WME Director of Structures, Sasa Popovic, shares his thoughts on the topic of parametric design, its place in the modern built environment and how WME are embracing it.

What are parameters?

A parameter is a quantity that influences the output or behavior of a mathematical object.

Parameters are closely related to variables. While the variables are values that are changeable by default, the parameters typically either do not change or change by choice.

As an example, in the mathematical function of a hyperbolic paraboloid used to create a roof surface

z = x2/a2 -y2/b2

function z, defines vertical position of the roof surface above the location of horizontal points under the roof, defined by variables “x” and “y”, while “a” and “b” are parameters that define curvature of the roof.

What is parametric design?

In the example of the above described roof, the parametric design would involve changing parameters (“a” and “b”) by architect or structural engineer during the design process in order to derive desired geometry either in terms of its appearance or in terms of the structural efficiency of the roof (and subsequently cost of the structure). Once the design of the roof is completed, the parameters would become fixed. The variables of the resulting roof shape “x” and “y” would still vary even when design is completed as they are related to the horizontal locations of the roof surface points. The parameters of the defined roof shape (i.e., “a” and “b”) would however at this point become constant.

Examples of parametric design?

Parametric design in built environment is nothing new. The roof gradient of a flat roof, crucial in ability of the roof to drain, described by parameter “a” in a roof plane defined by equation z = ax + b was varied by builders since construction of first roofs  in order to provide desired ability of the roof to drain. The parameter was not only different in dry versus wet climates but also for different materials used for roofing (e.g., hay versus shingles).

What has changed recently, is our ability to process enormous quantity of data in a short period of time, thereby allowing us to simultaneously test influence of several parameters on the design outcome.

Some more modern examples of parametric design are Sagrada Familia, Barcelona by Catalan architect Antoni Gaudi (Gaudi did not have computers but used ropes and mirrors to determine optimal geometry of the arches), Roof of the King’s Cross Station, London by John McAslan + Partners, façade of Louvre, Abu Dhabi by Jean Nouvel, Galaxy Soho complex, Beijing by Zaha Hadid Architects (any many other projects of hers), etc.

Why should WME develop effective parametric design capabilities?

            There are at least two reasons for WME to develop effective parametric design capabilities.

The first reason is our competitiveness and ability to support architects in conceptual developments of challenging projects that utilize rapid exploration of geometrical shapes.

The second, equally important reason is our ability to develop efficient forms and economical designs in short period of time. We owe this to our clients and our environment. Changing parameters to optimize forms in order to reduce use of materials is means of preserving and protection of our environment while at the same time giving our clients the best value for their money.


There are many software tools that could be used to support parametric design. WME will currently focus on Dynamo + Revit and Grasshopper + Rhino platforms, while looking into possibilities of design automatization by linking the above packages with structural analysis and design software.

Pitfalls of Parametric Design

It is important to consider parametric design as another tool at our disposal. The parametric design and its techniques should be adopted as means to achieve our end goals; that is, happier clients and sustainable future. It (parametric design) should not be developed for the sake of it.

Complex geometries achieved by use of parametric design techniques by the architects often lead to inefficient structural forms that defy logic and that cannot be analyzed by approximate methods using engineering judgment and intuition. This is a challenge but also one more reason for us, structural engineers, to adopt parametric design technics as means by which we could effectively and confidently influence architectural form finding towards more efficient forms.