In the historical progression of Gehry’s body of work, it is possible to trace the progressive development of paper surface geometries and their associated techniques of description and modeling. This progression shows a continuing expansion of the class of admissible paper surface forms, as improved representation and fabrication techniques permit less constrained geometries to be feasibly supported in the building process. The planar forms of Gehry’s early work, described in Section IV.A, represent the point of departure of this progression.
Cylindrical and conic forms begin to appear on relatively early projects, including the Winston Guest House, Edgemar Development, and the Chiat Day Building. These forms appear tentatively, sparing applied in an overall composition of planar forms. Prior to the introduction of computer modeling techniques in the firm’s process, paper surfaces take Euclidean forms, true cones and cylinders. Their more general counterparts were formulated as developable surfaces in Section VI.B. This constraint is imposed on these early projects by limitations of traditional documentation. The complexity of determining geometric relationships between more complex, non-Euclidean conic forms was simply beyond the capabilities of traditional architectural delineation.
The exploration of a vocabulary of conic forms continues to be expanded on Gehry’s projects until the introduction of computer modeling in 1990. The Weissman Museum (Figure VI-33) represents the culmination of this approach. Each face of the west façade is delineated through traditional geometric constructions. The difficulty of performing this construction though traditional architectural delineation is clearly evident in the construction documentation.
Figure VI-33: Conic form rationalization through traditional documentation (Weissman)
A. Physical design model B. Decomposition of the geometric construction, gaussian curvature analysis Figure VI-34: Conic form rationalization through digital documentation (DCH)
The early computer models of the Disney Concert Hall (Figure VI-34) document the extension of the firm’s manual approach to developing complex geometries through a vocabulary of Euclidean surface elements. In the initial design of the DCH project, prior to 1998, the project was intended to be clad in CNC milled stone panels. The project geometry attempted to achieve some of the economic benefits of mass production by the use of the quadratic surfaces. Economic constraints on the project dictated that certain economies of scale were necessary. The design team responded to these constraints by developing cost projections for different complexities of surface qualities. Planar surfaces were naturally assumed to be of lower cost than curved areas. In curved surface areas, distinctions were made between the relatively simple geometries of conic forms and fully free form areas. It was determined that economies of scale could be taken advantage of on conic surfaces, due to the regularity of panel elements across the latitude of a section through the conic form. A budget limiting percentages of the project’s surface area in these categories was developed prior to finalization of the concert hall’s shape.
It is worth noting that the initial design development on this project was conducted in 1992, when numerically controlled milling technologies were available, but computing performance and information distribution mechanisms were at an earlier stage of development than today.
Today, with improved efficiency of computational methods, the cost implications of CNC cutting are more directly tied to the machining time, and less to the computation and operator time necessary for generating the CNC tool paths for the cutting operations. Thus economic efficiencies of batch production of similar pieces, which must still be individually processed
by the CNC milling equipment, seem to be less significant than they must have seemed in 1989.
The project design was re-visited in 1998, when the decision was made to change the finish material from milled stone panels to stainless steel. The conic surfaces were re-interpreted as developable surfaces, involving a different strategy for the direction of sub-framing, but without altering the shapes of the surfaces. Significantly the same project forms admit two radically different approaches to efficiency of construction, one based on regularities of element shapes, the second on ruling lines and the unfolding of panel geometry.
The Guggenheim Bilbao project, represents a dramatic extension of the firm’s approach to the representation of paper surface forms.
While stone was initially selected for DCH, the surface of Bilbao is comprised of sheet metal surfaces. Thus economic constraints were presented to the design team in terms of limiting the surface forms to those that could be assumed by sheet materials. The physical design models on Bilbao were generated by folding large paper elements (relative to the overall scale of the project) into form. The
strategy presumed that shapes which were constructed of large paper surfaces in the scale physical models could be fabricated from individual sheet materials in actual construction.
During initial computer modeling exercises, the digitized data from the physical models were re-interpreted using developable surfaces. These initial results did not entirely satisfy the design team. The forms generated by developable surfaces were deemed too constrained relative to the initial physical design models. Additional CAD modeling operations were performed on the initial developable surfaces, where the surfaces were “puffed out” – deformed such that limited double curvature was introduced into the shapes. Heuristics were determined dictating the degree to which double curvature would be introduced into the surfaces. The utility of these heuristics was limited at the time. The fabricator determined that the surfaces up to a sixty foot sphere could be fabricated. CATIA allowed the curvature
Figure VI-35: Gaussian Curvature mapping on Bilbao Project
at individual points on the surface to be sampled. The principal radii at these sampled points was limited to a minimum of sixty feet in either of the two principal directions.
The geometric qualities of the EMP project represent in some sense a culmination of the firm’s paper surface modeling research and design explorations. On this project, the fully curved free form shapes of the original design were supported as a composition of gaussian curvature constrained paper surface forms. Admittedly, this support of fully free form shapes is approximate, as the forms are rationalized into shapes exhibiting curvature acceptable given constructibility constraints. These rationalization operations can be read in the final project (Figure VI-36).
In the period since the completion of EMP, developable surface and constrained gaussian curvature applications have developed in parallel. Although the gaussian curvature approach presents more generous constraints on project form, the economic efficiencies of straight lines of ruling presented by the developable surface approach are considerable. The tough constraints of developable surfaces on project forms seem to project the energy of the sheet material surfaces as they are formed in space better than the more relaxed qualities of the gaussian curvature approach. The Weatherhead project represents perhaps the most ambitious application of developable surface forms to date.
The two paper surface representations present remarkably different strategies for the representation of similar shapes. These differences are manifested in the substantially different approaches to construction suggested by each representation. However, both strategies require tight tolerances on the framing system required to achieve a form that will match the predicted shape. If the geometry of the framing system does not adequately provide a shape onto which sheet materials will form, then either substantial forming of the cladding material will need to be undertaken, or warping of the surface will occur. Failures of cladding or substrate materials may occur, or waterproofing requirements for the system may not be achieved, resulting in a roof or wall system that leaks. Certainly, the desired architectural quality of the surface will not be achieved, as the cladding buckles and ripples about fasteners and joints. For simple, canonical classes of paper surfaces such as planar, cylindrical or conical forms, the predictive capabilities required to assure developability of the surface are not particularly great. However, to achieve the freely flowing shapes allowed by the most general classes of paper surfaces, the predictive capabilities required to engineer
and fabricate cladding system elements while maintaining the accuracy required for system integrity are substantial.
A. Weatherhead: Developable system B. EMP: constrained curvature Figure VI-36:Rationalization comparison
The geometric constraints presented by the two approaches are sufficient to guarantee conformance of the system geometries with the behavior of sheet materials. However, these constraints come at a price. The control structures supported by the associated CAD techniques do not intuitively guide the user to feasible sheet material shapes. The NURBS surface representations – manipulated by control points – tend to produce shapes with localized variations in smoothness – exactly the opposite of the desired result. Similarly, manipulation of the edge curves that are used to generate developable surfaces will generally result in surfaces with triangle discontinuities. The actual operator activities required to produce paper surface forms using either of these techniques are not directly discernable from the input controls, and require substantial manipulation by experienced users to “tease out” surface imperfections.
Both techniques are developed as constraints on NURBS based parametric surface representations. The shapes produced by these techniques are largely irrespective of actual qualities of the materials used. For gaussian curvature controls, a wide range of material and fabrication phenomena are subsumed into a simple, and rather impoverished, metric. The developable surface technique predicts identical surface constraints irrespective of the actual materials employed.