{"title":"Circle-circle intersection. A universal method for solving typical surveying problems","authors":"Tadeusz Gargula","doi":"10.1007/s12518-024-00598-z","DOIUrl":null,"url":null,"abstract":"<div><p>The research problem of the article is to devise a universal mathematical procedure for calculating point coordinates from typical planar surveying measurements. The proposed solution involves calculating the intersection points of two circles with radii equal to the measured distances (the distance-distance intersection problem). The author demonstrates a straightforward method for reducing every typical surveying problem to the distance-distance intersection form. The procedure also verifies the accuracy of the calculated coordinates. The derived equations were tested numerically using practical examples. The devised procedure will be integrated into an exhaustive numerical algorithm for diverse surveying problems regardless of the geometric approach during measurements.</p></div>","PeriodicalId":46286,"journal":{"name":"Applied Geomatics","volume":"16 4","pages":"1047 - 1056"},"PeriodicalIF":2.3000,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12518-024-00598-z.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Geomatics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s12518-024-00598-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"REMOTE SENSING","Score":null,"Total":0}
引用次数: 0
Abstract
The research problem of the article is to devise a universal mathematical procedure for calculating point coordinates from typical planar surveying measurements. The proposed solution involves calculating the intersection points of two circles with radii equal to the measured distances (the distance-distance intersection problem). The author demonstrates a straightforward method for reducing every typical surveying problem to the distance-distance intersection form. The procedure also verifies the accuracy of the calculated coordinates. The derived equations were tested numerically using practical examples. The devised procedure will be integrated into an exhaustive numerical algorithm for diverse surveying problems regardless of the geometric approach during measurements.
期刊介绍：
Applied Geomatics (AGMJ) is the official journal of SIFET the Italian Society of Photogrammetry and Topography and covers all aspects and information on scientific and technical advances in the geomatics sciences. The Journal publishes innovative contributions in geomatics applications ranging from the integration of instruments, methodologies and technologies and their use in the environmental sciences, engineering and other natural sciences.
The areas of interest include many research fields such as: remote sensing, close range and videometric photogrammetry, image analysis, digital mapping, land and geographic information systems, geographic information science, integrated geodesy, spatial data analysis, heritage recording; network adjustment and numerical processes. Furthermore, Applied Geomatics is open to articles from all areas of deformation measurements and analysis, structural engineering, mechanical engineering and all trends in earth and planetary survey science and space technology. The Journal also contains notices of conferences and international workshops, industry news, and information on new products. It provides a useful forum for professional and academic scientists involved in geomatics science and technology.
Information on Open Research Funding and Support may be found here: https://www.springernature.com/gp/open-research/institutional-agreements
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