An Algorithm for the Inverse Solution of Geodesic Sailing without Auxiliary Sphere

Tseng, Wei-Kuo

doi:10.1017/s0373463314000228

Cited by 4 publications

(7 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…of which the constant coefficients are expressible by a Newton's generalised binomial coefficient as Tseng (2014), however this requires more number of calculations than the proposed recursive formula (13).…”

Section: Integrals Describing the Arc Of A Geodesic From The Equator ...mentioning

confidence: 99%

See 1 more Smart Citation

Theory, strict formula derivation and algorithm development for the computation of a geodesic polygon area

Nowak

Costa

2022

J Geod

View full text Add to dashboard Cite

The paper presents a coherent, original theory and an effective algorithm to calculate the surface area of a geodesic polygon, i.e. the area on an ellipsoid of revolution limited by geodesics, connecting pairs of subsequent vertices of known geographical coordinates. Using the cylindrical coordinate system and introducing an equatorial geodesic triangle, the novel strict recursive formulas were derived for the longitude on the ellipsoid and the distance along the geodesic and the area of a geodesic polygon. The area is determined by constant coefficients, not the values of finite series. The orthodromic properties of geodesics, which led to the detection of bifurcation lines composed of the double solutions of the inverse geodetic problem were analysed. The novel algorithm presented, integrating the problem with geodesic polygon area calculation, is based on the newly proposed parameterisation with two alternative working unknowns and a new formula to obtain the initial value of the geodesic C parameter. It allows solutions for all cases, including near-antipodal or near-vertices, and offers two solutions if bifurcation occurs. The algorithm presented was tested and verified using numerical examples from known publications. The numerical tests proved the accuracy of 1m2 of the computed geodesic area using standard IEEE 754 Double Floating Point PC arithmetic, for geodesic lengths up to ten thousand km.

show abstract

Section: Integrals Describing the Arc Of A Geodesic From The Equator ...mentioning

confidence: 99%

“…The extension defined by formulas (31-32) is fundamentally important since it makes it possible to apply formulas ( 24) and ( 25) to any arcs of geodesic. Moreover, it replaces the artificial determination of combinations of signs of individual components that occurs in Pittman's (1986) and Tseng's (2014) methods.…”

Section: Solution In Spherical Coordinatesmentioning

confidence: 99%

Theory, strict formula derivation and algorithm development for the computation of a geodesic polygon area

Nowak

Costa

2022

J Geod

View full text Add to dashboard Cite

show abstract

“…The methods of solving the above problems can be divided into two general categories: (i) using an auxiliary sphere, e.g., Bessel (1826), Rainsford (1955), Robbins (1962), Sodano (1965), Saito (1970), Vincenty (1975), Saito (1979), Bowring (1983), Karney (2013) and (ii) without using an auxiliary sphere, e.g., Kivioja (1971), Holmstrom (1976), Jank and Kivioja (1980), Thomas and Featherstone (2005), Panou (2013), Panou et al (2013), Tseng (2014). The methods which use an auxiliary sphere are based on the classical work of Bessel (1826) and its modifications.…”

Section: Introductionmentioning

confidence: 99%

Research Article. Geodesic equations and their numerical solutions in geodetic and Cartesian coordinates on an oblate spheroid

Πάνου

Korakitis

2017

Journal of Geodetic Science

View full text Add to dashboard Cite

Abstract:The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically using both geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical method. The solution provides the coordinates and the azimuths at any point along the geodesic. The Clairaut constant is not used for the solution but it is computed, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to evaluate the performance of the method in each coordinate system. The results for the direct geodesic problem are validated by comparison to Karney's method. We conclude that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.

show abstract

“…A number of errors in typesetting have been discovered in Tseng (2014), for which the Editor-in-Chief of The Journal of Navigation and Cambridge University Press apologise.…”

mentioning

confidence: 99%

An Algorithm for the Inverse Solution of Geodesic Sailing without Auxiliary Sphere

Cited by 4 publications

References 15 publications

Theory, strict formula derivation and algorithm development for the computation of a geodesic polygon area

Theory, strict formula derivation and algorithm development for the computation of a geodesic polygon area

Research Article. Geodesic equations and their numerical solutions in geodetic and Cartesian coordinates on an oblate spheroid

An Algorithm for the Inverse Solution of Geodesic Sailing Without Auxiliary Sphere – Erratum

Contact Info

Product

Resources

About