by Dušan Cvetković
Dušan Cvetković
Published February 9, 2021

Parametric architecture with the current computer era has pushed Architecture into a whole new magnificent field.

It almost seems like nothing is impossible to build.

What is Parametric architecture?

How to Define Parametric Architecture

Parametric Design can be defined as forms that are generated through changing a list of values that are plugged into multiple equations that create geometries.

Mathematical formula of Parametric Curve

Before computers, the architectural process had some rather limiting constraints that would keep geometries from getting too complicated.

That doesn’t mean that beautiful awe stricken architecture wasn’t possible. However, because the drawings process, even in the original CAD programs, was a completely additive process.

This means that as projects were iterated through drawings, it was much harder to change multiple parts of a project at once. Especially when it came to the form of a space. 

Parametric Design ilustration

Created by: Mary Wagner 

However, as 3D modeling and design advanced, projects began to be represented in terms of parameters, aka numerical values that could be changed, instead of written rules and constraints.

These values represent a lot however, I am certain that every 3D modeler or architect can tell you that even just can one value by a hundredth (.01) can create an entirely new form.

By defining architectural rules with numbers, this allows for the modeling of completely new and complex geometries.

I mean, these geometries you can’t even wrap your heads around. 

Grasshopper Window

Architecture form is no longer about squares, boxes, or combinations of known forms or shapes. We have transcended the constraints of construction, imagination, and sometimes comfortability.

Not only that, but because constraints are represented in numbers, iterations can be created in intense numbers that allow architects to choose from a list of computer generated forms. 

Parametric Table Design

Created by: Parametria

Of course, to pick from a computer catalogue of generated forms takes more than just choosing the form that looks good, but never before has an architect been able to visualize so many different solutions to a design problem.

But the computer programs and engines that computer aided design uses have not come out of thin air. Many of these programs are based on practices of past architects and innovators!

Parametric Architecture: A Not-So-New Concept

Some of the forms (but only some) that can be created using parameters are based on passed forms and techniques used by architects stretching all the way back to 1880’s.

Image of an old Parametric Design

Photo Credit: Dataphys / CC BY-SA 3.0

If we turn the clock all the way to Antoní Gaudí, the architect of La Sagrada Familia, who created these form found (a topic to be touched on later) models with hanging chains.

Sagrada Familia by Antoni Gaudi

Photo Credit: C Messier / CC BY-SA 4.0 

When these chains were hung, they created forms that when flipped would create the structure of a building.

Fast forward to the 1960’s, Luigi Moretti developed a set of mathematical equations with parameters used to analyze spatial relationships. He used these equations to develop the urban plan of Rome in 1962.

He himself coined the term Parametric Architecture.

Image of parametric curves

Of course you can’t discuss Parametric architecture with discussing Frei Otto who used bubbles to create parameters for minimal surface tensile structures. One of the first examples of optimization in architecture.

Tensile parametric architecture structure by Frei Otto

However, the first computer program that took advantage of mathematics and parametric equations was Sketchpad, a program developed by the famous Ivan Sutherland in 1963.

Sketchpad by Ivan Sutherland

This was the first program to use a Graphic User Interface and even defined lines that were drawn in the program as “master objects” and “Instance objects” which is something that every Autocad user knows about.

Pretty freaking innovative for a 1963 program.

Of course this program was a precursor to CAD (Computer Aid Design) programs like Autodesk (1982). Although CAD is still very widely used, there were still a rather strict kind of constraints that made many geometries impossible to create and understand three dimensionally and two dimensionally. 

First CAD computers

It wasn’t until 1989 when NURBS (Non-Uniform Rational B-Splines) was developed leading to programs like Rhinoceros. The first 3D modeling programs led to geometric operative words like “fold” or “Wrap” commonly used with the first contemporary parametric designs.

NURBS (Non-Uniform Rational B-Splines)

These NURBS modeling systems are the most commonly used programs in the world of Parametric Design which is exactly what led to the latest style of architecture announced by Patrick Schumacher as the “Parametric Architecture” era.

Creating The Impossible

In order to manifest three dimensional objects, we need to model them, draw them, and construct them.

How is that done exactly?

Parametric Architecture and Approach in Design

There are a lot of ways to create these odd forms that do not even look like shapes.

The easiest and most common ways to do this is through surface deformations and tessellations. Here meshes and surfaces in NURBS modeling software are changed based on certain parametric criteria.

Parametric structure in architecture

Image Credit: Kseniia Usenko

They could be Bent, Folded, Twisted, or Morphed.

Then these surfaces can be used to map grids, or other three dimensional objects creating repetitive shapes along a surface or a “Tessellation”.

Tessellated parametric architectural design

Photo Credit: Parametric House

Of course there are more complex and mathematical ways to create forms in these 3D modeling tools.

Parametric wooden structure

Studying the Design of Parametric Architecture: Spatial-Geometric, Structural, and Environmental Analysis

In order for these new complex forms to not just be sculptural, but be functional as well is be relating the forms to real world analysis.

This is where parametric modeling really comes to life, because this is where design constraints and rules can be interpreted as numbers and inform the values (parameters) that change the form of a model.

Parameters in parametric architecture

Using these tools as Parameters, you can model the magnificent forms similar to that of Antoni Gaudi and Frei Otto.

These Parameters are used to define Form Finding, and Moment and Shear Analysis. These can be used not only to minimize the structure used, but can also be used to define the shape and size of structural elements in a building.

Moment Analysis

Of course, building form can be informed through the environment of a site. This environment can be defined as parameters and equations in these NURBS modeling tools.

Creating the Best of the Best: Optimization and Customization

One of the most exciting parts of Parametric Design is form optimization and customization. The reason that people love the new iterative process.

That has always been the goal of parametric design, but have really gotten widely used recently as technology has improved.

Frei Otto built a whole career on minimal surfaces, but there are many other ways to optimize building form.

With the development of Artificial Intelligence (AI) computers have been able to respond to the values input by humans into parameters and develop hundreds of different iterations.

Parametric Architecture and Artificial Intelligence

Image Credit: Autodesk News

These iterations are then selected and processed again multiple times to acquire an “optimal” result in respect to many different parameters like solar gain, material usage, and even population circulation.

Form Finding in architecture

Image Credit: CAD-Magazine

Waffle Structure - parametric architecture

Photo Credit: Rubendene / CC BY-SA 3.0

This is a great advancement when discussing generative design, customization, and optimization as these design principles can even be used to create the best object per person.

An object that is created in regards to the personal characteristics of an individual.

Constructing Complex Parametric Architecture

Because these optimized geometries are so complex, the construction of these forms has to follow the same technological advancements.

The advancements have come in the form of 3D printing both on a small scale and a large scale. 

Ship 3D printing with robots
Parametric Architecture Fabrication by Robot

Photo Credit: daily3Dprints

Not only that, but computers are now used for bending large pieces of metal and for creating forms for concrete.

The most interesting part of parametric construction is the idea of the module: a repeated element that is moved and translated to create a building. This is probably the most common construction of parametric forms.

Serpentine Pavilion by BIG

Want to see some of these constructed, optimized forms?

Absolutely Insane Parametric Architecture Buildings

Heydar Aliyev Center by Zaha Hadid Architects

Heydar Aliyev Center by Zaha Hadid Architects

Photo Credit: Helene Binet

Zaha Hadid Architects is one of the many famous architecture firms for their use of parametric design and development.

Here, values are set to define the folds and curves of a surface that creates voids that are filled in with glass.

These folds and bends are great for creating beautiful new organizations in walls and ceilings, new thresholds, and even new interactions between users and building elements.

Broad Museum by Diller Scofidio

Broad Museum by Diller Scofidio

Photo Credit: Kerstin Bednarek / CC BY-SA 4.0 

This is a great example of the use of the tessellation and modular construction.

In this art museum, a concrete form was tessellation along the surfaces of a building envelope.

This tessellation was optimized to capture indirect light and reflect direct light; a very important aspect for Museums as direct light is damaging for museum objects. 

El Oceanografico by Félix Candela

El Oceanografico by Félix Candela

Photo Credit: Felipe Gabaldon

Stress follows a very strict parabolic path.

That shows in this form found structure were parameters are different forces and lengths are placed on these parabolas to change the height and width of these “arches”.

Selfridges by Jan Kaplický and Amanda Levety

Selfridges by Jan Kaplický and Amanda Levety

Photo Credit: Bs0u10e0

This shopping mall and buildings like this are an interesting outcome of parametric architecture known as BLOb architecture.

You are probably asking why BLOb is capitalized weirdly and that is because it is an acronym: Binary Large Object.

Of course, these objects are exactly what they're called. Parameters for these forms involved obviously the size of these forms, tensions between volumes of these forms, and the curvature of these forms.

There are of course so many different projects that involve Parametric architecture. In fact, almost all architecture now has some parametric element to them.

You can make these buildings too, the programs used to generate them are available to everyone, especially students.

The Best Software for Parametric Architecture

We couldn’t write this article without talking about the program that we use for all of our tutorials.

Rhinoceros by McNeel alone is a powerful NURBS modeling program that can be used to modeling anything with very few constraints.

Here, anything from a single nail to an entire city can be modeled and optimized.

Rhino and parametric architecture

Rhinoceros comes with one of the best parametric tools in our industry called Grasshopper. This tools allows us to create any kind of parametric shape imaginable.

In simple terms, Grasshopper allows us to write an algorithm for our building using graphical interface that contains thousands of individual components.

Grasshopper definition

Grasshopper has so many different plugins that are used in architecture industry today depending on the use case ranging from physics generators like Kangaroo to weather data analysis tools like Honeybee and Ladybug.

Lady bug analysis

Let's not forget evolutionary solvers that are great for generating hundreds of iterations such as Galapagos, a solver for optimization of geometry based on a given parameter, as well as Wallacei, evolutionary multi-objective optimization and analytic engine and many others.

How Can I Quickly Learn Rhino and Grasshopper

If you like the idea behind parametric architecture and if you're interested in learning Grasshopper, it's your lucky day, because we have plenty of resources and tutorials that will help you to bring your skills to the next level.

For starters, make sure to check out our free training on Rhino and Grasshopper. Here, you will get an idea of what Rhino and Grasshopper are really capable of and how you can leverage these tools for your own projects. 

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Parametric Architecture with How to Rhino

About the Author

Dušan Cvetković is a professional architect from Serbia with international experience in the industry. Collaborated with numerous clients all around the world in the field of architecture design, 3D modeling and software education. He's been teaching Rhinoceros3D to thousands of architects through How to Rhino community and various social media channels.