# Transverse Mercator with an accuracy of a few nanometers

```@article{Karney2010TransverseMW,
title={Transverse Mercator with an accuracy of a few nanometers},
author={Charles F. F. Karney},
journal={Journal of Geodesy},
year={2010},
volume={85},
pages={475-485}
}```
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

• Environmental Science
Mathematical Problems in Engineering
• 2021
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

• Mathematics
• 2011
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

• Physics
• 2012
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

• Computer Science
Applied Sciences
• 2021
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

• Engineering
• 2014
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

### NONZONAL EXPRESSIONS OF GAUSS–KRÜGER PROJECTION IN POLAR REGIONS

• Physics
• 2016
Abstract. With conformal colatitude introduced, based on the mathematical relationship between exponential and logarithmic functions by complex numbers, strict equation of complex conformal