The adjustment problem of the so-called combined (hybrid, integrated) network created with GNSS vectors and terrestrial observations has been the subject of many theoretical and applied works. The network adjustment in various mathematical spaces was considered: in the Cartesian geocentric system on a reference ellipsoid and on a mapping plane. For practical reasons, it often takes a geodetic coordinate system associated with the reference ellipsoid. In this case, the Cartesian GNSS vectors are converted, for example, into geodesic parameters (azimuth and length) on the ellipsoid, but the simple form of converted pseudo-observations are the direct differences of the geodetic coordinates. Unfortunately, such an approach may be essentially distorted by a systematic error resulting from the position error of the GNSS vector, before its projection on the ellipsoid surface. In this paper, an analysis of the impact of this error on the determined measures of geometric ellipsoid elements, including the differences of geodetic coordinates or geodesic parameters is presented. Assuming that the adjustment of a combined network on the ellipsoid shows that the optimal functional approach in relation to the satellite observation, is to create the observational equations directly for the original GNSS Cartesian vector components, writing them directly as a function of the geodetic coordinates (in numerical applications, we use the linearized forms of observational equations with explicitly specified coefficients). While retaining the original character of the Cartesian vector, one avoids any systematic errors that may occur in the conversion of the original GNSS vectors to ellipsoid elements, for example the vector of the geodesic parameters. The problem is theoretically developed and numerically tested. An example of the adjustment of a subnet loaded from the database of reference stations of the ASG-EUPOS system was considered for the preferred functional model of the GNSS observations.

Slope deformations, i.e., all types of landslides of rock masses (flow, creep, fall down, etc.), caused by gravitational forces, are the most widespread implementation of geological hazards and a negative geomorphological phenomenon that threatens the security of the population, destroy all utility values of the affected regions, negatively affects the environment, and cause considerable economic damage. Nowadays, the Global Navigation Satellite Systems (GNSS) provide accurate data for precise observations around the world due to the growing number of satellites from multiple operators, as well as more powerful and advanced technologies and the implementation of mathematical and physical models more accurately describing systematic errors that degrade GNSS observations such as ionospheric, tropospheric, and relativistic effects or multipath. The correct combination of measurement methods provides even more precise, i.e., better measurement results or estimates of unknown parameters. The combination of measurement procedures and their significant evaluations represent the essential attribute of deformation monitoring of landslides concerning the protection of the environment and the population’s safety in the interest areas for the sustainable development of human society. This article presents the establishment and use of a local geodetic network in particular local space for various needs. Depending upon the specific conditions, it is possible to use GNSS technology to obtain accurate observations and achieve the results applicable to the deformation survey for subsequent processing of the adjustment procedure.

With development of medical diagnostic and imaging techniques the sparing surgeries are facilitated. Renal cancer is one of examples. In order to minimize the amount of healthy kidney removed during the treatment procedure, it is essential to design a system that provides three-dimensional visualization prior to the surgery. The information about location of crucial structures (e.g. kidney, renal ureter and arteries) and their mutual spatial arrangement should be delivered to the operator. The introduction of such a system meets both the requirements and expectations of oncological surgeons. In this paper, we present one of the most important steps towards building such a system: a new approach to kidney segmentation from Computed Tomography data. The segmentation is based on the Active Contour Method using the Level Set (LS) framework. During the segmentation process the energy functional describing an image is the subject to minimize. The functional proposed in this paper consists of four terms. In contrast to the original approach containing solely the region and boundary terms, the ellipsoidal shape constraint was also introduced. This additional limitation imposed on evolution of the function prevents from leakage to undesired regions. The proposed methodology was tested on 10 Computed Tomography scans from patients diagnosed with renal cancer. The database contained the results of studies performed in several medical centers and on different devices. The average effectiveness of the proposed solution regarding the Dice Coefficient and average Hausdorff distance was equal to 0.862 and 2.37 mm, respectively. Both the qualitative and quantitative evaluations confirm effectiveness of the proposed solution.

The behaviour of energy levels and optical spectra of a charged particle (electron or hole) confined within a potential well of ellipsoidal shape is investigated as a function of the shape-anisotropy parameter. If two energy levels of the same symmetry intersect in a perturbation-theory approximation, they move apart on direct diagonalization of the appropriate Hamiltonian. The intersection of the energy levels leads to a discontinuity of the corresponding dipole-moment matrix element. The discontinuity of matrix elements is not reflected in the behaviour of transition probabilities which are continuous functions of the shape-anisotropy parameter. The profiles of a spectral line emitted or absorbed by an ensemble of ellipsoidally shaped nanoparticles with a Gaussian distribution of size are calculated and discussed.

A new method to transform from Cartesian to geodetic coordinates is presented. It is based on the solution of a system of nonlinear equations with respect to the coordinates of the point projected onto the ellipsoid along the normal. Newton’s method and a modification of Newton’s method were applied to give third-order convergence. The method developed was compared to some well known iterative techniques. All methods were tested on three ellipsoidal height ranges: namely, (-10 – 10 km) (terrestrial), (20 – 1000 km), and (1000 – 36000 km) (satellite). One iteration of the presented method, implemented with the third-order convergence modified Newton’s method, is necessary to obtain a satisfactory level of accuracy for the geodetic latitude ( σ φ < 0.0004”) and height ( σ h < 10 − 6 km, i.e. less than a millimetre) for all the heights tested. The method is slightly slower than the method of Fukushima (2006) and Fukushima’s (1999) fast implementation of Bowring’s (1976) method.

The paper presents a method of construction of cylindrical and azimuthal equalarea map projections of a triaxial ellipsoid. Equations of a triaxial ellipsoid are a function of reduced coordinates and functions of projections are expressed with use of the normal elliptic integral of the second kind and Jacobian elliptic functions. This solution allows us to use standard methods of solving such integrals and functions. The article also presents functions for the calculation of distortion. The maps illustrate the basic properties of developed map projections. Distortion of areas and lengths are presented on isograms and by Tissot’s indicatrixes with garticules of reduced coordinates. In this paper the author continues his considerations of the application of reduced coordinates to the construction of map projections for equidistant map projections. The developed method can be used in planetary cartography for mapping irregular objects, for which tri-axial ellipsoids have been accepted as reference surfaces. It can also be used to calculate the surface areas of regions located on these objects. The calculations were carried out for a tri-axial ellipsoid with semi-axes a = 267:5 m, b = 147 m, c = 104:5 m accepted as a reference ellipsoid for the Itokawa asteroid.