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The Development of the Geometric Concept of Relief Perspective


The aim of this paper is to give an overview of the history of relief perspective from its origins in Palladio’s century so as to position the mathematical concept of relief perspective and its development in the context of intellectual history and the philosophy of science. While this concept emerged in art as bas-reliefs and in scenography, its mathematical formulation occurred only in the nineteenth century. Sixteenth-century scenographical perspective, in particular, planted an important seed for the later mathematical concept: here the example is Vicenza’s Teatro Olimpico by Andrea Palladio—a project that was actually built and is extant today. The main stages of the development of relief perspective are analyzed herein via the reconstruction of approaches taken by notable authors such as Breysig, Poudra, Staudigl, and Burmester. Studying this concept historically offers us a deeper comprehension of the intellectual history of projective geometry and its connection to scenography and architecture.

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  1. Amoruso, Giuseppe. 2016. The Relief-Perspectives of Bitonti and Borromini: Design and Representation of the Illusory Space. In: Giuseppe Amoruso (ed.): Handbook of Research on Visual Computing and Emerging Geometrical Design Tools. Hershey: IGI Global.

  2. Amoruso, Giuseppe; Sdegno, Alberto; Manti, Andrea. 2019. Surveying and 3D Modelling of the Andrea Palladio’s Teatro Olimpico in Vicenza. First Studies on Geometric Analysis and Perspectives. In: Carlos L. Marcos (ed.), Graphic Imprints. The Influence of Representation and Ideation Tools in Architecture, 427-438. Cham: Springer.

  3. Baglioni, Leonardo; Salvatore, Marta. 2017. Images of the Scenic Space between Reality and Illusion. Projective Transformations of the Scene in the Renaissance Theatre. In: Proceedings of the International and Interdisciplinary Conference IMMAGINI? Image and Imagination between Representation, Communication, Education and Psychology. 2017, 1(9), 943;

  4. Barbaro, Daniele. 1556. I dieci libri dell’architettura di M. Vitruvio tradutti et commentati da Monsignor Barbaro eletto patriarca d’Aquileggia. Venice: Francesco Marcolini.

  5. Beyer, Andreas. 1987. Andrea Palladio. Teatro Olimpico. New edition, Berlin: Verlag Klaus Wagenbach, 2009.

  6. Breysig, Johann Adam. 1798. Versuch einer Erläuterung der Reliefperspektive zugleich für Mahler eingerichtet. Magdeburg: Georg Christian Keil.

  7. Burmester, Ludwig. 1883. Grundzüge der Reliefperspective nebst Anwendung zur Herstellung relief-perspectivischer Modelle. Leipzig: B. G. Teubner.

  8. Burmester, Ludwig. 1884. Grundlehren der Theaterperspektive. Allgemeine Bauzeitung 49, Wien: 39-40, 44-49, 53-57, Tables 25-27.

  9. Ciammaichella, Massimiliano. 2018. Temporary Theatres and Andrea Palladio as a Set Designer. Nexus Network Journal,

  10. Del Monte, Guidobaldo. 1600. Perspectivae libri sex. Pesaro: Girolamo Concordia.

  11. Fiedler, Wilhelm. 1871. Die Darstellende Geometrie. Ein Grundriss für Vorlesungen an technischen Hochschulen und zum Selbststudium. Leipzig: B. G. Teubner.

  12. Furttenbach, Joseph. 1640. Architectura Recreationis. Augsburg: Johann Schultes.

  13. Furttenbach, Joseph. 1663. Mannhaffter Kunst-Spiegel. Augsburg: Johann Schultes.

  14. Gournerie, Jules de La. 1859. Traité de perspective linéaire: contenant les tracés pour les tableaux, plans et courbes, les bas-reliefs et les décorations théâtrales, avec une théorie des effets de perspective. Paris: Dalmont et Dunod. Mallet-Bachelier.

  15. Hara, Mari Yoko. 2016. Capturing eyes and moving souls: Peruzzi’s perspective set for La Calandria and the performative agency of architectural bodies. Renaissance Studies. Journal of the Society for Renaissance Studies 31(4): 586-607.

  16. Hass, Ulrike. 2005. Das Drama des Sehens. Auge, Blick und Bühnenform. München: Wilhelm Fink Verlag.

  17. Lambert, Johann Heinrich. 1752. In: Max Steck (ed.). Schriften zur Perspektive. Berlin: Dr. Georg Lüttke Verlag 1943.

  18. Leopold, Cornelie. 2014a. Reliefperspektive. In: Loos Asplund Stirling Diener Hoch3, 1-4. Hoch3 Stirling. Park Books, Zürich.

  19. Leopold, Cornelie. 2014b. Perspective Concepts. Exploring Seeing and Representation of Space. Journal for Geometry and Graphics 18(2): 225-238.

  20. Leopold, Cornelie. 2017. Perspective Transformations for Architectural Design. In: Vera Viana (ed.). Geometrias’17 Proceedings. Coimbra: APROGED.

  21. Lordick, Daniel. 2005. Reliefperspektivische Modelle aus dem 3D-Drucker. IBDG 1: 33-42.

  22. Poncelet, Jean-Victor. 1822. Traité des propriétés projectives des figures. Paris: Gauthier-Villars.

  23. Poudra, Noël-Germinal. 1860. Traité de perspective-relief. Paris: J. Corréard.

  24. Pozzo, Andrea. 1707. Perspectiva Pictorum Et Architectorum. Rules and Examples of Perspective. Proper for Painters and Architects, etc. London. Rpt. New York, 1971.

  25. Schaal, Hermann. 1981. Reliefperspektive. Der Mathematikunterricht 27(3): 69-90.

  26. Scheffers, Georg. 1927. Lehrbuch der Darstellenden Geometrie in zwei Bänden, 2 vols., 2nd. ed. Berlin: Verlag von Julius Springer.

  27. Serlio, Sebastiano. 1584. Il Secondo Libro di prospettiva. In: Tutte l’Opere d’Architettura et Prospettiva. Venetia: presso Francesco de’ Franceschi.

  28. Staudigl, Rudolf. 1868. Grundzüge der Reliefperspektive. Vienna: Seidel & Sohn.

  29. Staudt, Karl Georg Christian von. 1847. Geometrie der Lage. Nürnberg: Friedrich Korn.

  30. Steiner, Jacob. 1832. Systematische Entwicklung der Abhängigkeit geometrischer Gestalten von einander. Berlin: Fincke.

  31. Taylor, Brook. 1715. Linear Perspective: Or a New Method of Representing Justly All Manner of Objects as They Appear to the Eye in All Situations. London: R. Knaplock.

  32. Wiener, Christian. 1884. Lehrbuch der Darstellenden Geometrie, vol 1. Leipzig: Teubner.

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My first encounter with relief perspective occurred during my studies at the University of Stuttgart with geometry professor Hermann Schaal. Much later, after experiments with our architecture students at the Technische Universität Kaiserslautern, beginning with the All School Charrette “Stirling Hoch3” (Leopold 2014a) in 2013, deeper research and wider applications could be undertaken during my visiting professorship at IUAV in Venice on the invitation of Professor Agostino De Rosa. My thanks to Amyrose McCue Gill of TextFormations for her editorial assistance.

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Correspondence to Cornelie Leopold.

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Leopold, C. The Development of the Geometric Concept of Relief Perspective. Nexus Netw J 21, 227–252 (2019).

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  • Perspective
  • Scenography
  • Projective geometry
  • Representation of space
  • Relief perspective