Academic Trajectories

This course is an important step in the curriculum of the program. Students move beyond design fundamentals and begin to deal specifically with the realities, constraints, and opportunities specific to buildings. Students must master the part-to-whole relationships embedded in building design. Rather than debate the merits of top-down or bottom-up design, this studio attempts to introduce a new approach to the part-to-whole relationship in which the both are scalar manifestations of a single idea of space, pressed through the architectural apparatus.

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THE PROJECTIVE PLANE EMPLOYED
The bedrock of architectural drawing, descriptive geometry, arose from the necessary cutting of stone parts to be reassembled into a predetermined whole.  This subdivision of three dimensional solids, as described by planar projections onto flat paper, influenced how architects were trained, evaluated and practiced for centuries to follow. These stereotomic projections not only directed the cutting of individual stone elements, but drove the seaming and patterning of the stones as they were assembled. What are the determining criteria for these patterns? Certainly structural considerations weigh heavily. Franois Derand would employ his skill in stereotomic techniques to achieve his ribless vaults at St Paul St Louis in Paris, delivering a smooth transition between intersecting cones that elevated the hierarchically lower stone seams. 

The act of drawing two dimensionally directly influenced the patterns. Robin Evans best describes the manner in which the act of drawing two dimensional traits pushes a three dimensional patterning into the squinches and trompes 16c France in his influential essay Drawn Stone.  Under close examination, one must acknowledge a third force wresting control of these patterns. 

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A COMPETING ORGANIZING THOUGHT
The geometric characteristics of the underlying surface topology of the assembled shape are not passive participants. Consider Jules-Hardouin Mansart’s shallow vault for Arles Town Hall. The isoparametric curves (see note 1) of these surfaces manifest themselves in the design. Both the u-generator ruling lines, as well as some of the v-base curves appear (projected down) in his reflected ceiling plan. It is not a pure interpretation. Mansart also traces and tracks the projected curves on the vault intersections, then offsets them (and projects up) along the edges. The ceiling is a visual display of two competing spatial organizations dueling it out in the seaming of stone. 

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Isoparametric curves and their U-V grid are a window into a related, but non-Euclidean means of organizing and describing space. Pioneered initially by Carl Frierich Gauss, Gaussian curvature is mostly employed by today’s computer scientists. Digitally native architects slip between the XYZ and UV world views increasingly often, but in most cases without the awareness that they are doing so. Gauss believed that describing curved surfaces with Cartesian coordinates was unfair. “The surface has its own properties and one should be able to investigate these properties without leaving the surface.” (see note 2) Gauss was dissatisfied with flattening and subsequent re-projection as a descriptive process. Mansart seems to have agreed, mixing methodologies, perhaps intuitively, in his design. The vault is a quilt of cones and cylinders, seamed together through a cohesive but mixed-method of patterning of iso-curves and ruling lines, and projective interpretations. 

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P-PLANE TO C-PLANE: the Architectural Apparatus in Reverse
Architects are still trained masters of the Euclidean plane. The opening screen in most 3D software - 4 views comprising a plan, two elevations, and a perspective (albeit typically 3-point perspective rather than a parallel view) traces back to these initial techniques of description developed for the French military in the 16th century.  While prevalent before, the modern environment of digital documentation tools elevated Descartes’ coordinate system. The Euclidean plan underlies the means to communicate directly with tools of production, specifically CNC driven machinery. The “N” of those 3D plotters, laser cutters, water jets, and robotic effectors is Descartes's XYZ coordinates, wholly dependent on the Euclidean plane. However free from the planarity of the paper we may be with the introduction of NURBS modeling, we are throttled in the export of these design ideas to the built world. Building components are constrained by the flatness of the initial drawing plane, now fully manifested as the flat water-jet bed, accommodating the flat cut of steel lying on it, shipped by the flat truck bed, - all so that we can communicate to the CNC jet exactly how to cut our curved profile. The plane-of-projection is now the plane-of-construction. A 21st century squinch is drawn in three dimensions and built in flat planes. We have reversed the apparatus of architecture, but the influence and potency of the apparatus remains. 

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Gauss would weep to see a curved surface reduced to a chipboard model achieved by extruding Descartes’ grid and built as an enlarged amorphous waffle. If we choose to imagine a world in curves, we need to increase our fluency in languages that better reflect their attributes. Our architectural apparatus is robust enough for this. If the end goal is an assemblage of flat parts, we need only develop the procedures to negotiate our flatness with a surface’s inherent divisions. Let’s pick up our plane of projection - the P-Plane and align it to each knot within the UV grid. Like Klee’s multitude of perspectival points, we may indulge in multiple coexisting P-planes, creating an adaptive map of the world for each moment of surface. 

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THE POTENCY OF CONSTRAINTS
This studio asks students to develop an understanding of the inherent nature of curved surfaces in pursuit of an appreciation and future implementation of this understanding. We proceed by rationalizing these surfaces in flat panels consistent with common constraints embedded within the construction industry. This rationalization makes apparent underlying surface characteristics that go unnoticed otherwise, many with architecturally expressive potential. Many surface exercises are assigned in order to develop a proficiency in negotiating between the UV grid and Euclidean plane. Finally, we ask students to explore the expressive potential within this negotiation, a fully embodied idea from part-to-whole.

 

notes:

1. An isoparametric curve of a surface is obtained by leaving one of the (u,v) parameters of the surface equation constant while the other varies from 0 to 1.

2. Lanczos, Cornelius. Space Through the Ages. New York, New York: Academic Press Inc, 1970.