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In maps covering larger areas, or the whole Earth, the map's scale may be less useful or even useless in measuring distances. The map projection becomes critical in understanding how scale varies throughout the map. [1] [2] When scale varies noticeably, it can be accounted for as the scale factor.
The instrument is most commonly used to measure the lengths of roads, rivers and other line features on maps. Opisometers designed for this purpose provide scales reading the measured distance in kilometers and miles.
Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic ...
Distance from the tangent point on the map is proportional to straight-line distance through the Earth: r(d) = c sin d / 2R [38] Logarithmic azimuthal is constructed so that each point's distance from the center of the map is the logarithm of its distance from the tangent point on the Earth.
The chain is the unit of linear measurement for the survey of the public lands as prescribed by law. All returns of measurement in the rectangular system are made in the true horizontal distance in links, chains, and miles. The only exceptions to this rule are special requirements for measurement in feet in mineral surveys and townsite surveys ...
This was the beginning of the coastline problem, which is a mathematical uncertainty inherent in the measurement of boundaries that are irregular. [6] The prevailing method of estimating the length of a border (or coastline) was to lay out n equal straight-line segments of length l with dividers on a map or aerial photograph. Each end of the ...
Converting ruler distance on the Mercator map into true (great circle) distance on the sphere is straightforward along the equator but nowhere else. One problem is the variation of scale with latitude, and another is that straight lines on the map ( rhumb lines ), other than the meridians or the equator, do not correspond to great circles.
Graph edit distance is a measure of dissimilarity between two graphs, defined as the minimal number of graph edit operations required to transform one graph into another. Wasserstein metrics measure the distance between two measures on the same metric space.
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