“Everyone knows the effects of volumes placed against the light: the result, as we know, is that the shadows reproduce these volumes.  We owe the birth of the art of painting to this phenomenon.”                                        Boullée, Architecture, Essai sur l’art


The research presents a study on Cenotaph of Turenne 1782 (Figure 1) by the visionary 18th century French architect Etienne-Louis Boullée.  The aim is to reconstruct the unbuilt architecture through physical and digital modeling to unfold the stereometric form and analyze its atmospheric and environmental effects.  The goal is to provide an alternative frame of reference by moving away from the metaphoric and the iconographic, and towards the analytical and the performative for reading and evaluating Boullée’s project.


From 1750 to 1780 Boullée began conceptualizing the grandeur of architectural monuments through the use of ink-wash drawings on hot-pressed straw paper.   Drawings produced during this period were expressed with originality and executed with exceptional draftsmanship.  The projected building in the design often exhibits clarity of formal character.  Scholars whom have written about Boullée’s ideas have addressed his theory through iconographic (Helen Rosenau, Emil Kaufmann, Susanne Von Falkenhausen) and allegorical (Pier Vittorio Aureli) narratives.  These reflections are largely formulated upon an overarching argument that Boullée is an avid believer in nature and reason by invoking his fondness for Newton through the commemorating project: Cenotaph for Newton. While his admiration of Newton might be true, it does not prevent us from questioning the rationality of his work.  How do we know Boullée is a rational thinker and architect? Could it be that we thought he is rational because he told us so and not because of the rational quality of his work?

Questions and motivation

When framing the problems for this research, the pertinent questions considered are:  archival information on Boullée’s work is limited in general, does the investigation proceed with wary operations to differentiate between evidence and speculation? Or inversely, does the investigation take advantage of the unattainable as a platform for unrestrained creativity when making the asserted claims and generating the rendered images?  Moreover, in an era where the ability to fabricate any image conceivable is boundless, to what extend should the rules be set?  Should the powerful and advanced computing tools be used to generate photo-realistic images, or to create whimsical mise-en-scène through visual effects and filters?
Having deliberated the above questions, my intention is twofold: to study and to challenge the perceived rationality that exists within the geometry of Boullée, and secondly to generate unseen imagery of the cenotaph.  Results from the exercises will form the basis, through the lens of atmospheric and environmental effects, to evaluate Boullée’s work.  With respect to the unseen images, a few rules were predetermined.  The renderings shall refrain from being stylized; they shall instead be composed to emulate those created by Boullée.  Through rationalization of the geometry, it allows a critical reading of the principles behind the sacred forms, while visualizing the unseen spaces provides further evidence and clues for evaluation.  The investigation will focus on what the archival documents do not reveal.  I aim to overturn the "preconception" on Boullée by using the Cenotaph of Turenne as a case.


The research methodology is organized in four phases: 

1.     Measure and Record- to forensically document the series of orthographic drawings, and to extract the geometric genesis and proportioning system;

2.     Interpret and Reconstruct- to investigate Boullée’s material sensibility in order to interpret and translate the geometries three dimensionally;

3.     Narrate the Unseen- render the interstitial spaces through advanced rendering engine to reveal spaces previously hidden;

4.     Analyze and Evaluate- to compare both the geometric organization of the visionary work, as well as the atmospheric effect between the original and the reconstructed.

Before analyzing the work, it is important to situate Boullée’s project in a theoretical context, which I will attempt to do in brief, as this has mostly been discussed at length by other researchers.

The drawing

The project commemorates the 17th century Marshal of France, General Vicomte de Turenne, a celebrated military commanders during the reign of Louis XIV.  It is among a series of cenotaph designs that articulates Boullée's philosophical ideas on nature, beauty and architecture. There are five ink-washed monochrome drawings known to portray the project and are identified with handlist number (HA), including a bird’s-eye view of the cenotaph surrounded by a square-formed ossuary; two plans, one is preparatory and another appears to be more definitive; a section; and an elevation.  With the exception of the bird's-eye view, all drawings are drawn orthographically. 

Boullée and his Architecture, Essai sur l’art

Born in 1728 Paris, Etienne-Louis Boullée was an architect whose mature adult life coincided with the French Revolution, together with Claude–Nicholas Ledoux, Jean-Jacques Lequeu these three contemporary visionaries have been commonly referred to by historians as “Revolutionary Architects”, and being considered as a tour de force of French Neoclassicism.  Boullée’s contribution to architecture lies in his prolific and powerful drawings, influential writing, and effective teaching at the École Nationales des Ponts et Chaussées.  In particular, the impact of Boullée's design ideology later transformed to become the pedagogical foundation for the École Polytechnique, augmented by his student Jean-Nicolas-Louis Durand (1761-1834).

Although Boullée’s seminal text Architecture, Essai sur l’art was written between 1790 to the time of his death in 1799 it was not until 1953 that the manuscript was published in Boullée’s Treatise on Architecture by Helen Rosenau. Despite his relatively small amount of writing, Boullée’s treatise is undoubtedly influential and is often cited alongside with other referenced architecture essays by Vitruvius and Laugier. There were two important contribution of the Essai: First, it attempted to define the guiding principles of architecture as a professional practice[1]; second, it advocated his views on the a priori nature of thinking and imagining a pictorial representation before materialization.

Nature as a source of architecture

Boullée’s ideas about form, nature, and rationality were part of a tradition that has guided architects such as Vitruvius and Averlino who believed in the underlying power ofpure forms, that such form when combined with an appropriate use of light triggers a deep emotional phenomenological reaction. Boullée’s use of stereotomic forms as an expression of the immense, eternal and infinite natural world.

Scholarly research of Boullée's theoretical position in architecture often stresses on his belief in nature, and how his early training in painting impacted his design and ideals[2].  In the Essai, Boullée discussed extensively the value of nature, articulating his belief that the basic principles of architecture are derived from nature.  For Boullée, “Nature ….is the source of all true beauty.  It is impossible to create architectural imagery without a profound knowledge of nature: the poetry of architecture lies in natural effects.”[3]  He goes on to state "it is beyond all question that no idea exists that does not derive from nature."  Boullée sees nature as the "source" rather than a "resource" for which ideas are built upon.

Boullée was influenced his teacher Jean-François Blondel (1705-74, not to be confused with François Blondel, the first director of the Academy of Architecture in France), whose definition of nature was new to him. When Boullée applied this acquired definition of nature to his architecture, it involves a greater concern for purpose and the proper use of materials, instead of implying the imitation of a universal pattern.[4] Where “first and foremost, nature was seen as productive, as the source of knowledge and, through agriculture and mining, of wealth.  Without its inexhaustible fecundity, there would have been no society of men, who derived their subsistence from it.”[5]

When articulating how nature would govern architectural principles, Boullée described symmetry as the image of order and clarity that conveyed a sense of beauty and perfection.  It allows the mind —which seeks understanding— to comprehend this natural external condition.  The proportion derived from nature, as he claimed, possesses an important function of beauty.  The simple, symmetrical, perfect and regular form for Boullée is the best iconographic representation of this understanding in nature.  It is clear that Boullée acted upon the hypothesis that there is a rational correlation between simple geometry, nature and the human’s perception, “Everything in nature is striving towards the goal of perfection.”[6]

Boullée distinguishes himself with Claude Perrault and Piranesi's arbitrary and whimsical principles of design. He refuted Perrault’s position that architecture comes from “pure fantastic invention” sourced from the mankind,[7] rather, he advocated that all ideas derives from Nature, including the principle of architecture.  He considered Piranesi's engravings to be the work of a dreamer composed of disconnected and scattered ideas with no particular order.[8]

Philosophical beliefs and architectural forms

On the basis of this belief in nature, and with pure and simple geometry as a form to represent its essence, Boullée began his conceptual and autonomous projects.  This autonomy of architecture through drawing helped create a distance and independence from its projected building.  In this instance the conceptual project becomes the totality of the work itself.

The projects designed with the principles articulated through his conception of nature, provided a general design approach to a number of public building typologies: library, museum, and opera house etc.[9]  The idea of the “public” or the “common” is important, since Boullée believed that public buildings must convey a sense of character and holds the capacity to produce meaning.[10]  This character of relating building typology to Character would be further elaborated through his theory on architecture parlante or “speaking architecture”.  This articulation between architecture and the city would later inspire the 20th century Italian neo-rationalist architect Aldo Rossi to formulate his influential essays on Architecture and the City. 

Rationality and order

Boullée’s work has been described by Pier Vittorio Aureli as having addressed and dealt with the technical requirements of the building as opposed to mere fantasy that embraces the monumental sublime, which is often associated with the drawing of Piranesi.  In Architecture as a state of exception, Aureli (2011) warns of misreading Boullée’s drawings as simply visionary, and calls for a wider acceptance of the view that Boullée has in fact articulated the “specific conditions” of each project through adopting “technically inventive and individual approaches to functional, programmatic, and even contextual problems...demonstrates a concern for public welfare with its unprecedented provisions for egress in the event of a fire.”[11]  But exactly how did Boullée accomplish that?  In the case of Turenne, there is certainly no evidence to support such assertion, where the giant spherical space with a span of 160 meters covering some 80,000 sq. meter of area offers only one mean of egress for the entire monument.

Similarly, in Rosenau's Boullée’s Treatise on Architecture (1953), she noted “It would be erroneous, to classify Boullée as a Romantic, since his individualism was based on a reasoned appreciation of function, and ruled by the recognition of the laws of nature.”[12]  Rosenau argued that by having cypress trees within his elevation, it served as a good example for his “endeavor to include the effects and the products of nature in his composition.”[13]  Critique and enunciation as such, made either by Boullée himself; Aureli or Rosenau addresses the issue of “nature” from innuendos which falls short of offering specific evidence to substantiate its claim on a measurable level.  As my analysis attempts to reveal, the tendency to rely upon the drawing to serve as iconography remains highly problematic.

Analysis and Evaluation

1. Scale and size of the drawing

The drawings for Cenotaph of Turenne are currently archived in the Bibliothèque nationale de France.  After obtaining high-resolution files of the drawings, they were carefully examined and speculated through cross correlation between Rosenau and J.C. Lemagny’s documented measurements.  With much surprise, the sizes of the drawings are much smaller than they implicitly suggested in respective publications.  The modest dimensions of the signifier provided an utmost contrast to the grandeur and monumentality that it seeks to signify.  In addition to the human figures that provided a sense of scale for the project, one may also refer to the various simple architectural elements: steps, units of masonry wall, pattern of coffers both inside and outside, height of colonnades and balustrade for establishing its architectural scale.

Of the two plans available from the archives, the smaller iteration, measuring approximately 9” x 9” appears to be drawn in preparation for the other and final version (Figure 2).  The evidence is shown in its somewhat hasty line-work, and narrowly varied line-weight. The preparatory drawing contains geometric genesis and is demonstrated in light-toned lines mark in X and a cross-centered about at the funerary altar.

The radial array of the semi-spherical rooms can be traced back through the dots along the ambulatory.  The jamb of the threshold into the ambulatory is also more primitive when compared with the final version.  While the preparatory drawings are drawn in ink, it appears that the final version combines both ink and graphite to widen the degree of contrast in line weight.   It also appears that the preparatory drawings are done is a smaller scale as verified by the stamp seal which Boullée uses for all the six available drawings.

2. Setting-out geometry

Two dimensionally and in section, one sees a defining geometric relationship between the triangle and the circle, both shapes capable of either extracting from, or extended to become the pyramid and the hemisphere.  It is also evident that the diameter (Ø) of the dome is half of the circumference (Cir.) that forms the outer extent of the triangle (Figure 3).

Three dimensionally, Cenotaph of Turenne is the interplay of composition between four primitives: pyramid, cone, spheres and cylinders, resulting in spectacular and mystified interior spaces.  Operation in three-dimensional disposition and subtraction of the primitive shapes, the cenotaph emerges as a monument with an exterior that is distinct from its interior composure.  Through differentiated drawing technique, Boullée created an intriguing juxtaposition between the tectonically articulated exterior with and an unadorned interior crowned with an oculus.

Facing the city, the outer form is composed of a truncated pyramid subtracted by an interior cone with a spherical top.  Within the conic shape, it is further intersected by a large hemispheric dome structure surrounded by 16 smaller domes with coffer patterns overhead.  Three primary datum were established horizontally.  First, an upper plinth connecting to the ground level through a pair of grand stairs (a); second, the ground level ambulatory formed by 16 intermittent hemispheric rooms connects the interior with the city (b); and third, the shrine sunken below grade as a gesture of connection to earth (c).

In addition to visual inspection of the line work, a step-by-step digitization took place to convert the analogue drawing into the digital environment.  First a two-dimension tracing before a series of three-dimensional extrapolations are implemented.  The first interesting finding was an apparent "oversight" between Boullée’s theoretical rhetoric and the corresponding production.  When describing the design for the Cenotaph, Boullée asserts that the pyramid, which forms the outer surface of the cenotaph, was designed based on an “equilateral triangle”.  Boullée expressed that “the perfect regularity” and simple form is what are found in nature, as he wrote,  “I have given the Pyramid the proportion of an equilateral triangle because it is perfect regularity that gives a form its beauty.”[14]However, when examined closely, only half of the statement is true.

Due to his training as a painter, Boullée was perhaps more interested in the visual effects of the painterly kind, rather than the exactitude of geometry.  The appearance of the “equilateral triangle” pyramid is in fact an isosceles triangle with a vertex angle at 53.13 degree and two base angles at 63.435 degree.   The perfect equilateral occurs only in projection.  The inconsistency can be proven in both the mathematical and graphic methods (Figure 4).

3. Figurative Poche

Poche as a form of surplus strategy is deployed by Boullée as a necessary mediator between the boolean interior forms and the primitive exterior shape.  It serves as an interfacing agent between the primitive geometries, allowing the juxtaposition to be absorbed within the walls. Such juxtaposition between the geometries is not immediately evident when looking at individual drawings— only when oscillating between the drawings that the condition is revealed.

While the deployment of poche is an intent occurs in the plan, it is in the section where Boullée exploited the potential to its fullest.  Through thickening of the poche, scale of the cenotaph is further exaggerated by the augmentation of the massing.  It is also utilized to differentiate the construction principles between the inside and outside, while the staggered exterior implies a system of unitary construction.  The austere, unembellished interior suggests a smooth possibly plaster finish enhancing the scaleless reading of the surface, and to receive a play of light upon it.  The disposition of poche is located where a lack of exactitude is needed.  For instance, as demonstrated, it is impossible to match the plan with the section, and the perfect alignment between the square boundary of the pyramid and the circular ambulatory does not actually exist.

The ambulatories at the base of the pyramid as shown in the section drawing indicate an impossibly thin wall, where the poche’s thinning is taken to the maximum extremity.  The fact that it appears to support the coffered dome above is defying any structural and material logic— a condition contravening basic gravitational law of nature(Figure 5).  Incoherence is also evident in the ways the dome is represented.  One could read this articulation of the dome as either a section or an elevation, but not simultaneously, even if one were ready to suspend the belief that a thin wall is in fact possible.

4. Dark space

A sketch model which contains principle geometric traits of the cenotaph was created in Rhino and rendered in 3ds Max to simulate lighting effect of Boullée's design (Figure 6).  The simulated model of the cenotaph was positioned at the latitude and longitude coordinates of Paris, at 48.864716, 2.349014.  It was set up as if the cenotaph were constructed in half section, therefore allowing natural light to penetrate into the interior space.  This is the only possible way of rendering since the cenotaph was designed without the possibility for admitting natural light. The oculus of the hemisphere, while recalling the Pantheon, deceives the reader into reading it as a lighting aperture, only to discover another conic space over and above it, eliminating the possibility of light admission.  Unlike the Monument for Newton where the motivation was to display a contrast between day and night, universe of stars and the sun, between light from inside out and outside in, Cenotaph for Turenne does not appear to hold such intention or ambition.  No literature I could find, discusses the purpose of this peculiar oculus, given the hermetic characteristic of the project, perhaps it is a design maneuver to address the issue of ventilation?

Based on the renderings produced, it appears that noon of summer solstice, where solar angle is high and does not cast direct shadow from the cenotaph, is a particular moment best reflective of the image rendered by Boullée, without the manipulation of imaging software in the likes of Photoshop.  Despite the best intentions to capture, it is difficult to simulate the shadow effects of the original.

Narrate the unseen

Images in the subsequent section are produced from digital models reinterpreted from the drawings (Figure 7).  It offers glimpses of unseen spaces from within the Cenotaph of Turenne.  The four sets of images shown in the following articulates one sequential movement along a linear axis, from the city to the cenotaph in four representative positions: the triumphal arch entrance; the circular corridor; the ambulatory; and the sunken funerary.  Each frame is rendered in two-lens settings: 10mm and 24mm situated at eye level, one for a more neutral and naturalistic rendition while another capturing a broader and perhaps inclusive view of the interior spaces.

Physical model

In addition to images generated from the computer model, physical models of different scales were also produced to study the atmospheric effects, and to visualize the geometric and material challenges that the design possesses (Figure 8 & 9).  Scaled at approximately 1:400, the physical model was constructed through “Sectioning”[15] by layering multiple laser-cut sheets of cardboards, a process best reflective to the construction logic of the cenotaph.  Particularly on the exterior elevations, the drawings indicate a modular construction, which implicitly suggest a form of masonry construction.  While on the interior surface, a coat of plaster finish was applied to stipulate a textureless surface rendered by Boullée.  The differentiation between inside and outside is further exacerbated through the use of color that magnifies the reading of the poche.

One part of the cenotaph that involves repetitive calculation to resolve its geometry is the vaulted ceiling in the ambulatory.  An algorithmic Rhino 3d model with Grasshopper was built to conduct a focused study on this area with the hypothesis that the three-dimension coffer was projected from a two-dimensional pattern in plan(Figure 10).  To construct the ambulatory, there were two circles serving as the geometric genesis to the exercise.  The first circle defines the hemisphere that forms the overall ambulatory ceiling.  The second circle offsets from the first and rotates centripetally around it 36 times.  Or in the case of this arrangement, a parameter defined to allow for variable numeric inputs.  Additional parameter defines the width and depth of the coffer ribs.


This research began with the premise to offer an alternative frame of reference for reading and evaluating Boullée’s project.  Despite discovering a number of inconsistencies and phenomenological impossibilities that lies within the cenotaph —whether it is the challenge of spanning significant distances by the dome, or painting the interior spherical surface with daylighting, or the lack of passage for air within the funerary, or an imprecise reference to the use of perfect geometry for the pyramid— it would be erroneous and inconclusive to draw a conclusion discrediting the rational basis of Boullée.

Asserting the disclaimer is not to render this part of the research trivial or peripheral.  Rather, it highlights the importance of defining the lens for evaluating his work, whether on the one hand, to negate the constructability of the work by focusing on its conceptual and symbolic representation.  Or, to associate the works produced to our perceptual understanding of a gravity-bounded phenomenological world.  Perhaps a provisional conclusion is that Boullée’s autonomous architecture must not be separated between the drawing and his manifesto.  Instead, the two endeavors support and complement one another, a work that needs to be read in oscillation.

On the digital side of this study, what the investigation indirectly revealed is, within the broad spectrum of computing software and tooling, there lies a role for its participation in the discourse of architecture beyond design applications, perhaps to seek the advancement of, and to provide a new level in the research of architectural history and theory subjects.   In the case study of Turenne, one sees the realization of the rendered images and the models as not necessarily the main purpose, but rather helps to ask better question in terms of theory and philosophy in architecture.  Lastly, an on-going research on Boullée is needed with the long-term intention to calibrate and contextualize Cenotaph of Turenne with other works of his in order draw a more critical and immutable position.


[1]In the first part of Architecture, Essai sur l’art, Boullée discussed in detail a profession where the architect’s imagination is limited by time and patron’s discretion for commission. “The gifted architect must refrain from any resistance, he must not listen to the voice of his genius but descend to the level of those he must please. ”Etienne-Louis Boullée, Architecture, Essai sur l’art, (New York: Academy Editions, 1976 transl.): 84.

[2]Boullée sees Painters as being “free and independent; they can choose their subjects and follow the bent of their genius”, ibid., 84.

[3]Ibid., 88.

[4]Richard Patterson, ‘Three Revolutionary Architects, Boullée, Ledoux, Lequeu’, (Boston: Butterworth Architecture, 1995): 149 – 161.

[5]Antoine Picon, French Architects and Engineers in the Age of Enlightenment (Cambridge: Cambridge Press, 1992): 108.

[6]Relating the perfection of nature to the perfect geometry of primary shapes is a position most convincingly argued by Antoine Picon in addressing Boullée’s concept of drawing.

[7]Claude Perrault's (architect for the East facade of the Louvre) controversial declaration of arbitrary and positive beauty in the 17th century was at the center of debate between Perrault and Francois Blondel, Picon, French Architects (note 5), 106.

[8]Boullée, Architecture, Essai sur l’art, 86.

[9]Pier Vittorio Aureli, The Possibility of an Absolute Architecture, (Cambridge, Mass.: MIT Press, 2011): 151.

[10]Susanne von Falkenhausen, “ The Sphere: Reading a gender metaphor in the architecture of modern cults of identity,” Art History: Journal of the Association of Art Historians 20 (June 1997): 243.

[11]Aureli, 142-143.

[12]Helen Rosenau, Boullée’s Treatise on Architecture, (London: Alec Tiranti LTD, 1953): 12.

[13]Ibid., 19.

[14]Boullée, Architecture, Essai sur l’art, 106.

[15]Sectioning is described by Lisa Iwamoto as: “rather than construct the surface itself, sectioning uses a series of profiles, the edges of which follow lines of surface geometry.  The modeling software’s sectioning or contouring commands can almost instantaneously cut parallel sections through objects at designated intervals”. Lisa Iwamoto, Digital fabrications: architectural and material techniques, (New York: Princeton Architectural Press, 2009): 10.


Charmaine HUI (editing), LIU Chun Ting Larry (digitization and parametric modeling), CHEE King Hei Thomas (draft digitization, rendering and 3D additive printing), LEUNG Kai Shu Calvin (physical modeling), Jisoo PARK (plastering), Stanislaus FUNG (history and theory references) and Belinda LAW.  Research study supported in part by the Chinese University of Hong Kong, Faculty of Social Science Direct Grant.