Interactive Parametric Design and the Role of Light in Byzantine Churches

1. Interactive Parametric Design and the Role of Light in Byzantine Churches Iakovos Potamianos1, Wassim Jabi2 1 Democritus University of Thrace, Greece 2 New Jersey Institute of Technology, U.S.A. ipota@tee.gr , jabi@njit.edu

2. Interactive Parametric Design and the Role of Light in Byzantine Churches • Natural light was used in Byzantine churches to strengthen the meaning and symbolism of the liturgical acts. • Certain methods employed for lighting the dome and the altar have been investigated elsewhere. • It has been shown that the intention of generating light shafts falling onto the altar has determined the orientation of the church main axis in a significant number of churches. • In this paper the following issue is investigated: If, in fact, a light shaft was calculated to enter the church through the apse windows and be directed toward the altar is it probable for this intention to have determined the geometry of the apse?

3. Issues involved • The light shaft enters at a particular time of day, on a particular celebration date and falls on the point before the altar representing symbolically the descent of the Holy Ghost onto the bread and wine causing their consecration. • The time of day when this happens is the third Byzantine hour, i.e. the middle of the morning, which varies according to the season. • The celebration day depends on the dedication of the church. • Cathedrals are often oriented toward the third hour of the equinox in order to be able to capture light from the side windows in various dates and so accommodate great feasts throughout the year.

4. Observations • The geometry of the apse varies considerably from one church to another. It forms various polygons and semicircles, assuming sometimes odd shapes. • The variety of polygons is usually attributed to stylistic preference. • The orientation of the main axis varies considerably from one church to another • The number of windows varies in number usually from one to three to six. • The windows vary in size and in distance from one another.

5. Design Principles • The constant design principles of the apse are: • 1. The interior of the apse has been designed as a circle with its center at the junction of the main axis with the interior side of the wall of the main building. • 2. This circle contains the altar and passes through the point where the priest stands before the altar. • 3. Usually, a circumscribed polygon is established around this circle. • 4. The number of its sides depends on the difference between the angles of incidence of light on the two most important celebration dates of the particular church.

6. Case Studies • These design principles have been derived from the study of 6th century churches. • They were particularly studied on the church of Hagia Sophia of Constantinople • Hagia Sophia is oriented toward the third hour of the equinox and receives light from the southernmost window of the apse on Christmas. • This church is dedicated on the Nativity of Christ. • The angular difference of light incidence on the third hour of these two dates is 24.6 deg. which is best served by a heptagon. • This method has been tested on the 18th century church of Xeropotamou on Mt. Athos and shown to hold true and account for the dodecagonal shape of its apse.

7. Parametric Model: Hagia Sophia – Heptagon (7-sided) • Software: Bentley System’s Generative Components. • Definition of top-level independent Graph Variables. • The parametric model allowed the user to navigate between Constructive and Procedural design spaces. • After constructing the parametric model, the user can trigger a script to search for the optimum design solution based on a desired set of parameters. • The design process does not stop there, the user can then continue to build on the parametric model.

8. Parametric Model: Hagia Sophia – Heptagon (7-sided)

9. Parametric Model: Xeropotamou Monastery – Dodecagon (12-sided)

10. Parametric Model

11. Parametric Model: Neusis Construction

12. Anthemius’ Reflector • The image of Pantocrator, often placed at the apex, is not lit directly by sunlight but, since he is considered to be the distributor of “true light” to the world, is made to appear to emit constant light. Practically, such an impression could not occur by chance. Instead it would be the result of a specific study by Byzantine architects. • A study of this kind seems to have been undertaken in Hagia Sophia resulting in an impressive solution. Written evidence to this is provided in the extant writings authored by its architect Anthemius of Tralles in the form of solid geometry propositions for the construction of reflectors. • One of these reflectors was designed for the purpose of directing solar light at a single point within a building, taking into account the varying positions of the sun throughout the day and the seasons. • Anthemius’ reflector QZHLMNXO reflects sunlight coming from either D, G , or e, and passing through B, to A. D represents summer solstice, e winter solstice and G the equinox.

13. Anthemius’ Reflector (Reflection of Light on the Concave Side of a Spherical Catoptrical Surface) • All contemporary accounts agree that the original dome had a precariously flat curvature which, as modern scholars have repeatedly speculated, might have caused its subsequent downfall. • The architect’s choice should be attributed not to his lack of knowledge, in which case he would have followed time-honored antecedents, but, instead, to his will to defy technological limitations in order to achieve a highly desired effect. • The explanation regarding the vertical profile of the dome is probably found in another reflector design by Anthemius.The significance of this reflector design lies on its similarity to the original dome profile, on the one hand, and to a peculiarity observed in the process of its solution, on the other. This problem deals with the issue of the reflection of light on the concave side of a spherical catoptrical surface. • Anthemius’ reflector ABHG reflects any ray parallel to DB, such as ZH , to K. An illustration of light behavior when incident rays are oblique (superimposed over Anthemius’ original reflector diagram)

14. Anthemius’ Reflector (Reflection of Light on the Concave Side of a Spherical Catoptrical Surface) • Anthemius’ reflector diagram superimposed over a cross-section of Hagia Sophia (with original and current domes). (Source: Anthemius and Mainstone).

15. Parametric Model: Verification of Anthemius’ Reflector • Software: Bentley System’s Generative Components. • Definition of top-level independent Graph Variables. • The parametric model was built exactly according to the description of Anthemius. • After constructing the parametric model, the user can modify top-level parameters to test its robustness. • The parametric model behaved exactly as Anthemius described.

16. Parametric Model: Verification of Anthemius’ Reflector • No parapet remained after dome collapse. • When superimposing the reflector from the parametric model on the cross section, light rays converge on the apex of the original dome.

17. Lighting Model • Sources describe the dome as having an “incessant gleam” • We set out to simulate the lighting of the dome using the proposed parapet design according to Mainstone vs. a parapet design based on Anthemius’ reflector as generated by the parametric model. • Used 3D Studio MAX to model dome using both parapet designs. • Applied the most accurate advanced lighting method (Radiosity combined with ray-tracing with high-accuracy settings)

18. Lighting Model

19. Lighting Model • Rendered the dome looking up into it. • Using Adobe Photoshop, we applied the same curve distortion to both original images to better discern the light distribution in the dome. • It is clear that the ellipsoidal model created a brighter and more uniform light distribution. The geometry of the curved mirror and the flat geometry of the dome combined to create an effect of an “incessant gleam” as suggested by accounts from that period. The solution proposed by Mainstone provided a much more uneven lighting condition with artifacts due to the sudden change from an inclined cornice to a vertical parapet. Ellipsoidal Reflector Mainstone Parapet

20. Conclusions • Light and geometry played an important role in the design of Byzantine churches and in the design of Hagia Sophia in particular. • The advent of sophisticated parametric digital tools and advanced lighting models has allowed us to test many of the theoretical propositions and discover new findings regarding the behavior of architectural constructions. • The model allowed us to synthesize Anthemius’ research on reflectors with the geometry of Hagia Sophia. Furthermore, it also provided an accurate visualization of the lighting conditions. This visualization could then be compared to historical documentation and other evidence.

21. Future Work • Many of the results presented in this paper require further verification and elaboration. • Future work will include the design of more sophisticated 3D parametric models and the testing of other churches and noted works of architecture. • The dome of Hagia Sophia requires further elaboration of the pendetives to fully account for their role and lighting. • The geometry of the windows at the base of the model is largely unknown and requires further investigation to determine its attributes and resulting effect on the lighting of the dome. • The parametric tools are of value in of themselves for analysis as well as design. We intend to develop generalized parametric tools that will help the designer specify desired conditions and explore alternatives created through the manipulation of parameters and geometric relationships.

22. Interactive Parametric Design and the Role of Light in Byzantine Churches Thank You Iakovos Potamianos1, Wassim Jabi2 1 Democritus University of Thrace, Greece 2 New Jersey Institute of Technology, U.S.A. ipota@tee.gr , jabi@njit.edu