Architectural historians agree that Filippo Brunelleschi, the great master architect of the Renaissance, rediscovered perspective at the beginning of the 15th century. Perspective is a method of foreshortened drawing with vanishing points of the objects' linear outlines.Brunelleschi's rediscovery is depictedi by an episode. He stood inside the door of Santa Maria del Fiore which is located at one side of the Piazza del Duomo and took out a small board with a peephole in the middle. This board was set up so that people could see through this hole the Santo Giovanni di Firenze, the baptistery in the center of the Piazza del Duomo. He then took out a flat, lead-backed mirror, which had just began to be produced in Venice, and raised it at an arm's length in front of the board with the peephole. This mirror, obstructing the view toward the baptistery, instead reflected the backside of the board with the peephole. And on this backside of the board, Brunelleschi had painted a reversed image of the baptistery. People were invited to see this painting reflected on the mirror and compare it with the view of the real baptistery by removing the mirror (fig. 1).
fig. 1 Brunelleschi understood the principles of perspective, and was able to construct the painting of the baptistery in true perspective. With his careful and highly skilled rendering, the difference between the view of the real baptistery and the mirrored image of his painting was said to be almost impossible to distinguish. After this, Brunelleschi did a similar experiment with another painting in Piazza della Signoria. Both of these paintings have been lost and the formation of the Piazza del Duomo was changed by the extension of Santa Maria del Fiore. However, these episodes show that a perspective can reproduce an image of a three dimensional world on a two dimensional picture plane which can be highly accurate with respect to human perception.
Historically, perspective was used in paintings far before the 15th century, and some historians point out its earliest appearance in Greek scenography, the backdrop of a stageset depicting cityscape. Anaxagoras in the 5th century B. C. mentioned that “[S]cenography is a part of optics and is concerned with how buildings must be reproduced in painting.”ii Democritus and Euclid were among those who studied perspective. However, perspective was not widely used in paintings and architectural drawings, and its art was not conveyed or developed rigorously until Brunelleschi revived this lost technique and acknowledged its advantage and significance. Thus Brunelleschi's episode is established as one of rediscovery.
After Brunelleschi, perspective regained its popularity and a number of Renaissance artists, architects, and mathematicians developed scientific methods of perspective constructions, utilized these in their own work, and left relevant treatises with beautiful illustrations. Leonardo da Vinci discussed perspective in his A Treatise on Paintingiii, and used a single vanishing point perspective in The Last Supper for Santa Maria delle Grazie in 1498. Leon Battista Alberti's On Painting iv was published in 1511 and it explained the principles of perspective construction as projecting the outline of objects in space onto a picture plane using the visual cone emanating from the eye to the objects through the plane. Also mentioned was a method to calculate the foreshortening ratio of objects in perspective. This book is said to be the first scientific treatise on perspective.
Another significant publication, Albrecht D殲er's The Painter's Manualv, appeared in 1525 where he introduced several so-called perspective apparatuses, which not only served practically to produce perspective images of an object but also to show the principle of perspective projection in the clearest way. Figure A is his elegant illustration of the second perspective apparatus, which consisted of three threads, a picture frame and a swinging tablet hinged to the frame. The first thread was hooked through a needle fixed onto a wall and tensioned by a lead weight attached to one end. The needle denotes the view point of the perspective drawing. The painter's assistant would grab an iron pointer attached to the other end of the thread, and would point at various positions on the outline of the lute. The painter prepared two more threads and would pin one of them horizontally on the picture frame and the other vertically so that their intersection point matched the spot where the first thread would pass through the picture frame. Then he loosened the first thread, swung the tablet back into the frame, and with a pencil, marked the intersection point of the vertical and horizontal strings. By repeating this process of marking various points while opening and closing the swinging tablet, the painter could scan the entire lute and “its points [would] have been transferred to the tablet.” Durer explained that connecting all the points on the tablet produced a correct perspective of the lute.
fig. A
While D殲er's apparatuses elucidate the principle of perspective projection, other Renaissance scholars elaborated methods of constructing perspective images on paper without the help of such devices. For instance, Sebastiano Serlio's second book in Five Books of Architecture,vi written between 1537 and 1547 included a chapter called “On Perspective” with numerous illustrations of one and two vanishing point perspectives (fig. 2). This earliest non-Latin text was widely read by his contemporaries.
fig. 2 Since then, perspective has played an important role in architecture. It is widely used by architects to conceive the formal, spatial quality of a design in progress, as well as to help the client understand the form of an unbuilt environment. The perspective techniques developed in the Renaissance primarily projected objects in three dimensional space onto a flat two dimensional picture plane, but other types of perspective have been developed to make use of cylindrical and spherical picture planes. M. C. Escher is one of those who exploited the possibilities of these projections. Today, computer graphics technology have enabled instant computation of any type of perspective projection from a three dimensional geometric modeling database. With the help of rendering algorithms such as ray tracing and global illumination, it is possible to produce a photorealistic image of form and space without the hands of Brunelleschi.
In the summer of 1993, I had an opportunity to work on a project with my colleagues, Professor Jorge Silvetti and Dr. Sungah Kim at Harvard University. Our subject of study, Hagia Sophia, one of the most significant buildings in Istanbul, is now used as a museum after serving as an Islamic mosque. Originally built as Justinian's main church in 537, this grand scheme has a monumental ceremonial space under the main dome of over 30 meters in diameter which springs up from its base ring at a height of over 40 meters from the ground. The masonry technology to support this grandiose dome and its spectacular spatial effect had little competition until the wake of Modern architecture. With its strategic location between the East and the West, the building charmed many travelers including historians and architects. A number of later churches and mosques with a similar spatial configuration focused around a central dome had been discovered at different places by architectural historians. Hagia Sophia has been proven to be one of the prototypes for the domed structure. Architects and theoreticians who have been able to influence their contemporaries often made references to Hagia Sophia. Auguste Choisyvii and Le Corbusierviii are among them (fig. 3 and 4). In Towards a New Architecture, Le Corbusier used an illustration by Choisy of a sectional axonometric of the church in a chapter entitled “Three Reminders to Architects.” It served as an example of the function of plan with a caption: “The Plan influences the whole structure : the geometrical laws on which it is based and their various modulations are developed in every part of the building.”
fig. 3 fig. 4 fig. 5 In this project, we are interested in the analysis of Hagia Sophia in its original pre-Islamic form. After Justinian's original construction, the church was heavily damaged by the earthquake of 557 and converted into a mosque at the time of the Ottoman conquest. Throughout this period, it was repaired and renovated. To convert it into a mosque, four impressive minaret structures (fig. 5) were added as well as numerous interior ornaments.
We used geometric modeling techniques and aimed at visualization with the help of computer graphics. Most of the documentation about the church's form in the year 537 was provided by Professor Silvetti and Rowland Mainstone's recent book on Hagia Sophia.ix Dr. Kim prepared major portions of the three dimensional geometric model while I worked on the computer graphic visualizations from the model with a ray tracing based software. Through the use of computer graphics technology, we prepared various images from the same modeling database, each meant to convey specific features of the complex church (fig. C, D, and E).
The diameter of the central dome of Hagia Sophia is similar in size to the dome of the Pantheon in Rome, which was constructed by Hadrian in 117, some 400 years before Justinian (fig. 6). While the Pantheon's dome sits on a cylindrical base, the dome of Hagia Sophia is set on a squared central bay in plan and raised to a height of over 40 meters. To realize this grand structure with stone masonry before the era of steel and reinforced concrete, an ingenious tectonic system was elaborated by its architects, Anthemius and Isidorus. Both these architects, also scholars of geometry and mechanical engineering, used their knowledge of calculation and building technology to create this dome with a system of pendentive; a building method that historians believe to have achieved after a long history of development its greatest manifestation here. The enormous load of the central dome is held by giant masonry arches, which in turn are supported by four buttress structures at its side and the hemispherical domes in its front and back (fig. D, top).
Computer graphics permit us to show and hide portions of the geometric model at will and to manipulate the visualization of the various systems embedded in the architectural form. The spatial organization of the church consists of the main bay under the main pendentive dome, a secondary two story system of various domes and vaults around it, four ramp enclosures at each corner and the precinct atrium at the front of the complex (fig. D, bottom). The sequence of vaulted and domed space units around the center can be clearly shown by the reversion of void and material (fig. C, bottom). The process of constructing this geometric model started by the preparation of these spatial units; solid modeling software was used to subtract these interior units from the exterior massing model (fig. E, top). Solid modeling software is also capable of producing sectional geometry from the building at any cutting plane (fig. E, bottom). These drawings show the extreme skillfulness of Anthemius and Isidorus who succeeded in creating this dynamic spatial ensemble with a complex, thin cover of stone masonry structure (fig. C, bottom).
fig. C fig. D fig. E To model domes and vaults of various dimensions and shapes effectively, I have devised a small generative modeling software with the help of Dr. Kim. Its original purpose was to automate the process of generating them from basic geometric attributes such as its width, length, and height. In the course of programming, I have learned an interesting fact about the geometric principle of the shape of the dome. On the second story, each side of the church consist of a sequence of spherical pendentive domes, in contrast to the sequence on the first floor which uses different domes with diagonal ridges (fig. 7). This design probably reflects the fact that the first story's ceiling height is restricted by the floor of second story, and thus the former is smaller than the latter (fig. 8). The ridged domes on the first story have a geometry resulting from two crossing vaults which are barrel shaped. Curiously, if one enlarges the radius of this barrel shape gradually, it reaches a point in which the ridged dome becomes a completely spherical pendentive dome. In other words, the spherical pendentive dome on the second floor is a unique case of a more general ridged dome. The generative software I created was programmed with this principle and as such it generates a ridged dome as well as a spherical pendentive dome when a specific value is given for the height parameter in relation to the diagonal length of the bay (fig. 9).
Once the geometric model is completed, computer graphics software enables one to view the model from any view point inside or outside (fig. F and G). One may cut sections of the model. Also, rendering software can be used to simulate materiality and lighting effects. After all, this project resulted in several hundreds of computer graphic slides and a short animation clip, which represent spatial organization, structural and tectonic systems as well as the material and lighting performance of Hagia Sophia.
fig. 6 fig. 7 fig. 8 fig. 9 fig. 10
In this exhibition, I have been interested in providing the best presentation technology to exhibit the result of this particular project, and designed a projection apparatus custom-made for that purpose (fig. H). This apparatus, the “DIGITARAMA”, has been designed to display information interactively about the architecture, to operate in response to bodily action of the viewer, and to expose and visualize its operational principles for intuitive comprehension.
fig. F fig. G To instantaneously retrieve a vast amount of graphic information, interactive computing has been a convenient technology. With the help of computer graphics, this apparatus displays analytical images of Hagia Sophia on a projection screen and on a flat panel display, each attached to one end of a rotating arm.
A small physical model will be placed at the center of this arm, which rotates vertically and horizontally around this model. When the viewer rotates the arm, its spatial relationship to the fixed model changes, and appropriate images of the building are retrieved and displayed. The flat panel display close to the viewer displays exterior perspectives of various geometric models with their view angle adjusted to that of the viewer towards the physical model. The projection screen at the far end of the arm displays an interior perspective of a geometric model with its view angle adjusted to that of an imaginary camera inside the physical model toward the direction of the screen.
Greek scenography depicted the life-size cityscape on the backdrop of the stage set, and Brunelleschi's episode took place in front of the real baptistery in Piazza del Duomo. In these examples, we see a comprehensible scale and positional relationships between the viewers and the viewed objects which sensationalized the viewing experience more than just their accuracy. The inspiration of the apparatus that I designed originates from a desire to regain the proximity between the object and the viewer which tends to get lost in computerized presentation systems.
The operating principle of the apparatus is quite straightforward. The rotation angles of the arm are sensed by pen tablets, computer software computes the view angles from them, retrieving appropriate images, and then sends output signals to the flat panel display and the LCD projector. To keep the rotating arm light, one design problem was to keep the projector off the arm while maintaining the correct projection. I have placed the projector underneath the arm's supporting axis and devised a mirror attached to this axis in order to reflect the projection beam to the screen. To precisely keep the reflected beam aimed at the screen attached to the rotating arm, the mirror must rotate by exactly half of the angle of the vertical rotation of the arm. The solution is provided by a set of four change gears which create 1 to 2 speed ratio between rotations (fig. 10). All mechanical parts of the apparatus are designed to be left exposed so that the viewers can intuitively understand the process from the sensing of rotation to the output of images.
As I write this article two months before the opening of the exhibition, my team has produced two preliminary versions (DIGITARAMA, prototype A and B), and is in the process of assembling the third version from aluminum tubes (fig. B). The physical model to be placed in the center of the apparatus will be cast by a three dimensional printer, a CAD/CAM machine originally developed at MIT's engineering department. The computer rendering of the church's interior perspective is also undergoing major changes with the help of a cutting-edge visualization software based on a global illumination algorithm. Hagia Sophia is a building with a complex exterior form and a dramatic single interior space. The custom-made apparatus being developed is capable of displaying an interior perspective from a fixed view point and an exterior perspective around a fixed target. I would like visitors to judge if this apparatus is well suited for an interactive graphic representation of Hagia Sophia within a museum setting.
fig. H
Among the projects I run at MIT, one is titled “The Unbuilt”, co-directed by my colleague, Kent Larson. This project aims at creating computer graphic representations of form and space of lost classical buildings or unrealized architectures which are of historic importance. Some of this representational work includes Andrea Palladio's scheme for a palazzo in Vicenza, modeled from Palladio's 20 sketches (collaboration with Ti-Wai Shi), and a visualization of the Danteum designed by Giuseppe Terragni and Pietro Lingeri for Mussolini before the end of the World War II. Some of the outcomes of this project are planned to be displayed in an exhibition, End of the Century, opening in Tokyo next spring. The experience of developing these projects suggests to me the enormous, open-ended potential of computer graphics for the representation and analysis of architectural form and space. My ambition is to utilize this potential for my own architectural design practice. I hope there will be another chance to talk about it soon.
fig. B I would like to thank Peter Morley and Ritsuko Taho for invaluable suggestions and assistance on the design and construction of my apparatus. Many thanks are given to NEC corporation for the provision of the display equipment.
i This episode is introduced in James Burke, The Day the Universe Changed (Boston, Little, Brown and Company, 1985). A documentation by Antonio Manetti is discussed in Chapter 3 of John White, The Birth and Rebirth of Pictorial Space (London, Faber and Faber 1967).
ii I took this quote from Bartschi A. Willy. [1976]. Linear Perspective. Trans. Fred Bradley. New York: Van Nostrand Reinhold Company.
iii Leonardo, da Vinci. A Treatise on Painting. Trans. John Francis Rigaud. London: J. Taylor. 1802.
iv Alberti, Leon Battista. [1511]. 1991. On painting. Trans. Cecil Grayson. London: Penguin Books.
v Durer, Albrecht. [1525]. 1977. The Painter's Manual. Trans. Walter L. Strauss. New York : Abaris Books.
vi Serlio, Sebastiano. [1537-1547]. 1982. The Five Books of architecture. Trans. New York: Dover Publications.
vii Choisy, Auguste. [1899]. 1964. Histoire de lユarchitecture. Paris: Editions Vincent, Freal et Cie.
viii Le Corbusier. [1923]. 1946. Towards a New Architecture. Trans. Frederick Etchells. London: The Architectural Press.
ix Mainstone, Rowland. J. 1988. Hagia Sophia. New York: Thames and Hudson.
 |
 |
 |
