Transverse Mercator with an accuracy of a few nanometers

  title={Transverse Mercator with an accuracy of a few nanometers},
  author={Charles F. F. Karney},
  journal={Journal of Geodesy},
Implementations of two algorithms for the transverse Mercator projection are described; these achieve accuracies close to machine precision. One is based on the exact equations of Thompson and Lee and the other uses an extension of Krüger’s series for the mapping to higher order. The exact method provides an accuracy of 9 nm over the entire ellipsoid, while the errors in the series method are less than 5 nm within 3900 km of the central meridian. In each case, the meridian convergence and scale… 

Approximations, Errors, and Misconceptions in the Use of Map Projections

This work explores and questions the validity of some of approximations that are routinely implemented and quantifies the corresponding impact, including the impact of neglecting meteorological corrections, reduction to ellipsoid and grid scale factors for distances, meridian convergence and arc-to-chord correction for angles, and mixing up with different frames and reference systems.

Concise Derivation of Extensive Coordinate Conversion Formulae in the Gauss-Krüger Projection

Although the set of Gauss-Krüger projection formulae recognized and used worldwide thus far is “the 2nd formulae”, which is limited to use within certain longitudinal zones, the recently discovered

The Gauss-Krueger projection: Karney-Krueger equations

The Gauss-Krueger projection has two forms. One has the Karney-Krueger equations capable of micrometre accuracy anywhere within 30° of a central meridian of longitude. The other has equations limited

A proposal to include conformal harmonic polynomials in GIS software

This paper proposes a way to implement the algorithms to be used in any geographic software and provides an algorithm for the reversion of polynomials with micro-metric accuracy.

Reprojection of VIIRS SDR Imagery Using Concurrent Gradient Search

  • A. Trishchenko
  • Environmental Science, Mathematics
    IEEE Transactions on Geoscience and Remote Sensing
  • 2018
The application of the gradient search method for reprojection of Visible Infrared Imaging Radiometer Suite (VIIRS) satellite data record (SDR) imagery is described, demonstrating the excellent geometric performance of the VIIRS Suomi National Polar-orbiting Partnership sensor and are consistent with those reported by the VII RS geolocation teams.

Analysis of Universal Transverse Mercator projection and Coordinate System

The familiar Mercator projection used on so many world maps is a cylindrical projection, meaning the globe is encircled by an imaginary cylinder touching at the equator, and the earth is projected

Accurate Algorithms for Spatial Operations on the Spheroid in a Spatial Database Management System

This paper presents the implementation of two algorithms that solve with high accuracy (less than 100 nm) and efficiently (few iterations) two basic geometric calculations on the ellipsoid that are essential to build more complex spatial operators: the intersection of two geodesics and the minimum distance from a point to a geodesic.

Comparison of Numerical Techniques for Coordinate Transformation: The Case Study of Nigeria Transverse Mercator and Universal Transverse Mercator

It can be inferred that the numerical techniques serve as effective tools for coordinate transformation from NTM system to UTM system, however, cubic spline technique proved to be more accurate and reliable but less economical of computing time and computer memory spaces than the Newton’s divided difference technique.

On the Conversion of Coordinates from Nigeria Transverse Mercator to Universal Transverse Mercator Using a Simple Mathematical Model

In this paper, effort has been made to transform coordinates from Nigerian Transverse Mercator (NTM) system to Universal Transverse Mercator (UTM) system using a Simple Mathematical Model. The data


Abstract. With conformal colatitude introduced, based on the mathematical relationship between exponential and logarithmic functions by complex numbers, strict equation of complex conformal



The Universal Grids: Universal Transverse Mercator (UTM) and Universal Polar Stereographic (UPS). Edition 1

Abstract : This manual describes geographic to grid and grid to geographic conversions for the Universal Transverse Mercator (UTM) and the Universal Polar Stereographic (UPS) grids. It also discusses

NIST Handbook of Mathematical Functions

This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators and is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun.

Map Projections: A Reference Manual

1.Introduction 2. General Theory of Map Projections 3. Map Projections with Straight Parallels 4. Map Projections with Parallels in the Shape of Concentric Circles 5. Map Projections with Parallels

A Course of Modern Analysis

The volume now gives a somewhat exhaustive account of the various ramifications of the subject, which are set out in an attractive manner and should become indispensable, not only as a textbook for advanced students, but as a work of reference to those whose aim is to extend the knowledge of analysis.

Numerical calculation of elliptic integrals and elliptic functions

This paper contains anALGOL program for the incomplete elliptic integral of the third kind based on a theory described in [4] and replaces the inadequate one based on the Gauβ-transformation which was published in [2].

A new method of solving numerical equations of all orders, by continuous approximation

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and

Numerical computation of real or complex elliptic integrals

Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the

A Computer Algebra System

Risa/Asir consists of the Risa engine for performing operations on mathematical objects and an interpreter for programs written in the Asir user language. In Risa/Asir, polynomials are represented in

Die der transversalen Mercatorkarte der Kugel entsprechende Abbildung des Rotationsellipsoids.

In der Landesvermessung wird die winkeltreue Abbildung des Rotationsellipsoids in die Ebene angewandt, bei der ein Achsenschnitt in eine Gerade mit konstanter Längenvergrößerung abgebildet wird. Aus

Conformal Projections Based On Jacobian Elliptic Functions