In this paper, we present techniques for ellipsoid fitting which are based on minimizing the sum of the squares of the geometric distances between the data and the ellipsoid. The literature often uses "orthogonal fitting" in place of "geometric fitting" or "best-fit". For many different purposes, the best-fit ellipsoid fitting to a set of points is required. The problem offitting ellipsoid is encounteredfrequently intheimage processing, face recognition, computer games, geodesy etc. Today, increasing GPS and satellite measurementsprecisionwill allow usto determine amore realistic Earth ellipsoid. Several studies have shown that the Earth, other planets, natural satellites, asteroids and comets can be modeled as triaxial ellipsoids Burša and Šima (1980), Iz et all (2011). Determining the reference ellipsoid for the Earth is an important ellipsoid fitting application, because all geodetic calculations are performed on the reference ellipsoid. Algebraic fitting methods solve the linear least squares (LS) problem, and are relatively straightforward and fast. Fitting orthogonal ellipsoid is a difficult issue. Usually, it is impossible to reach a solution with classic LS algorithms. Because they are often faced with the problem of convergence. Therefore, it is necessary to use special algorithms e.g. nonlinear least square algorithms. We propose to use geometric fitting as opposed to algebraic fitting. This is computationally more intensive, but it provides scope for placing visually apparent constraints on ellipsoid parameter estimation and is free from curvature bias Ray and Srivastava (2008).
Finding the orthogonal (shortest) distance to an ellipsoid corresponds to the ellipsoidal height in Geodesy. Despite that the commonly used Earth reference systems, like WGS-84, are based on rotational ellipsoids, there have also been over the course of the years permanent scientific investigations undertaken into different aspects of the triaxial ellipsoid. Geodetic research has traditionally been motivated by the need to approximate closer and closer the physical reality. Several investigations have shown that the earth is approximated better by a triaxial ellipsoid rather than a rotational one Burša and Šima (1980). The problem of finding the shortest distance is encountered frequently in the Cartesian-Geodetic coordinate transformation, optimization problem, fitting ellipsoid, image processing, face recognition, computer games, and so on. We have chosen a triaxial ellipsoid for the reason that it possesess a general surface. Thus, the minimum distance from rotational ellipsoid and sphere is found with the same algorithm. This study deals with the computation of the shortest distance from a point to a triaxial ellipsoid. Keywords: Orthogonal (Shortest) Distance; Triaxial Ellipsoid; Coordinate Transformation; Fitting Ellipsoid. RESUMOEncontrar a distância orthogonal a um elipsóide corresponde a altura elipsoidal em Geodésia. Apesar de os sistemas de referência da Terra mais comumente usados, como WGS-84, são baseados em elipsóides rotacionais, tem tido por anos, investigações científicas permanentes feitas em diferentes aspectos do elipsóide triaxial. A pesquisa geodésica tem sido tradicionalmente motivada pela necessidade de uma aproximação cada vez mais próxima da realidade física. Diversas (1) is quite simple and smooth but geodetic computations are quite difficult on the ellipsoid. The main reason for this difficulty is the lack of symmetry. Triaxial ellipsoid is generally not used in geodetic applications. Rotational ellipsoid (ellipsoid revolution, biaxial ellipsoid, spheroid) is frequently used in geodetic applications.Today increasing GPS and satellite measurement precision will allow us to determine more realistic earth ellipsoid. Geodetic research has traditionally been motivated by the need to continually improve approximations of physical reality.Geodetic research has traditionally been motivated by the need to approximate closer and closer the physical reality. Several investigations have shown that the earth is approximated better by a triaxial ellipsoid rather than a rotational one.Furthermore, non-spherical celestial bodies such as planets, physical satellites, asteroids and comets can be modeled by a triaxial ellipsoid. Also, the present day accuracy requirements and the modern computational capabilities push toward the study on the triaxial ellipsoid as a geometrical and a physical model in geodesy and related interdisciplinary sciences Panou et al (2013).First, the basic definition of ellipsoid starts with giving mathematical equations to explain the concepts. To show how computatio...
Background: The energy issue is of great importance for energy dependent countries like Turkey. Some legislative regulations such as the Energy Efficiency Law and the Energy Performance Regulation of Building have recently been made in our country. Although the Energy Performance Certificate for buildings has been put into practice , a national green building certification system is not available yet. The most widely used certification systems in the world are BREEAM (Bre Environmental Assessment Method) and LEED (Leadership in Energy and Environmental Design), which do not produce very realistic results. Therefore, it is essential to establish a national certification system. For this purpose, studies have been started by ÇEDBİK (the Turkish Green Building Council) and Mimar Sinan Fine Arts University (MSFAU). However, it has not yet been legally validated.Methods: In this study, a survey was conducted to highlight the importance of the category of land management, one of the criteria of the green building certification systems, and to identify sub-criteria under this title more objectively. Worldwide valid certification systems and parts of the certification systems regarding land management that are tried to be established in Turkey were examined to determine the survey questions and in line with this, a literature review was performed. The experts in Turkey were interviewed to gather ideas and insights. By listing the answers from these experts using the AHP method, the criteria and sub-criteria of land method were determined.Conclusions: In this study, a green building certification system to be established in our country was discussed under the category of land management to which great importance has been attached, especially by survey engineers, and the criteria under this category has been identified. A survey was conducted to determine these criteria, and the results were examined.The subcriteria of the category of land management were identified, and their weights were calculated. A sample program was written in the Microsoft Visual Studio Net 2013 programming language to determine the scores of buildings according to these weights.
In this paper, we will see that the determination of direct bearing angles. As it is known, in bearing angles are often computed used formulas with arctan function. The arctan function gives an angle values between-90 o and +90 o. However, the bearing angle is by definition 0 o to 360 o. Consequently, it is inevitable to examine the process of obtaining the azimuth angle. Classic formulas only work correctly if the edge is in the 1 st quarter. If the edge is located in the other quarters, the angles of the bearing should be examined. In this work we proposed new formulas for direct bearing angles on globe (sphere). Using the formula that we propose will save execution time in codes with intensive geodesic calculations.
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