12/18/2010

The Opus by Zaha Hadid Architects

This review is a perfect illustration of a recent body research developed on architectural geometry. As mentioned by Helmut Pottmann, geometry plays a roll more and more important in architectural design. The new Zaha Hadid Architects' project, The Opus, is not yet completed. The analysis I propose will focus on certain aspects of this building, particularly its form. I will stress recent research on PQ Meshes, or Planar Quadrilateral Meshes. Mathematics data have been selected among a large number of mathematics literature. Then I decided to write the subscripts by using _ and reducing the size of the type, that is for instance e_i,j. I will follow the evolution of this construction, meaning I will reactualize as soon as possible the review of The Opus.

The Opus, Zaha Hadid Architects' new project, is a mixed-use commercial and retail development located in Dubai. The Business Bay District will have  fluid, spatial building refuting traditional definitions of office functionality.

The Opus — Render, Zaha Hadid Architects, © Zaha Hadid Architects

The masterplan
The masterplan shows buildings connected by a series of low rise podia and streets. These urban elements create with the canal a unity, that is the Dubai Business Bay.

The building: subdivision and planarization
Focusing on the masterplan that seeks interconnectedness and uniqueness, Zaha Hadid Architects proposes a building that unifies three separate towers. This cubic building appears to hover from the ground with a distinctive free form void.
Fluidity, interconnectedness, layers, spatiality, planar, surface, unity are the key elements of this architectural project.
Zaha Hadid Architects uses the polyhedral subdivision rules to facilitate the design of this building. It is made of polyhedral surfaces with planar quadrilateral faces. This is called PQ Meshes.
This consists of iterated steps of optimization and subdivision. This process destroys planarity and leads to a planar quad mesh design useful in practice.
The Opus — Render, Zaha Hadid Architects, © Zaha Hadid Architects


PQ meshes, or planar quadrilateral meshes, are the study of quad meshes with planar faces. They possess useful properties with respect to architectural design and modeling.
As a number of research on PQ Meshes, among others that of led by Evolute, TU Wien, points out, PQ Meshes precisely offer offset properties. Offset properties are useful for realizing multilayer constructions. They facilitate the torsion and free nodes and lightweight connections of joining members. They reduce the need for material which results in cost reduction, and a good overall aesthetics insofar as the mesh appears less dense.
As various researchers observe, PQ meshes are a discrete counterpart of conjugate curve networks on surfaces. PQ meshes firstly appeared in the mathematics literature under the name of quadrilateral meshes, or quad meshes. Quad meshes mean that all quads are planar.
In architectural design, planar surfaces are easier to manufacture as opposed to non planar ones. Moreover quadrilaterals are cost effective compared to triangular meshes.
Mathematics literature gives precious information on the PQ Meshes function. I will choose Murtaza Safri's research on PQ Meshes entitled "CS 888 Project: PQ, Conical and Circular Meshes for Architectural Design" to illustrate my analysis.
PQ Meshes can be obtained by minimizing the following function:
F_PQ,Penality = W_1f_f air + w_2f_close + µf_det + vf_angle (*)

Where for each vertex v_i,j
f_f air := ∑_i,j[||v_i+1,j - 2_v_i,j + v_i-1,j ||^2 + || v_i,j+1 - 2_v_i,j-1||^2
and foot point y_i,j
f_close = ∑_i,j||v_i,j - y_i,j||^2

Then, for each equilateral Q_i,j the unit vectors along the four sides e_i,j, e_i+1,j, f_i,j and f_i,j, f_det is computed as four individual terms (*)
f_det := c^1_det,ij =  det(e_i,j, e_i+1,j, f_i,j)^2 = 0,
c^2_det,ij = det(e_i,j, e_i+1,j, f_i+1,j)^2 = 0,
c^3_det,i,j = det(e_i,j, f_i,j, f_i+1,j)^2 = 0,
c^4_det,i,j = det(e_i+1,j, f_i,j, f_i+1,j)^2 = 0

Figure showing result of PQ Mesh planarization, Murtaza Safri, © Murtaza Safri

The use of PQ Meshes provides a surface refitting by automatically perturbing the coarse representation in a way that it will fit the target surface best when subdivided and planarized (Schmiedhofer, Brell Cokcan, Schiftner, Ziegler, 2006).
The Opus — Spider Web, Drawing, Zaha Hadid Architects, © Zaha Hadid Architects


"Simple Geometric operation producing perfect PQ-meshes", Heinz Schmiedhofer, Sigrid Brell Cokcan, Alexander Schiftner, René Ziegler, analyzing The Sage Gateshead, Foster and Partner, 2004, © Foster and Partner. Originally appeared on "Design and Panelization of Architectural Freeform-Surfaces by Planar Quadrilateral Meshes"
Subdivision Fitting automatically perturbs the coarse representation in a way that it will fit the target surface best when subdvisided/Planarized, Heinz Schmiedhofer, Sigrid Brell Cokcan, Alexander Schiftner, René Ziegler, analyzing The Opus, Zaha Hadid Architects, © Zaha Hadid Architects. originally appeared on "Design and Panelisation of Architectural Freeform-Surfaces by Planar Quadrilateral Meshes" 










This methodology differs to that of used for the design of The Sage Gateshead built by Lord Norman Foster in 2004. The envelop of this building consists of flat, trapezoidal panels of glass. If one compares to the envelope of the Opus, one observes that the Sage Gateshead is based on a Basic PQ Design which, according to Schmiedhofer, Brell Cokcan, Schitner and Ziegler, is "insufficient for the design of arbitrary free-form shapes", such as Zaha Hadid Architects' The Opus. This comparison is nonetheless very interesting insofar as it enlightens how PQ Meshes facilitate architectural design.
The Sage Gateshead, Foster and Partners, 2004, © Foster and Partner. Originally appeared on Academic.
The Opus — Render, Zaha Hadid Architects, © Zaha Hadid Architects


This results in a free-form building that will be clad with a fully engineered curved glass curtain wall. Reflexive fritting patterns in the form of pixilated striations will be applied on the glass facade to offer a degree of reflectivity and materiality to the cubic building. It, also, aims at reducing solar gains inside the building.
The Opus — Render, Zaha Hadid Architects, © Zaha Hadid Architects

The Opus — 7th Floor, Drawing, Zaha Hadid Architects, © Zaha Hadid Architects
The Opus — Lower Ground Floor, Drawing, Zaha Hadid Architects, © Zaha Hadid Architects
The Opus — Section, Drawing, Zaha Hadid Architects, © Zaha Hadid Architects

The following video presents the guideline of the Opus.



Technical information:
Program: Office Tower
Architects: Zaha Hadid Architects
Client: Omniyat Properties
Structural Engineer: Whitbybird Ltd
Area: 84,345 m sq. m. /21 levels
Width: 100m
Depth: 67 m
Height: 93 m
Date of completion: Not specified
All drawings, images, renders, courtesy © Zaha Hadid Architects except The Sage Gateshead constructed by Foster and Partner
Photograph and diagram of The Sage Gateshead, Courtesy © Foster and Partners
Video: Courtesy © Zaha Hadid Architects

Reference
Safri Murtaza, CS 888 Project: PQ, Conical and Circular meshes for Architectural Design.
Heinz Schmiedhofer, Sigrid Brell Cokcan, Alexander Schiftner, René Ziegler, Design and Panelization of Architectural Freeform-Surfaces by Planar Quadrilateral Meshes, 2006.

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