On auxiliary latitudes
Charles F. F. Karney (SRI International)
TL;DR
This paper reviews methods for converting auxiliary latitudes in cartography with high precision, introduces new formulas for minimal roundoff error, and provides detailed error analysis and convergence estimates.
Contribution
It offers new formulas for rectifying and authalic latitudes with minimal roundoff error and detailed convergence analysis for series expansions.
Findings
Series truncation errors are precisely measured.
New formulas reduce roundoff errors in latitude conversions.
Convergence radii estimates improve conversion accuracy.
Abstract
The auxiliary latitudes are essential tools in cartography. This paper summarizes methods for converting between them with an emphasis on providing full double-precision accuracy. This includes series expansions in the third flattening, where the truncation error is precisely measured and where estimates of the radii of convergence are given. Also new formulas are given for computing the rectifying and authalic latitudes with minimal roundoff error.
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Taxonomy
TopicsHistorical Geography and Cartography · Geophysics and Gravity Measurements · Geodetic Measurements and Engineering Structures