Determination of the Geometric Form of Hierapolis Theater in Pamukkale, Turkey
Publication: Journal of Surveying Engineering
Volume 140, Issue 3
Abstract
This work addresses the issue of fitting a geometrical shape to the Hierapolis theater near the city of Denizli, Turkey. The aim of the study was to determine the geometrical shape of the theater that would best fit the set of measured site data points. The geometrical form of the theater was surveyed by using an electronic total station instrument. Because theater rings are generally elliptical in shape, the well-known ellipse-fitting algorithm was presented for computing the geometrical parameters. In this study, the authors plan to analyze the fitting algorithm presented, determine the best-fitting geometrical shape (e.g., an ellipse, a circle) to the Hierapolis theater, and characterize its features. Because the fitting accuracies are not sufficient to decide which geometrical shape is appropriate, a statistical testing procedure was applied to identify statistical differences between the related geometries. The most probable geometrical shapes for this purpose were determined with the use of the statistical equivalence test.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study has been developed with the project “An investigation on the determination of geometrical structures of antique Rome amphitheaters located in Turkey” supported by Kocaeli University, Scientific Research Projects Unit (Project Number: 2009/48).
References
Ahn, S. J., Rauh, W., and Warnecke, H. J. (2001). “Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola.” Pattern Recognit., 34(12), 2283–2303.
Astori, B., Bonora, V., and Spanò, A. (2003). “Integrated and multiscale spatial data to base a GIS for the ancient city of Hierapolis in Phrygia.” Proc., Int. Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XXXIV, Part 5/W12, ISPRS Archives, 34–39.
Birardi, G., Carlucci, R., Ferrara, E., Giannoni, U., and Maru, G. (1988). “The photogrammetric survey of the Coliseum in Rome.” Proc., Int. Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XXVII, Part B5, ISPRS Archives, 44–88.
Bonfanti, C., Chiabrando, F., and Spano, A. (2007). “Studies and knowledge fusion in archaeological site maps managed in a 3D GIS.” Proc., Int. Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XXXVI-5/C53, ISPRS Archives.
Castrianni, L., Di Giacomo, G., Ditaranto, I., and Scardozzi, G. (2010). “High resolution satellite ortho-images for archaeological research: Different methods and experiences in the Near and Middle East.” Adv. Geosci., 24, 97–110.
Duvernoy, S. (2002). “Architecture and mathematics in Roman amphitheaters.” Nexus Netw. J., 4(3), 81–93.
D’Andria, F., and Caggia, M. P. (2007). Hierapolis di Frigia I. Le attività delle campagne di scavo e restauro 2000–2003, Ege Yayinlari, Istanbul.
D’Andria, F., Scardozzi, G., and Spanò, A. (2008). Atlante di Hierapolis di Frigia, Ege Yayinlari, Istanbul.
Fitzgibbon, A. W., Pilu, M., and Fisher, R. B. (1999). “Direct least square fitting of ellipses.” IEEE Trans. Pattern Anal. Mach. Intell., 21(5), 476–480.
Goldman, R. N. (1983). “Two approaches to a computer model for quadratic surfaces.” IEEE Comput. Graph. Appl., 3(6), 21–24.
Golvin, J. C. (1988). L’amphitheatreromain: Essai sur la theorisation de sa forme et de ses functions, Diffusion de Boccard, Paris.
Hines, T. G. (2001). “The Ancient Theater Archive.” 〈http://www.whitman.edu/theatre/theatretour/hierapolis/introduction/hierapolis.intro2.htm〉 (Sep. 12, 2013).
MATLAB 6.5 [Computer software]. Natick, MA, MathWorks.
Michetti, A. (2000). “Possibili costruzioni delle ellissi del Colosseo.” Disegnare Idee Immagini, 18-19, 89–98.
Nuzzo, L., Leucci, G., and Negri, S. (2009). “GPR, ERT and magnetic investigations inside the Martyrium of St Philip, Hierapolis, Turkey.” Archaeol. Prospect., 16(3), 177–192.
Rosin, P. L. (1996). “Assessing error of fit functions for ellipses.” Graphical Models Image Process., 58(5), 494–502.
Rosin, P. L. (2001). “On Serlio’s constructions of ovals.” Math. Intelligencer, 23(1), 58–69.
Rosin, P. L., and Pitteway, M. L. V. (2004). “The ellipse and the five-centred arch.” 〈http://www.cs.cf.ac.uk/User/Paul.Rosin/resources/papers/oval8.pdf〉 (Oct. 1, 2012).
Rosin, P. L., and Trucco, E. (2005). “The amphitheatre construction problem.” 〈http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.160.1574&rep=rep1&type=pdf〉 (Oct. 1, 2012).
Sciacchitano, E. (2000). “Il Colosseo. Geometria dell’impianto.” Disegnare Idee Immagini, 18-19, 107–116.
Spath, H. (1997). “Orthogonal distance fitting by circles and ellipses with given area.” Comput. Stat., 12(3), 343–354.
Trevisan, C. (2000). “Sullo schema geometrico costruttivo degli anfiteatri romani: Gli esempi del Colosseo e dell’arena di Verona.” Disegnare Idee Immagini, 18-19, 117–132.
Ziebart, M., Arthur, J., Bateman, N., Rauxloh, P., Lees, D., and Brown, J. (2007). “Determination of the parameters of the Guildhall Amphitheatre ellipse in London.” J. Archaeolog. Sci., 34(9), 1505–1514.
Information & Authors
Information
Published In
Journal of Surveying Engineering
Volume 140 • Issue 3 • August 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: May 14, 2013
Accepted: Nov 14, 2013
Published online: Nov 16, 2013
Discussion open until: Jul 18, 2014
Published in print: Aug 1, 2014
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.