Eventually the form of the

veneer was given by the same overall equation, with minor adjustments for the seating areas, which required their own custom calculations. Figure 12. Named after the ubiquitous index I (reappearing here as a steel beam), the iThreads provide the physical edge and lateral stability of the surface form. In space, the pillow resembles an egg-crate-like arrangement of peaks and depressions. Its double-curved areas form a tapestry of

5,0 modular boards, each varying by a single degree every few metres and all tapered to measure. IJP and RSP Architects Planners and Engineers, Henderson Waves, Singapore, 2008

View of the central span and completed deck in May 2008. The project begins with a timber pathway linking the springing point of the bridge to the busy vehicular loop on Mount Faber – shown in the lower-right corner of the plan. It involves an infrastructural intervention with a complex structure and a simple brief: to link two ridge summits with a continuous plane on the southern coast of the island of Singapore. The project continues with the bridge itself and concludes with a ramp that connects the bridge to another existing circular path, winding its way around the summit of Telok Blangah Hill (in the upper-left corner of the plan). For designers skilled in this methodology, visualising the act of ‘writing form’ is not strictly necessary, but it is useful in helping to alleviate the abstraction of the process. The ‘parametric pillow’ is the product of three space-relations: the first may be diagrammed as an oblique plane; the second is more complex and produces a flowing periodic oscillation; and the third (and most intricate) represents a product of periodic out-of-phase

і •*- last_in+ 1

тту

і *- last_in+ 1

ttz

і *- last_in + 1

j *- last_jn+ 1

j *- last_jn+ 1

j *- last_jn + 1

a *- matrix ( і, j, FinalX)

a *- matrix (і, j, FinalY)

a *- matrix (і, j, FinalZ)

a

a

a

modulo of M0D_Bin, jn:= — –

point/inverse ^(cOM_Y_Bin> jn – INVy)2 + (cOM_X_Bin> jn – INVx)2 + (cOM_Z_Bin> jn – INVz)2

_INVERSION CONE В

equations FinalX_B (x, у) := (cOM_Y_Bx_ y) • M0D_Bx> y – INVy (mOD_Bx, y – 1)

FinalY_B (x, у) (cOM_X_Bx> y) • M0D_Bx t y – INVx – (mod_bx, у – 1) FinalZ_B{X, y) C0M_Z_Blt> y-M0D_BJC>y – INVz-(mOD_B>Xiy – 1)

і *- last_in+ 1

TTBy

і *- last_in+ 1

TTBz :~

і *- last_in+ 1

j *- last_jn+ 1

j *- last_jn+ 1

j ■*- last_jn+ 1

a *- matrix (і, j, FinalX_B)

a *- matrix (і, j, FinalY_B)

a *- matrix ( і, j, FinalZ_B)

a

a

a

(TTy, TTx, TTz),(TTBy, TTBx, TTBz)

_matrices TTBx

Figure 11. The surface of discrete analytic mathematics does not actually exist: what the parametric formulas produce is only a discrete array of indexical threads grouped in two sets, notated I and J (after which IJP is named). Such worksheets (greatly simplified here for purposes of publication) lie at the heart of the office’s methodology. Ultimately, the key question raised by the deployment of analytic mathematics in design is whether it produces material efficiencies. Largely in evidence in its completed form, the recurrence of kinks along its surface indicates that it is discontinuous. IJP Yeosu 2012 Thematic Pavilion, Yeosu, South Korea, 2009

Partial mathematical formulation. The entrance pathway, bridge deck and connecting ramp are given the same steel and timber treatment and can hardly be distinguished. The centre-lines of the steel members shown (central arch, edge member, mid-height member and curved ribs) are determined by a single set of parametric equations. IJP and RSP Architects Planners and Engineers, Henderson Waves, Singapore, 2008

Location plan of the bridge and timber end-works by IJP (competition stage). IJP and RSP Architects Planners and Engineers,

Henderson Waves, Singapore, 2008

Timber deck of the main span under construction. Too large to be prefabricated off-site and craned into position, it was assembled on a makeshift platform directly above Henderson Road, then raised into position by a battery of hydraulic jacks. oscillations spreading in perpendicular dimensions. Along the other dimension, the J threads fulfil the gravitational demands of the structure, and the piles sit at both ends of each span where the surface self-intersects and the section of the structure is reduced to a single beam. As the ranges vary, it divides like a cell into two, three, or N swelling bulges, as if held in place by knots. Eventually all morphogenetic results can be traced back to fundamental issues of algebraic modulation; there are various machinery-consistent equations, in other words some better suited to sheet-cutting, others to lamination. In terms of structural expression, the bridge systematises and amplifies the problem of converting selected indexical threads into centre lines of material members with structural roles. IJP’s first built project (in collaboration with RSP), the Henderson Waves Bridge is a project commissioned by the Urban Redevelopment Authority (URA), Singapore, following an open international competition. This conceptual model ensures a stable transition to materiality: if the threads are two-dimensional, they are used to define centre lines for laser-cut material profiles.