# Perspective in Stage Design: An Application of Principles of Anamorphosis in Spatial Visualisation

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## Abstract

The goal of this paper is to demonstrate the various models of perspective anamorphosis used in the visual arts, which are also applicable to stage design. Through comparative analysis, borderline conditions emerge through which certain perspective models assume traits of anamorphosis, as well as conditions for their use in stage design. The idea is to provide practical instructions which are usable on the stage. This effort saw the use of constructive perspective methods, projective and descriptive geometry, while retaining a pictorial and an optical-physiological perspective. The examples of stage design that are shown in the paper are mostly from the National Theatre in Belgrade, the oldest theatre in Belgrade, and an institution that collaborates with the Faculty of Applied Arts. The perspective models of anamorphosis, analysed here, were chosen according to the unique features of the stage and its elements, which include: a perspective image projected on multiple planes, relief perspective as the anamorphosis of space, and the cylindrical perspective.

## Keywords

Descriptive geometry Stage design Relief perspective Cylindrical perspective Representations of architecture Virtual architecture CAD Viewing angle Constructive perspective Pictorial perspective## Introduction

Perspective anamorphosis is a type of optical anamorphosis, made according to the principles of constructive perspective and observed from the viewpoint from which it’s constructed. In a wider sense, as with other types of anamorphoses, it is a form to which specific projections give more meaning (Čučaković and Paunović 2015, p. 605). Having in mind how important the method of performing scenography is in stage design, its simplicity, its optimal viewing by the audience, and its utilisation by the actors, the purpose of this research is to identify the potentials of certain spatial models of perspective anamorphosis in stage design and to provide a set of recommendations for their realisation. The paper was intended to emphasise the technical possibilities of anamorphosis, without prejudice to its historically determined mythological and magical meanings, and their context.

Looking at the greatest examples, such as Palladio’s Teatro Olimpico in Vicenza, Borromini’s colonnade in the Pallazzo Spada, and Bramante’s Santa Maria presso San Satiro in Milan—which are the subjects of relief perspective of applied geometry classes at the Faculty of Applied Arts in Belgrade—we decided to show and analyse examples from our locality. The reason the analyses of perspective anamorphosis were performed using the example of the stage of The National Theatre in Belgrade was based on the fact that the Faculty of Applied Arts and this theatre have a tradition of many years of collaboration.

Students from the departments of stage costume and scenography of the aforementioned faculty have the benefit of being able to acquaint themselves better with relevant practical work through the relationship with this theatre. The National Theatre in Belgrade was built in the Principality of Serbia in 1869 by architect Aleksandar Bugarski, as a symbol of the country’s liberation. Historians compare the façade of the theatre with La Scala in Milan, but additionally emphasise the interior finishes (with applied motifs of the Renaissance, Baroque and Rococo style), which are significantly more luxurious than the reduced exterior (Kadijević 2005, p. 301).

It was within a short space of time that the theatre first underwent reconstruction, and one of the biggest of these was within 40 years of initial construction, and was carried out by architect Josif Bukavac. The most recent reconstruction was in 1986—performed by the main architects Ljubomir Zdravković and Slobodan Drinjaković, when the stage was modernised. The interior was realised according to the projects of Milan Pališaški. Currently the theatre has a *Main Stage* with 559 seats and the “*Raša Plaović*” stage with 285 seats.

*Main Stage*of the National Theatre in Belgrade (Fig. 1), there are noticeable potentials for implementing perspective anamorphosis. The centre stage (which encompasses the floor surface and the airspace behind the proscenium arch, and is intended for performing stage programs), and upstage (the space behind the centre stage, which is less wide or as wide the centre stage, and is used as a reserve space in situations where a theatre performance with greater depth is required), and on which it is impossible to implement monumental perspective decor (Fig. 1a), are framed by cycloramas (large-dimension semi-circular pieces of canvas that are horizontally movable via electro-motors). The first cyclorama has the form of a rotational semi-cylinder and is used as the backdrop of the centre stage, while the second one is parallel to the upstage walls, given its rounded corners (Fig. 1b).

^{1}Aside from the aforementioned, a parallel plane anamorphosis model is often used to achieve greater spatial depth (Fig. 2c) where the effect depends on pictorial principles. This anamorphosis has an imaginary painting (the initial sketch), which is diffused into parallel planes and is visible from all angles, given that the centre of the projection is in infinity. From a technical perspective, the planes are often emphasised with stage curtains and soffits arranged tonally by depth, sometimes in such a way as to expand the deeper they go, thereby closing the field of view and emphasising the perspective through an empty performance space, which assumes the form of a truncated pyramid.

An important task of a scenographer is to enable the optimal visibility of the stage elements from all angles, or to make certain points of view satisfying and acceptable. Therefore, the examples of certain models of perspective anamorphosis, which are applicable in stage design, are displayed.

## Perspective Image Projected on Multiple Planes

Perspective anamorphoses projected on multiple planes are spatial models where the object image is obtained when vision rays pass through multiple planes, all originating from a certain viewpoint. Depending on the position of the object towards the aforementioned projection planes, the perspective on some planes can contain one, two or three vanishing points.

This means that the image on some planes is positioned according to the conventional principles of perspective projection with acceptable deformations (visual angle^{2} is optimally between 60° and 90°), while on others the image has pronounced deformations due to the increased visual angle. In order for the perspective image to have the traits of anamorphosis, it has to fulfil the conditions of unrecognisability, which means that it is recognisable only when it is viewed from a certain viewpoint or a viewpoint field. When talking about scenography, the audience most frequently notices just the effect of the perspective or anamorphosis (unless it is a part of the scenery) without being able to understand its nature, due to their inability of being able to notice the distortion effect. However, the question of whether the perspective projection is an anamorphosis, or not, is important to a stage designer, as the anamorphosis significantly disrupts the control and verification of potential constructive and artistic mistakes. By gaining experience in creating such stage designs, the designer becomes accustomed to viewing distortions both from different orthogonal projections and other view angles. “The scientific solution of representation derives from the reduction of three-dimensional forms to the plane by means of projective and descriptive geometry, but in actual fact architects resorted to plane sections for the study of three-dimensional objects, even before these were codified” (Rossi 2006, p. 112).

Image unrecognisability in a multi-plane perspective is achieved by using two factors: the visual representation division and the size of the visual angle. The more planes the image is projected onto, the more pronounced the unrecognisability.

*dv*for the vertical and the other

*dh*for the horizontal drawing plane.

Depending on how the imaginary object (or image) is placed in relation to the drawing plane, we can differentiate a combination of perspective projections and thereby form groups of these models.

## Frontal Perspective

Varini’s (Felice Varini) anamorphosis (Fig. 3b) has an imaginary image, which lies in a plane parallel to one of the walls of a square-shaped room, which means that this image can be solved on all walls by using a frontal perspective. On the aforementioned frontal wall and on the parallel walls, the perspective image enlarges with distance, without deformations. On the walls that are orthogonal to the imaginary image plane, the projection is outside of the distance circle, which creates the distortion and unrecognisability effects (except when perceived from the point it originates from).

Apart from this, it has two viewpoints from which images are constructed so as to create the impression of a single enlarged space. Despite the fact that the three internal box panels (ceiling, frontal wall and floor) are visible from both viewpoints, the fields of vision do not overlap, meaning they encompass different parts of the aforementioned panel. Perspective images, which are viewed from both viewpoints, undermine the spatial relations of the box by creating the illusion of a larger internal space. The ceiling anamorphosis, visible through the left peephole (Fig. 5b), creates an impression for the viewer of a ribbed ceiling on a higher elevation than the actual box.

*d*fl

*, d*fr), ceiling (

*d*lb) and floor (

*d*tr), than those on the left (

*d*lr) and right (

*d*rl) surface. Images are projected on the frontal panel, ceiling and floor through both peepholes located outside of the distance circle (Fig. 6), thereby creating deformation.

## Angular Perspective

The vanishing points on the left Nlx, Nly and the right Nrx, Nry of the horizontal x and y direction box, as well as the vanishing points of the horizontal diagonals (under a 45° angle) N*dl* and N*dr,* which are resolved using AutoCAD 3D models, are displayed in axonometry (Fig. 7a). The real sizes of the box sides, as well as the perspective images on them, are visible in the disassembly (Fig. 7b). Vanishing point N*ly* on the left perspective image and vanishing point N*ry* on the right, as a result of the same parallel ray, converge in a common point on the vertical edge of the box.

## Relief Perspective

The relief perspective is a distortion of space which looks non-distortive when projected and viewed from a single viewpoint, and which uses the perspective method to resolve space with the aim of creating an illusion of greater spatial depth than is actually there (in the theatre, it is the depth of the stage space). Many examples of relief perspective application are known, both in stage design and in architecture.

### Immediate Method

The perspective collineation between imaginary 3D and the stage space is established by using the plane of a proscenium arch such as a collineation plane, so the scene backdrop (frontal) is taken as the perspective image of the most distant frontal wall of the original 3D space. The point of view is the centre of the perspective collineation of these two spaces and is taken in place of the “optimal viewer”. Aiming to create as accurate a spatial illusion for the viewer as possible, several median perspectives are adopted, i.e. several points of view (Anagnosti 1988, p. 112).

*of the “perspective relief” determines the distance of vanishing point N from viewpoint O. By increasing the depth of relief*

**a***, the distance of vanishing point N from viewpoint O also grows.*

**a**^{3}

### Indirect Method

_{ n }where vanishing points Nr

_{y}and Nr

_{x}of the relief perspective is freely chosen within technical limitations. The initial object’s Point 1 is obtained by restituting the perspective image 1

_{p}in the π plane of the proscenium arch. The first thing to be resolved is the image restitution, followed by the perspective relief. Perspective image 2

_{p}of Point 2 in a relief perspective isn’t solved consistently. Due to practical reasons, it is lowered into the horizontal plane 2

_{rh}, which is done for all points in the base plane. In order for the perspective of this relief to be convincing, it is necessary to mask such “lowered points” with moving decor.

^{4}can be achieved by using contrast (Fig. 11a) and using harmony (Fig. 11b).

## Cylindrical Perspective

A theatre cyclorama is a curtain that is used as a backdrop, most frequently utilised to depict skies, open spaces or painted with neutral colours in order to hide back-stage.

In practice, the ends of the cyclorama are often blocked with stage curtains and soffits, but by using different projection methods, its function can be expanded.

When the position of a viewpoint is on the rotational vertical semi-cylinder’s axis, the projections of the parallel horizontal lines are a curve (semi-ellipses) that passes through two vanishing points. Those vanishing points are intersection points of a view ray, parallel with some horizontal line, through a cylindrical surface. The horizon line is a semicircle, while the projections of the vertical lines, or straight parallel lines with the axis of a cylinder, stay parallel also in perspective, as the point of axial rotation of the aforementioned semi-cylinder is infinitely far.

In order to achieve such projects in practice, it is necessary to present the cylindrical perspective in the plane as an image on a rotational cylinder’s unfolded layer.

^{5}of a circle and its parts (Fig. 14). The height of the rectangle that is a grid of the cylinder layers is equal to the height of the cylinder.

The perspective on the half-cylinder is the image of an imaginary space projected on the layer of the half-cylinder.

In this case, the vertical line, as well as when the viewpoint is on the rotational cylinder axis, has a vanishing point as the projection of an infinitely distant point of a vertical parallel ray.

However, all lines, except the ones whose parallel rays (*Up* _{ 3 }, *Up* _{ 4 }) are within the α angle, which enclose the tangential planes O*t* _{ 1 } and O*t* _{ 2 } on the cylinder through viewpoint O, have imaginary vanishing points (Fig. 15a). On the internal layer of the rotational cylinder, the perspective images of the lines that do not pass through the viewpoint are part of an ellipsis. Using Gellinek’s method (Nikolić 2008, p. 38) the relationship between a determined visual angle and a cylindrical surface which encompasses that angle, on the main stage sample cyclorama at the National Theatre in Belgrade, is analysed (Fig. 15b). When the visual angle of 30° from viewpoint O_{1} on the cyclorama surface symmetry axis, which is in the field of view, is smaller than the half-cylinder, the entire surface of the cyclorama is in a field of view under a 60° angle.

^{6}as well as in another plane characteristic of a certain field of vision (Fig. 15b). In this sense, the problem of the curved line perspective on the theatre cyclorama can be practically solved by using different perspective grids which will first be constructed on the unfolded layer of a rotational semi-cylinder (Fig. 16), but also by creating

^{7}and utilising different dedicated software and applications to simplify the creation of the perspective projections on the cylinder.

## Conclusion

Seeing as how stage design directly impacts a theatre play’s visual effects, by using 3D perspective anamorphosis in stage design one can achieve extraordinary 2D and 3D illusory spatial effects, especially the effects of multi-plane or cylindrical surface penetration, which contribute to the overall theatrical experience.

This study emphasises the importance of an inter-disciplinary approach in creating visual plays with interactions between various disciplines like geometry, art, architecture, optics, physiology and perception theory.

The constructive-geometrical analysis of carefully selected examples of 3D models of perspective anamorphosis gives the opportunity to establish a framework for a more efficient and more accurate projection and stage design creation. Such models can be applied in modern conditions on different levels of the realisation. The results of analysing models of this type of optical anamorphosis are unfolded images and grids that are applicable in projections of every individual element of stage decor, based on different fields of view, as well as stage design in its entirety. At The National Theatre in Belgrade it will significantly contribute to stage design.

The techniques of 3D mapping, reflected anamorphic images and augmented reality projections are used in contemporary stage design. In modern, minimalistic design those virtual images replace natural decor, whose scenography takes on a new function. All these listed geometrical procedures create content which can assume new meanings and forms through the process of digitalisation.

## Footnotes

- 1.
- 2.
The visual angle is different from the viewing angle and is defined as an angle in a certain plane, most often the horizontal or vertical one, where the main visual ray is perpendicular to the drawing plane or a curved surface’s tangential plane. The viewing angle has the viewpoint as the vertex, and the rays are in the tangential planes of the object. This is explained in the optical-physiological perspective, in which the process of optical perception is successive, temporal phenomena.

- 3.
“If the relief depth is zero, we get the usual perspective.” (Leopold 2014, p. 236).

- 4.
“The pictorial perspective method involves any visual element such as devices whose physical properties can increase, reduce or neutralise the impression of spatial depth” (Marcikić 2002, p. 12).

- 5.
Rectification (Lat.

*rectificatio*) is the straightening of a curved line into a part of a line and the determination of the length of its parts. - 6.
Many authors have demonstrated the method of shifting the orthogonal surface onto a curved plane: Andrea Pozzo, author of illusionistic painting,

*The Apotheosis of St. Ignatius*, on the nave vault of Sant’Ignazio in Rome, c. 1690–1694 demonstrates how to map a flat grid of squares onto a cylindrical vault (Andersen 2007, p. 394); Inácio Vieira in*Tractado de Prospetiva*(1716) demonstrates a sketch of the aforementioned model (Cabeleira and Coelho 2011, p. 326); also engraver Abraham Bosse 1653 in part of plate 2. (Andersen 2007, p. 464); John Kirby has shown an unfolded layer of a rotational half-cylinder grid (Andersen 2007, p. 558). - 7.
An application of anamorphosis in stage design, which was discovered by Celestino Soddu in his research (Soddu 2010) into images generated by his own computer software, would be interesting.

## Notes

### Acknowledgments

As the authors, we wish to express our gratitude to the Ministry of Science and Technological Development of the Republic of Serbia, for supporting our research, which is part of Project No. TP 36008 entitled: Development and Application of Scientific Methods in Design and the Building of Highly Cost Effective Structural Systems with the Application of New Technologies.

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