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
Interactive Parametric Design and the Role of Light in Byzantine Churches
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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?
Issues involved
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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.
Observations
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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.
Design Principles
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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.
Case Studies
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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.
Parametric Model: Hagia Sophia – Heptagon (7-sided)
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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.
Parametric Model: Hagia Sophia – Heptagon (7-sided)
Parametric Model: Xeropotamou Monastery – Dodecagon (12-sided)
Parametric Model
Parametric Model: Neusis Construction
Anthemius’ Reflector
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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.
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 (Reflection of Light on the Concave Side of a Spherical Catoptrical
Surface)
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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)
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 (Reflection of Light on the Concave Side of a Spherical Catoptrical
Surface)
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Anthemius’ reflector diagram superimposed over a cross-section of Hagia Sophia (with original
and current domes). (Source: Anthemius and Mainstone).
Parametric Model:Verification of Anthemius’ Reflector
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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.
Parametric Model:Verification of Anthemius’ Reflector
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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.
Lighting Model
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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 highaccuracy settings)
Lighting Model
Lighting Model
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Ellipsoidal Reflector
Mainstone Parapet
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.
Conclusions
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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.
Future Work
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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.
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