### Direct and Inverse Problem on Triaxial Ellipsoid

#### Sebahattin Bektas 1*

1 Geomatics Engineering, Faculty of Engineering, Ondokuz Mayis University, Samsun, Turkey

### Abstract

In this paper, we aim to show how to generalization of the Direct and Invers problem on triaxial ellipsoid. When we look at the studies related to the subject, it seems that the solution of the direct and invers geodetic problems with geographical coordinates on the triaxial ellipsoid is very difficult. In order to overcome this difficulty, in this work, we made the direct and invers problem with Cartesian coordinates instead of geographical coordinates. We will also use slope length that directly connects two points instead of the geodesic curve length. We think that our choice is also meaningful at the same time. This is because the geodesic curve lengths cannot be measured with the measuring instruments and cannot be applied to the ground, while the slope lengths can easily be measured with modern measuring instruments and can applied to the surface. In addition to we will see how to solve the conversion between the geographical coordinates with Cartesian coordinates or vice versa on triaxial ellipsoid.

### Keywords

Triaxial Ellipsoid, Direct and Invers Problem, Coordinate Transformation, Geographical Coordinates, Cartesian Coordinates

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