The article develops ideas and formulas of analytical geometry for spherical surface of the Earth globe in relation to main tasks of global geodesy and navigation. It examines peculiarities of sphere inner geometry and properties of its primary, secondary and higher-order curves. It was proved that spherical hyperbola and parabola are spherical ellipses with specific parameters. The Cartesian ordinates were introduced into the sphere and the relation between them and polar spherical coordinates was established. With the help of central projection of sphere points on tangential plane the corresponding elliptical plane with beltrami ordinates was introduced. The article describes main formulas of analytical geometry for projected elliptical plane, which correspond to geometry of projected sphere. It also introduces several formulas for primary, secondary and higher-order curves for this sphere.
For the local geodetic surveys carried out with the help of the receivers of satellite radionavigation systems, it is offered to use the affinne conversion of flat coordinates, is well known in analytical geometry in the plane. The algorithm of the solution of a problem of such coordinate conversion is given. The testing of the implementation of this algorithm used for electronic-cartographical support of intelligent transportation systems, in real service conditions of intelligent transportation systems is described.
Presents the results of full-scale observation of the state of rail crane tracks in the period of their operation. It is established, that at a geodetic control of a craft of the crane equipment, special attention should be paid to the bridge cranes and the status of crane rails in the plan.
The contactless technology of creation of a high-precision digital copy of objects on an example of porcelain figurines from a collection «People of Russia» of the Museum at the Imperial Porcelain Manufactory is presented. The technique of field works and processing of the received materials at use of the manual laser scanner with submillimetric accuracy is considered.