The geometry of trifocal curves with applications in architecture, urban and spatial planning
In this paper we consider historical genesis of trifocal curve as an optimal curve for solving the Fermat’s problem (minimizing the sum of distance of one point to three given points in the plane). Trifocal curves are basic plane geometric forms which appear in location problems. We also an...
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| Format: | Article |
| Language: | English |
| Published: |
Institute of Architecture, Urban & Spatial Planning of Serbia
2014-01-01
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| Series: | Spatium |
| Subjects: | |
| Online Access: | http://www.doiserbia.nb.rs/img/doi/1450-569X/2014/1450-569X1432028P.pdf |
| _version_ | 1829465831988264960 |
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| author | Petrović Maja Banjac Bojan Malešević Branko |
| author_facet | Petrović Maja Banjac Bojan Malešević Branko |
| author_sort | Petrović Maja |
| collection | DOAJ |
| description | In this paper we consider historical genesis of trifocal curve as an optimal
curve for solving the Fermat’s problem (minimizing the sum of distance of one
point to three given points in the plane). Trifocal curves are basic plane
geometric forms which appear in location problems. We also analyze algebraic
equation of these curves and some of their applications in architecture,
urbanism and spatial planning. The area and perimeter of trifocal curves are
calculated using a Java application. The Java applet is developed for
determining numerical value for the Fermat-Torricelli-Weber point and optimal
curve with three foci, when starting points are given on an urban map. We
also present an application of trifocal curves through the analysis of one
specific solution in South Stream gas pipeline project. |
| first_indexed | 2024-12-13T17:01:22Z |
| format | Article |
| id | doaj.art-c8ece05157b342c2906d3b792e17e177 |
| institution | Directory Open Access Journal |
| issn | 1450-569X 2217-8066 |
| language | English |
| last_indexed | 2024-12-13T17:01:22Z |
| publishDate | 2014-01-01 |
| publisher | Institute of Architecture, Urban & Spatial Planning of Serbia |
| record_format | Article |
| series | Spatium |
| spelling | doaj.art-c8ece05157b342c2906d3b792e17e1772022-12-21T23:37:47ZengInstitute of Architecture, Urban & Spatial Planning of SerbiaSpatium1450-569X2217-80662014-01-01201432283310.2298/SPAT1432028P1450-569X1432028PThe geometry of trifocal curves with applications in architecture, urban and spatial planningPetrović Maja0Banjac Bojan1Malešević Branko2Faculty of Transport and Traffic Engineering, BelgradeFaculty of Electrical Engineering, Belgrade + Faculty of technical sciences - Computer Graphics Chair, Novi SadFaculty of Electrical Engineering, BelgradeIn this paper we consider historical genesis of trifocal curve as an optimal curve for solving the Fermat’s problem (minimizing the sum of distance of one point to three given points in the plane). Trifocal curves are basic plane geometric forms which appear in location problems. We also analyze algebraic equation of these curves and some of their applications in architecture, urbanism and spatial planning. The area and perimeter of trifocal curves are calculated using a Java application. The Java applet is developed for determining numerical value for the Fermat-Torricelli-Weber point and optimal curve with three foci, when starting points are given on an urban map. We also present an application of trifocal curves through the analysis of one specific solution in South Stream gas pipeline project.http://www.doiserbia.nb.rs/img/doi/1450-569X/2014/1450-569X1432028P.pdfFermat-Torricelli-Weber pointtrifocal curveJava applet |
| spellingShingle | Petrović Maja Banjac Bojan Malešević Branko The geometry of trifocal curves with applications in architecture, urban and spatial planning Spatium Fermat-Torricelli-Weber point trifocal curve Java applet |
| title | The geometry of trifocal curves with applications in architecture, urban and spatial planning |
| title_full | The geometry of trifocal curves with applications in architecture, urban and spatial planning |
| title_fullStr | The geometry of trifocal curves with applications in architecture, urban and spatial planning |
| title_full_unstemmed | The geometry of trifocal curves with applications in architecture, urban and spatial planning |
| title_short | The geometry of trifocal curves with applications in architecture, urban and spatial planning |
| title_sort | geometry of trifocal curves with applications in architecture urban and spatial planning |
| topic | Fermat-Torricelli-Weber point trifocal curve Java applet |
| url | http://www.doiserbia.nb.rs/img/doi/1450-569X/2014/1450-569X1432028P.pdf |
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