Classification

Conic

Identifier

murdoch3

Graticule

Meridians: Equally spaced straight lines converging at one of the poles.

Parallels: Equally spaced concentric circular arcs.

Poles: Arcs, one of which might become a point in the limit.

Symmetry: About any meridian.

Features

This is an equidistant projection that is minimum-error. Scale is true along any meridian and is constant along any parallel. Scale is also true along two standard parallels. These must be calculated, however (see remark on parallels below). The total area of the mapped area is correct, but it is not equal-area everywhere.

Parallels

The parallels for this projection are not standard parallels, but rather limiting parallels. The special feature of this map, correct total area, holds between these parallels. The default parallels are [15 75].

Remarks

Described by Patrick Murdoch in 1758, with errors corrected by Everett in 1904.

Limitations

This projection is available only for the sphere. Longitude data greater than 135º east or west of the central meridian is trimmed.

Example

landareas = shaperead('landareas.shp','UseGeoCoords',true);
axesm ('murdoch3', 'Frame', 'on', 'Grid', 'on');
geoshow(landareas,'FaceColor',[1 1 .5],'EdgeColor',[.6 .6 .6]);
tissot;

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