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The polar planimeter is restricted by design to measuring areas within limits determined by its size and geometry. However, the linear type has no restriction in one dimension, because it can roll. Its wheels must not slip, because the movement must be constrained to a straight line.
the point's direction from the pole relative to the direction of the polar axis, a ray drawn from the pole. The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth. [1] The pole is analogous to the origin in a Cartesian coordinate system.
To measure planimetrics a planimeter or dot planimeter is used. This rather advanced analog technology is being taken over by simple image measurement software tools like, ImageJ, Adobe Acrobat, Google Earth Pro, Gimp, Photoshop and KLONK Image Measurement which can help do this kind of work from digitalized images.
A useful application for this type of projection is a polar projection which shows all meridians (lines of longitude) as straight, with distances from the pole represented correctly. The flag of the United Nations contains an example of a polar azimuthal equidistant projection.
The universal polar stereographic (UPS) coordinate system is used in conjunction with the universal transverse Mercator (UTM) coordinate system to locate positions on the surface of the Earth. Like the UTM coordinate system, the UPS coordinate system uses a metric-based cartesian grid laid out on a conformally projected surface.
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