THE GEOMETRIC ALGORITHM OF INVERSE AND DIRECT PROBLEMS WITH AN AREA SOLUTION FOR THE GREAT ELLIPTIC ARCS

Authors

Wei-Kuo Tseng, Department of Merchant Marine, National Taiwan Ocean University, Keelung, TaiwanFollow
Jiunn-Liang Guo, Department of Merchant Marine, National Taiwan Ocean University, Keelung, Taiwan
Chung-Ping Liu, Department of Merchant Marine, National Taiwan Ocean University, Keelung, Taiwan

Abstract

The definition of the connecting edge(s) between two vertices in a geography type is the great elliptic minor arc in Microsoft SQL Server’s Geography Type. Similar to the way an edge is defined by Microsoft SQL Server, an edge in Geodyssey’s Hipparchus library is also defined as a great circle arc on a reference sphere. Using Hipparchus for their computations, IBM’s DB2 Geodetic Extender and Informix Geodetic Datablade share this definition. Compact formulae are given for the great elliptic sailing on a spheroid providing solutions to both the forward and inverse problems with exceptional accuracy, and latitude in terms of longitude. The solution incorporates a closed form for the azimuth and the derivation of the algorithm is presented and illustrated. In addition, the area of polygon bounded by the elliptic arcs is treated. This paper also shows that a computer algebra system is a powerful tool to solve mathematical derivations in navigation, geodesy, and cartography

Recommended Citation

Tseng, Wei-Kuo; Guo, Jiunn-Liang; and Liu, Chung-Ping (2015) "THE GEOMETRIC ALGORITHM OF INVERSE AND DIRECT PROBLEMS WITH AN AREA SOLUTION FOR THE GREAT ELLIPTIC ARCS," Journal of Marine Science and Technology: Vol. 23: Iss. 4, Article 11.
DOI: 10.6119/JMST-014-1120-1
Available at: https://jmstt.ntou.edu.tw/journal/vol23/iss4/11