Keywords

1 Introduction

The instrumental availability and technological research being carried out on spherical images requires some clarification in order to better understand the whole and the origin of these - apparently disruptive - new possibilities of perception and representation of three-dimensional space. At the basis of these innovations is the geometric definition of equirectangular projections - also known as cylindrical equidistant - whose conception, dating back to Marinus of Tyre (AD 70–130), was also the basis for the oldest terrestrial cartographies. The problem of planar unwinding of spherical surfaces was subsequently reinterpreted using different geometric protocols, depending on specific purposes and related accuracy and deformation issues.

The current computational possibility of interpolating, and digitally translating, between the geometries adopted in the various spherical representations has been made relatively manageable by the now widespread and proven conversion protocols of current digital cartographic softwares (Yang et al. 2000). Similarly these geometries, already applied in the representation of the spherical convex shape of the earth, have also been adopted for the description and astronomical restitution of the configuration of celestial space, which surrounds the earth as an ideal spherical concave configuration of the universe from the point of view of our planet. Obviously, recent discoveries about the far position and relative distances of the stars in the space of the universe have made it possible to evolve these original polar and angular views, arranged on a spherical map, into computational models of three-dimensional and dynamic representations.

However, verified the antecedent and relevance of a cultural and mathematical heritage experienced in studies generated in the cartographic and astronomical fields, this paper focuses on the use of spherical views in the representation of perceived space at an architectural and environmental scale, as an extension and simultaneous re-presentation of the observer’s entire empirical visual field. Some of my previous publications on spherical photo-cameras, and on the devices for displaying these images through AR/VR viewers (Brunetti 2021), are here contextualised in particular around the case of research on the meticulous spatiality conceived and experimented by the architect Camillo Boito (1836–1914) in some significant projects. This further experience on the field made it possible to verify the functionality and effectiveness of the visualisation of spherical views not only in technological terms, but in a comparative manner with respect to the usual methods of representing architecture, implying some methodological deductions.

In this short essay I therefore briefly propose the methods and results of the survey - in the meantime - from two case studies of 19th century interior spaces, through the graphic aspects that can be visualised by the geometric algorithms for their treatment as spherical images, and finally some considerations deduced from these experiments in the process of geometric visualisation of the designed space.

2 Boito Architetto Archivio Digitale

The inter-institutional university research between the Politecnico di Milano and the Accademia di Brera (2021–2022)Footnote 1 to which this survey participated, has collected, classified and shared in digital formats the various archival and documentary sources about this architect. Camillo Boito was one of the most significant and authoritative architects in the historical and cultural period of the Unification of Italy (1871); his work carried on a lively debate in the culture of design the new civil necessities and the foundation of a stylistic contemporary language, heir to a millenary historical tradition to be preserved and revived, using well-accepted and refined methods of representation. This 19th century author expressed himself in a decidedly interdisciplinary way between tradition, innovation, identity, applied arts and theoretical debate, thanks to a solid foundation in geometric design, material knowledge of building and consolidated skills in the craft resources then available. In his architectural, theoretical and didactic work, the art of drawing (Boito 1882) was at the foundation of design knowledge: both in the relief of existing monuments and in the building of new ones, based on geometric skills in two and three dimensions - as can be seen in his and his students’ drawing templates - with orthogonal projections of plans, sections, facades and perspectives. These general rules are enhanced by the expertise also derived from ornamental traditions and archaeological studies on the origin of geometry as a regulatory and symbolic tool of Romanesque cosmatesque stone inlay. In this era, the frequent use of stone in construction had still maintained an intense contribution from the study of stereometry, conceived as a precise forecast of the solids geometry in the designing role of each individual construction element, compared to the three-dimensional drawing of the whole: from the working of stone for the static realization - and initially on the ground - of architectural works, as well as a numbered repertoire of forms for use by the competent workers for the realisation of artefacts. The spatial, formal and material attention of Camillo Boito was at the same time directed towards the valorisation and integration of the now consolidated serial procedures - and no longer only artisan/pre-industrial - for the realization of constructive components: he managed a national level specialized publishing, and an in-depth cultural debate also for the development of technical training schools. These skills, founded on the study of compositional and geometric languages of the past (Zucconi 1997), were based in geometry and drawing, almost like as an “algorithm” of comprehension and application of a common language. Such methods in Architectural debate can be compared to different but similar references in the Arts and Craft movement by William Morris in Great Britain, or even in the Deutscher Werkbund in Germany founded by H. Muthesius and in Austria in the Wiener Werkstätte, founded by Koloman Moser and Josef Hoffmann. While maintaining a rare executive and direct competence in architectural drawing - as documented by the numerous dossiers and design drawings collected and digitised for the exhibition - it is interesting to note that, from a certain threshold onwards, the focus on innovations in architectural representation techniques is highlighted by the new role assumed by photography. Shortly after the invention of photography, the distinguished professor C. Boito began also to collect the first available prints and to use this new technique for the visual representation of the various phases in the study of architecture: in the systematic survey of historical buildings, in the comparative documentation of the phases of construction sites between the original state and completion in restoration works, in the comparative cataloguing of samples of elements produced serially by the industrial arts for the decoration of buildings (Brunetti 2018). The foundation of academic institutional photolibraries were conceived, in consequence, as iconographic repertoire for the ‘remote’ study of the monumental and artistic heritage.

3 The Global Frame of Equirectangular Picture

In order to better understand the experimentation that I am presenting, it could be useful to recall some geometric fundaments - presented here with simple proportional graphic diagrams - used in spherical photography. At a first level of description I would like to remember and clarify the process of mutual interaction between the equirectangular image (in the specific standard of the current digital spherical cameras available) and the digital optical space that is captured, and subsequently returned to the viewing or projection environments. Available; AR/VR and 360°Theatre (and/or planetary) (Fig. 1).

Fig. 1.
figure 1

a): equirectangular proiection: reticular grid of a sperical surface; flat planmap, with centred observer orientaton indices. b), c): equirectangular proiection views; reticular grid of a sperical surface: with centred observer orientaton indices; b) (left): concave interior, c) (right): below pole concentric inside. (2 and 3 dimensional graphic diagrams by the Author, made by equirectangular image processing software)

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Fig. 2.
figure 2

a), b), c): a) (left): 360° Sperical picture: extended flat planmap of the equirectangular proiection survey file, with centred observer orientaton indices; b) (center): concave interior view, c) (right): below pole concentric inside view (courtesy of: Liceo Artistico di Brera, Milano. Spazio Hajech: interior view of the conference and exhibition hall; spherical picture by the Author, digital elaboration with equirectangular image processing software).

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The spherical cameras – twin or multiple lens - capture all the image surrounding from the shooting point and implement all the specific different directions views into a single equirectangular digital matrix of 1:2 format (equivalent to the projection of two “front-rear” hemispheres into “panoramic” view composed of two squares placed side by side), with embedded metadata concerning picture orientation (Fig. 2 a), b), c)).

With appropriate vector softwares it is possible to generate equirectangular raster image files from three-dimensional models of projects, as well as from 3D scans survey.

4 From Original Vintage Photographs to Wide-angle Architectural Photographic Views and Current Digital Spherical Experiments

A second analysis here concerns some specific case study adopted, in the context of the exhibition “Boito architect Archivio Digitale”, examining the different types of architectural photographs taken in the evocative interior architectural environments.

Two important interior spaces have been chosen as case studies for this investigation in reason of their peculiar typology as well as of the decorative apparatuses that characterise them designed by C. Boito: the complex and very articulated staircases of the staircase of Palazzo Cavalli Franchetti (1886) in Venice (Romanelli 1989) (also compared with some century pictures), and the former Museo Civici del Santo (1879) in Padua.

The comparison below presented - some also with reference to rare 19th century photographic images from the historical archive of C. Boito - with those obtained with traditional wide-angle cameras, can be compared with equirectangular spherical shots.

The progressive widening of the field of vision is immediately evident from the comparison in the previous images. This factor, originating from the geometric theories of perspective, (linear and later also curvilinear) has various causes and motivations.

These qualities derive first of all from the intrinsic characteristics of the optical equipment used (evidently limited in the case of 19th century images, then more available in today’s wider conventional optics, and furtherly extended to the spherical through digital treatment in the equirectangular). It must be considered as well the technical relationship (photo-graphia) between the shooting optics and the storage medium (analogue - digital), and finally from the sharing of visual canons (or iconographic codes) relating to the perception of images. These evolutions of the iconographic code can be identified in the convention in the span of these images (Fig. 3 a, b, c):

  1. 1)

    the limits of the average ocular field [30°–60°] (without any significant consequent aberrations of the sphericity of the retina, i.e. within the visual field of the perspective canons of scenography);

  2. 2)

    the iconographic acceptance of the wide-angle extension [90°–120°] (with relative critical awareness of the percepted variation in of the communicated spatial amplitude);

  3. 3)

    Finally, the equirectangular [360° spherical] projection, developed by means of multiple optic camera device, managed by specific algorithm on a computational support (on a digital matrix in 1:2 format): currently usable through observation with interactive viewers using the metadata embedded in the file structure, or projected in a spherical theatre. The planar equirectangular presentation (as in the case of the pages of this publication) is also interesting because - if appropriately composed and after an adequate introduction and experience of geometric decipherment (see Sect. 1) - it allows one to grasp the observer’s lateral and rear visual fields (Fig. 4 a, b, c)

The 19th century architects soon understood how the photography released a great opportunity of producing finely accurate images of their case studies, obtaining an important documentary supplement to the survey drawing of specific objects and artefacts; just as for the visual culture of the 20th century the wide-angle view represented a significant cognitive extension towards a broader and more complex understanding of the context and between the relationships present in the field of observation.

Fig. 3.
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a: (Left quatrain): Venezia, Palazzo Cavalli Franchetti, 1886. Collezione fotografica of Camillo Boito, (Courtesy of¨Accademia di Brera – iconographic apparatuses for research doctorate Thesis of: PhD Federico Alberto Brunetti ©1997); view of exterior, staircase: industrial arts decoration sample details. b: (Right quatrain): Venezia, Palazzo Cavalli Franchetti: staircase interior wide views: zenith sight of muses decorations, frontal section between the floors, mid landing passage. Focal length: 12–24 mm. photography of architecture ©2021 by the Author. c: Venezia, Palazzo Cavalli Franchetti, staircase interior global views: decorations, mid landing passage. 360° Spherical picture, photography of architecture ©2021 by the Author

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Finally, the possibility - already theorised for a long time in the field of geometry and cartography - of capturing the global field of view from a point of view that is stored on a digital support and that can be interacted with through appropriate devices, represents for the current visual culture a mode of experience (see Sect. 5) consistent with contemporary awareness of the translation of reality into digital data.

It is worth mentioning here the pioneering and original work of C.M. Escher (1898–1972) who, in analogue era, explored through his brilliant graphic work the perceptual limits of the visual field, towards extended representation of space opened to spherical perspective, and some other the paradoxes of vision, inaugurating a new iconographic codes of a “surrounding vision”; his research was appreciated and also carried out in collaboration with various mathematicians, including Douglas Hofstadter.

Fig. 4.
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a: Padova. Camillo Boito; ex Musei Civici del Santo. Staircase interior global views: decorations, mid landing passage. 360° Sperical picture ©2021 photography by the Author. b, c: Padova. Camillo Boito; ex Musei Civici del Santo. Staircase interior wide views: b) (left quatrain): zenith sight: ceiling decorations, frontal section between the floors, mid landing passage. Focal lengt: 12–24 mm.; c) (right quatrain): 360° Sperical pictures ©2021 by the Author

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In fact, these widened images are not so much the responsibility of the frontal visual memory, but of the environmental perception in the mnemonic maps reconstructed in order to coordinate the spatial orientation - static and dynamic - and the ergonomic and postural movements of the individual. Considerable recent researches from the area of neuroscience, relating to vision and tridimensional and dynamic mnemonic modelling of space, are particularly concerned with the multisensory interactions that pertain to this cognitive domain. These mental activities, while based on direct vision, are integrated experiences through memory, by articulated movements of the eyes, head and whole body, and finally through hypothetical and deductive cognition. New behavioural measurements, integrated with the mapping of the specific activated brain areas, are making now possible to better understand the complex dynamics of vision, and not just of sight, in the global experience of space. For all these integrated reasons, which here are only summarised, I can consider that 360° vision (a broad definition that goes beyond the view) and spheric representation can be assumed - similarly to perspective for Renaissance culture - as a ‘symbolic form’ of the current digital era.

5 Spherical Projections Experience at Politecnico di Milano 360°Theatre

Starting from these assumptions, and having available the spherical images of the Boito’s internal amplifiers, the third element of verification concerns the specific characteristics of the functioning of the new Teatro360° of LaborA in the Politecnico of Milano, both for the compositional and algorithmic aspects of the adopted geometry, and for the perceptive and environmental experience that this device has demonstrated to be able to offer to the visitors.

The opportunity to project the spherical images created in Boito’s interiors in the theatre360° LaborA of the Politecnico di Milano, allowed me to test, and better understand, the compositional formats of the specific digital scenic device, and also to observe directly, and indirectly, the perceptive and experiential interactions of such a representation apparatus (Fig. 5). The partitions of the original spherical equirectangular image, in this surrounding circular digital room, are subdivided and managed by different algorithms on two contiguous, accurately coinciding surfaces as follows (Fig. 6a, b, c, d):

  1. A)

    a surrounding cylindrical panoramic projection,

  2. B)

    a circular planar projection at the base:

  1. A)

    i.e.: the overview towards the surrounding horizon (indicated in the diagram in the band between the double lines) is composed of a continuous sequence proportioned 1:8 (in the diagram: oriented with the front view “C” into the centre, the two lateral views respectively to the left “SX” and to the right “DX”, the two symmetric positions behind the observer respectively “−R” and “+R”, with the respective index of angular directions (−180°, −135°, −90°, −45°, −0+, +45°, +90°, +135°, +180°) (Fig. 6 a)

  2. B)

    i.e.: the horizontal surface report within the remaining circular base perimeter (therefore indicated in the diagram between the lower double line band and the horizontal line focusing in the “S” pole), which reports the surface converging to the shooting point and below the observer. A system of 4 panoramic projectors, positioned and obscured in the ceiling of the hall - and 2 towards the floor - provide the splitting and stitching of the original equirectangular picture. A digital post-production control unit allows to manage the files of still or dynamic video images - from real shots or virtual simulations - in the space of the immersive 360° theatre.

Fig. 5.
figure 5

Spherical immersive photographic projections at: Politecnico di Milano 360°Theatre at: LaborA - physical and virtual modelling. Spherical image composition calibration test, projection display for Boito Architetto Archivio Digitale exhibit presentation, visitors experiences 2022.01-02.

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Fig. 6.
figure 6

a), Politecnico di Milano 360°Theatre at: LaborA Spherical image composition calibration test. b), c) d): up/down – image composition calibration test (compare with: Fig. 1 a) b), c):

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Fig. 7.
figure 7

a): image composition calibration test, verification maquettes display for: Boito Architetto Archivio Digitale exhibit presentation, visitors experiences; .b), .c) .d): image composition calibration test, verification maquettes display; first layout, cilindrical and spherical planar projection

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Due to the typology and functionality of the hall, unlike what could take place in a semi-dome of a planetarium, the vertical space towards the “N” pole of the image above the horizontal panoramic band is not visible, as it is dedicated to locate the projectors system in the ceiling ((Fig. 6 a), b), c), d)). In any case, the observer’s perceptive experience of the surrounding and underlying visual field of an architectural context is decidedly realistic, interesting and involving. I realized a short series of verification maquettes, using the same geometric diagrams and the respective images shown here, finalized to understand analogically and illustrate this tridimensional procedure of subdivision, treatment and digital projection (Fig. 7 a, b), c) d)).

6 Some Deductions from 360°Theatre Test

It is definitely interesting to verify the representation by the shooting of spherical images, than re-presented in the environment of immersive 360° projection, compared to the spatiality described and prefigured by the original Boitian projects (digitalized, gathered and shared for the exhibition). The geometric description presented in the original orthogonal projections design templates, evidently prefigure a spatial complexity that would be fully revealed in the three-dimensional construction of the work.

In methodological terms, and potentially in a more general sense, it is possible to identify some innovative elements that these visual technologies present for a greater understanding of the perception of the global space around the observer.

These “spherical perspective” images allow to describe in detail, and therefore to be able to analyse, and prefigure, some further field of design intervention, both in optical-visual and mnemonic experience of designed spaces.

7 From Equirectangular Geometry to “Experience Design”

Some methodological considerations therefore arise regarding some of the epistemological issues involved in these experiments. The new technologies offered by these scenarios and communication tools, in particular for vision, seem progressively oriented towards bridging the distance between the observer and the image of the represented data. The wearability of immersive visors has now become an emblematic individual point of contact between a peripheral device with a system of technological platforms - remote and dominant – to a virtual world whose suggestion seems to be able to propose itself perceptively almost as a seductive alternative to the real world.

The available power to those who manage these ‘augmented’ potentials of the ‘meta’-real is even made evident by the socio-economic phenomena that this development has triggered, generating the enrichment and power over data, i.e. as an effective resource of the present and future economy. On other hand is evident the opportunity for a responsible educational collaboration by these new media is strategic in relation to global, ecological, social sharing, and newfound social and ethical values emergencies. The understanding and knowledge of these new (digital, and powerfully iconographic) languages is an argument of great responsibility for those who seek to orient present and future culture and education. Also these scenarios the opportunity offered by virtual theatres are particularly interesting for advanced geometric disciplines and neuro-visual sciences, which could find here a particularly relevant field of interaction (Tatler and Land 2011). For the specific representation of the urban environment and architecture, the possibility of presenting to the observer with a global field of view - from real life footage or virtual design models - analogous to the usual panoramic view of the surroundings (360° at the horizon of the field of view) and of the ground space (in a wide range of horizontal interaction), allows a perception that is decidedly verisimilar to the conditions of environmental visibility and practicability of the space around the individual.

The reactions of the visitors into the “wunderkammer” of the 360° virtual theatre revealed spontaneously them led to “move” in the available horizontal space, thus experiencing not only the aspect of the complete enveloping overview, but also of the immediate viability of the represented environment. These experiences are developed with remarkable proxemic spontaneity by some intuitive actions (see: Fig. 5): gesturing to details that catch one’s eye, starting in trying to climb the projected steps, conversing willingly and commenting on the qualities of the place displayed with other person in the room. Even though this is not are not stereoscopic projections, the perception of the shown environment is felt as an experiential proxemics depth, probably because the observer’s entire body is free to generate an immediately and spontaneously effective interaction in the modification of the obtainable “points of view”. The increase in “degrees of freedom” that a virtual theatre offers, and the immediacy of the possible immediate and simultaneous sharing between several co-present users, requires a commitment to investment and technological management on a completely different range compared to the self-referencing of AR/PC platforms, however much they may be networked remotely with other users. A first conclusion that I would like to underline is that the contemporary image is the increasingly dematerializing from a material support (a painting, a panel, a wall, an “object”) and presents itself in visual terms as an autonomous and individual interacting spatiotemporal experience.

These dynamics has been well described in the recent literature defined “Experience Design”: such definition underlines the user or observer’s active ability to inwardly grasp the relations and relationships of a work, is tentatively replaced by a generation of artefact proposed as an active experience in itself Pine and Gilmore (1999).

The 360°theatre, far away from a possible alienation and although requiring a decidedly significant technological apparatus, seems to offer a space of representation in which the observer can rediscover the (prio)perception of his own initiative and authority towards to the image he virtually inhabits. Equirectangular pictures and surrounding visual experience proves to be a system of representation which has the communicative possibility of sharing and disseminating knowledge of reality, leaving the irreducible experience of the direct encounter between the individual and concrete reality, establishing situations in which the interaction between perception, intelligence, astonishment and surprise can still be part of the true cognitive discovery of the world.

$$ \text{``}The\, horizon\, of\, sky\, and\, earth\, ends\, in\,the\, same\, line\text{''}. $$

This essential phrase by Leonardo da Vinci seems to summarise precisely the dynamic between perception and concept (Trattato della pittura. Dell’orizzonte. §.928).

This quotation remembers that the experience of reality is however synthesised by the intelligence of vision, in forms that are the basis of descriptive and re-creative knowledge of the world, that is, as a presupposition of the modes of representation and its design regeneration. As analogously in history, an innovation in the possibility of representation can reveal an innovative conception of the composition of the designed space.

A new mode of representation, extended to the entire surrounding geometric space and visualised by the individual, can therefore advance the knowledge of the architecture experience, of its mental formalisations and therefore of the compositional processes in which geometry, vision and matter can interact by way of the project.