The Nature of Gridshell Form Finding

Grids, shells, and how they, in conjunction with the study of the natural world, can help us develop increasingly complex structural geometry.

Foreword

This post is the third installment of sort of trilogy, after Shapes, Fractals, Time & the Dimensions they Belong to, and Developing Space-Filling Fractals. While it’s not important to have read either of those posts to follow this one, I do think it adds a certain level of depth and continuity.

Regarding my previous entries, it can be difficult to see how any of this has to do with architecture. In fact I know a few people who think studying fractals is pointless.

Admittedly I often struggle to explain to people what fractals are, let alone how they can influence the way buildings look. However, I believe that this post really sheds light on how these kinds of studies may directly influence and enhance our understanding (and perhaps even the future) of our built environment.

On a separate note, I heard that a member of the architectural academia said “forget biomimicry, it doesn’t work.”

Firstly, I’m pretty sure Frei Otto would be rolling over in his grave.

Secondly, if someone thinks that biomimicry is useless, it’s because they don’t really understand what biomimicry is. And I think the same can be said regarding the study of fractals. They are closely related fields of study, and I wholeheartedly believe they are fertile grounds for architectural marvels to come.

7.0 Introduction to Shells

As far as classification goes, shells generally fall under the category of two-dimensional shapes. They are defined by a curved surface, where the material is thin in the direction perpendicular to the surface. However, assigning a dimension to certain shells can be tricky, since it kinda depends on how zoomed in you are.

A strainer is a good example of this – a two-dimensional gridshell. But if you zoom in, it is comprised of a series of woven, one-dimensional wires. And if you zoom in even further, you see that each wire is of course comprised of a certain volume of metal.

This is a property shared with many fractals, where their dimension can appear different depending on the level of magnification. And while there’s an infinite variety of possible shells, they are (for the most part) categorizable.

7.1 – Single Curved Surfaces

Analytic geometry is created in relation to Cartesian planes, using mathematical equations and a coordinate systems. Synthetic geometry is essentially free-form geometry (that isn’t defined by coordinates or equations), with the use of a variety of curves called splines. The following shapes were created via Synthetic geometry, where we’re calling our splines ‘u’ and ‘v.’

A-Barrel-Vault
Uniclastic: Barrel Vault (Cylindrical paraboloid)

These curves highlight each dimension of the two-dimensional surface. In this case only one of the two ‘curves’ is actually curved, making this shape developable. This means that if, for example, it was made of paper, you could flatten it completely.

B-Conoid

Uniclastic: Conoid (Conical paraboloid)

In this case, one of them grows in length, but the other still remains straight. Since one of the dimensions remains straight, it’s still a single curved surface – capable of being flattened without changing the area. Singly curved surfaced may also be referred to as uniclastic or monoclastic.

7.2 – Double Curved Surfaces

These can be classified as synclastic or anticlastic, and are non-developable surfaces. If made of paper, you could not flatten them without tearing, folding or crumpling them.

C-Dome.gif
Synclastic: Dome (Elliptic paraboloid)

In this case, both curves happen to be identical, but what’s important is that both dimensions are curving in the same direction. In this orientation, the dome is also under compression everywhere.

The surface of the earth is double curved, synclastic – non-developable. “The surface of a sphere cannot be represented on a plane without distortion,” a topic explored by Michael Stevens: https://www.youtube.com/watch?v=2lR7s1Y6Zig

D-Saddle.gif
Anticlastic: Saddle (Hyperbolic paraboloid)
This one was formed by non-uniformly sweeping a convex parabola along a concave parabola. It’s internal structure will behave differently, depending on the curvature of the shell relative to the shape. Roof shells have compressive stresses along the convex curvature, and tensile stress along the concave curvature.
Pringle
Kellogg’s potato and wheat-based stackable snack
Here is an example of a beautiful marriage of tensile and compressive potato and wheat-based anticlastic forces. Although I hear that Pringle cans are diabolically heinous to recycle, so they are the enemy.
11 Tensile and Compressive behaviour of shells.jpg
Structural Behaviour of Basic Shells [Source: IL 10 – Institute for Lightweight Structures and Conceptual Design]

7.3 – Translation vs Revolution

In terms of synthetic geometry, there’s more than one approach to generating anticlastic curvature:
E-Hyperbolic-Paraboloid-Saddle.gif
Hyperbolic Paraboloid: Straight line sweep variation

This shape was achieved by sweeping a straight line over a straight path at one end, and another straight path at the other. This will work as long as both rails are not parallel. Although I find this shape perplexing; it’s double curvature that you can create with straight lines, yet non-developable, and I can’t explain it..

F-Hyperbolic-Paraboloid-Tower.gif
Ruled Surface & Surface of Revolution (Circular Hyperboloid)
The ruled surface was created by sliding a plane curve (a straight line) along another plane curve (a circle), while keeping the angle between them constant. The surfaces of revolution was simply made by revolving a plane curve around an axis. (Surface of translation also exist, and are similar to ruled surfaces, only the orientation of the curves is kept constant instead of the angle.)
 
Cylinder_-_hyperboloid_-_cone.gif
Hyperboloid Generation [Source:Wikipedia]

The hyperboloid has been a popular design choice for (especially nuclear cooling) towers. It has excellent tensile and compressive properties, and can be built with straight members. This makes it relatively cheap and easy to fabricate relative to it’s size and performance.

These towers are pretty cool acoustically as well: https://youtu.be/GXpItQpOISU?t=40s

 

8.0 Geodesic Curves

These are singly curved curves, although that does sound confusing. A simple way to understand what geodesic curves are, is to give them a width. As previously explored, we know that curves can inhabit, and fill, two-dimensional space. However, you can’t really observe the twists and turns of a shape that has no thickness.

Geodesic Curves - Ribon.jpg
Conic Plank Lines (Source: The Geometry of Bending)

A ribbon is essentially a straight line with thickness, and when used to follow the curvature of a surface (as seen above), the result is a plank line. The term ‘plank line’ can be defined as a line with an given width (like a plank of wood) that passes over a surface and does not curve in the tangential plane, and whose width is always tangential to the surface.

Since one-dimensional curves do have an orientation in digital modeling, geodesic curves can be described as the one-dimensional counterpart to plank lines, and can benefit from the same definition.

The University of Southern California published a paper exploring the topic further: http://papers.cumincad.org/data/works/att/f197.content.pdf

8.1 – Basic Grid Setup

For simplicity, here’s a basic grid set up on a flat plane:

G-Geocurves.gif
Basic geodesic curves on a plane

We start by defining two points anywhere along the edge of the surface. Then we find the geodesic curve that joins the pair. Of course it’s trivial in this case, since we’re dealing with a flat surface, but bear with me.

H-Geocurves.gif
Initial set of curves

We can keep adding pairs of points along the edge. In this case they’re kept evenly spaced and uncrossing for the sake of a cleaner grid.

I-Geocurves.gif
Addition of secondary set of curves

After that, it’s simply a matter of playing with density, as well as adding an additional set of antagonistic curves. For practicality, each set share the same set of base points.

J-Geocurves.gif
Grid with independent sets

He’s an example of a grid where each set has their own set of anchors. While this does show the flexibility of a grid, I think it’s far more advantageous for them to share the same base points.

8.2 – Basic Gridshells

The same principle is then applied to a series of surfaces with varied types of curvature.

K-Barrel
Uniclastic: Barrel Vault Geodesic Gridshell

First comes the shell (a barrel vault in this case), then comes the grid. The symmetrical nature of this surface translates to a pretty regular (and also symmetrical) gridshell. The use of geodesic curves means that these gridshells can be fabricated using completely straight material, that only necessitate single curvature.

L-Conoid
Uniclastic: Conoid Geodesic Gridshell

The same grid used on a conical surface starts to reveal gradual shifts in the geometry’s spacing. The curves always search for the path of least resistance in terms of bending.

M-Dome
Synclastic: Dome Geodesic Gridshell

This case illustrates the nature of geodesic curves quite well. The dome was free-formed with a relatively high degree of curvature. A small change in the location of each anchor point translates to a large change in curvature between them. Each curve looks for the shortest path between each pair (without leaving the surface), but only has access to single curvature.

N-Saddle
Anticlastic: Saddle Geodesic Gridshell

Structurally speaking, things get much more interesting with anticlastic curvature. As previously stated, each member will behave differently based on their relative curvature and orientation in relation to the surface. Depending on their location on a gridshell, plank lines can act partly in compression and partly in tension.

On another note:

While geodesic curves make it far more practical to fabricate shells, they are not a strict requirement. Using non-geodesic curves just means more time, money, and effort must go into the fabrication of each component. Furthermore, there’s no reason why you can’t use alternate grid patterns. In fact, you could use any pattern under the sun – any motif your heart desires (even tessellated puppies.)

6 - Alternate Grid
Alternate Gridshell Patterns [Source: IL 10 – Institute for Lightweight Structures and Conceptual Design]

Here are just a few of the endless possible pattern. They all have their advantages and disadvantages in terms of fabrication, as well as structural potential.

Biosphere Environment Museum - Canada
Biosphere Environment Museum – Canada

Gridshells with large amounts of triangulation, such as Buckminster Fuller’s geodesic spheres, typically perform incredibly well structurally. These structure are also highly efficient to manufacture, as their geometry is extremely repetitive.  

Centre Pompidou-Metz - France
Centre Pompidou-Metz – France

Gridshells with highly irregular geometry are far more challenging to fabricate. In this case, each and every piece had to be custom made to shape; I imagine it must have costed a lot of money, and been a logistical nightmare. Although it is an exceptionally stunning piece of architecture (and a magnificent feat of engineering.)

8.3 – Gridshell Construction

In our case, building these shells is simply a matter of converting the geodesic curves into planks lines.

O - Saddle 2
Hyperbolic Paraboloid: Straight Line Sweep Variation With Rotating Plank Line Grid

The whole point of using them in the first place is so that we can make them out of straight material that don’t necessitate double curvature. This example is rotating so the shape is easier to understand. It’s grid is also rotating to demonstrate the ease at which you can play with the geometry.

Hyperbolic-Paraboloid-Plank-Lines
Hyperbolic Paraboloid: Flattened Plank Lines With Junctions

This is what you get by taking those plank lines and laying them flat. In this case both sets are the same because the shell happens to the identicall when flipped. Being able to use straight material means far less labour and waste, which translates to faster, and or cheaper, fabrication.

An especially crucial aspect of gridshells is the bracing. Without support in the form of tension ties, cable ties, ring beams, anchors etc., many of these shells can lay flat. This in and of itself is pretty interesting and does lends itself to unique construction challenges and opportunities. This isn’t always the case though, since sometimes it’s the geometry of the joints holding the shape together (like the geodesic spheres.) Sometimes the member are pre-bent (like Pompidou-Metz.) Although pre-bending the timber kinda strikes me as cheating thought.. As if it’s not a genuine, bona fide gridshell.

Toledo-gridshell-20-Construction-process
Toledo Gridshell 2.0. Construction Process [source: Timber gridshells – Numerical simulation, design and construction of a full scale structure]

This is one of the original build method, where the gridshell is assembled flat, lifted into shape, then locked into place.

9.0 Form Finding

Having studied the basics makes exploring increasingly elaborate geometry more intuitive. In principal, most of the shells we’ve looked are known to perform well structurally, but there are strategies we can use to focus specifically on performance optimization.

9.0 – Minimal Surfaces

These are surfaces that are locally area-minimizing – surfaces that have the smallest possible area for a defined boundary. They necessarily have zero mean curvature, i.e. the sum of the principal curvatures at each point is zero. Soap bubbles are a great example of this phenomenon.

hyperbolic paraboloid soap bubble
Hyperbolic Paraboloid Soap Bubble [Source: Serfio Musmeci’s “Froms With No Name” and “Anti-Polyhedrons”]
Soap film inherently forms shapes with the least amount of area needed to occupy space – that minimize the amount of material needed to create an enclosure. Surface tension has physical properties that naturally relax the surface’s curvature.

00---Minimal-Surface-Model
Kangaroo2 Physics: Surface Tension Simulation

We can simulate surface tension by using a network of curves derived from a given shape. Applying varies material properties to the mesh results in a shape that can behaves like stretchy fabric or soap. Reducing the rest length of each of these curves (while keeping the edges anchored) makes them pull on all of their neighbours, resulting in a locally minimal surface.

Here are a few more examples of minimal surfaces you can generate using different frames (although I’d like stress that the possibilities are extremely infinite.) The first and last iterations may or may not count, depending on which of the many definitions of minimal surfaces you use, since they deal with pressure. You can read about it in much greater detail here: https://tinyurl.com/ya4jfqb2

Eden_Project_geodesic_domes_panorama.jpg
The Eden Project – United Kingdom

Here we have one of the most popular examples of minimal surface geometry in architecture. The shapes of these domes were derived from a series of studies using clustered soap bubbles. The result is a series of enormous shells built with an impressively small amount of material.

Triply periodic minimal surfaces are also a pretty cool thing (surfaces that have a crystalline structure – that tessellate in three dimensions):

Another powerful method of form finding has been to let gravity dictate the shapes of structures. In physics and geometry, catenary (derived from the Latin word for chain) curves are found by letting a chain, rope or cable, that has been anchored at both end, hang under its own weight. They look similar to parabolic curves, but perform differently.

00---Haning-Model
Kangaroo2 Physics: Catenary Model Simulation

A net shown here in magenta has been anchored by the corners, then draped under simulated gravity. This creates a network of hanging curves that, when converted into a surface, and mirrored, ultimately forms a catenary shell. This geometry can be used to generate a gridshell that performs exceptionally well under compression, as long as the edges are reinforced and the corners are braced.

While I would be remiss to not mention Antoni Gaudí on the subject of catenary structure, his work doesn’t particularly fall under the category of gridshells. Instead I will proceed to gawk over some of the stunning work by Frei Otto.

Of course his work explored a great deal more than just catenary structures, but he is revered for his beautiful work on gridshells. He, along with the Institute for Lightweight Structures, have truly been pioneers on the front of theoretical structural engineering.

9.3 – Biomimicry in Architecture

There are a few different terms that refer to this practice, including biomimetics, bionomics or bionics. In principle they are all more or less the same thing; the practical application of discoveries derived from the study of the natural world (i.e. anything that was not caused or made my humans.) In a way, this is the fundamental essence of the scientific method: to learn by observation.
Biomimicry-Bird-Plane
Example of Biomimicry

Frei Otto is a fine example of ecological literacy at its finest. A profound curiosity of the natural world greatly informed his understanding of structural technology. This was all nourished by countless inquisitive and playful investigations into the realm of physics and biology. He even wrote a series of books on the way that the morphology of bird skulls and spiderwebs could be applied to architecture called Biology and Building. His ‘IL‘ series also highlights a deep admiration of the natural world.

Of course he’s the not the only architect renown their fascination of the universe and its secrets; Buckminster Fuller and Antoni Gaudí were also strong proponents of biomimicry, although they probably didn’t use the term (nor is the term important.)

Gaudí’s studies of nature translated into his use of ruled geometrical forms such as hyperbolic paraboloids, hyperboloids, helicoids etc. He suggested that there is no better structure than the trunk of a tree, or a human skeleton. Forms in biology tend to be both exceedingly practical and exceptionally beautiful, and Gaudí spent much of his life discovering how to adapt the language of nature to the structural forms of architecture.

Fractals were also an undisputed recurring theme in his work. This is especially apparent in his most renown piece of work, the Sagrada Familia. The varying complexity of geometry, as well as the particular richness of detail, at different scales is a property uniquely shared with fractal nature.

Antoni Gaudí and his legacy are unquestionably one of a kind, but I don’t think this is a coincidence. I believe the reality is that it is exceptionally difficult to peruse biomimicry, and especially fractal geometry, in a meaningful way in relation to architecture. For this reason there is an abundance of superficial appropriation of organic, and mathematical, structures without a fundamental understanding of their function. At its very worst, an architect’s approach comes down to: ‘I’ll say I got the structure from an animal. Everyone will buy one because of the romance of it.”

That being said, modern day engineers and architects continue to push this envelope, granted with varying levels of success. Although I believe that there is a certain level of inevitability when it comes to how architecture is influenced by natural forms. It has been said that, the more efficient structures and systems become, the more they resemble ones found in nature.

Euclid, the father of geometry, believed that nature itself was the physical manifestation of mathematical law. While this may seems like quite a striking statement, what is significant about it is the relationship between mathematics and the natural world. I like to think that this statement speaks less about the nature of the world and more about the nature of mathematics – that math is our way of expressing how the universe operates, or at least our attempt to do so. After all, Carl Sagan famously suggested that, in the event of extra terrestrial contact, we might use various universal principles and facts of mathematics and science to communicate.

4th May 2015 Tutorials

Hello everyone, here are couple pictures from our last tutorial showing some of the best future cities that our students are currently working on in response to the Brief03:FutureCities.

From an open-source green city living in symbiosis with the Amazonian forest to a terra-forming city on Mars made from 3d printing robots carrying giant Fresnel lenses all the way to a rent-for-advertisement growing infrastructure covered with LED screens – we are look forward to discovering with you the cities of tomorrow from our wonderful and creative DS10 students next Thursday at the Interim Crit.

Joe Leach's green city, built in harmony with the Amazonian forest, based on an open-source catalogue of beautiful curved wooden trusses
Joe Leach’s green city, built in harmony with the Amazonian forest, based on an open-source catalogue of beautiful curved wooden trusses
Alex Berciu's Cellular Automata city providing an 3d Printed infrastructure for the people
Alex Berciu’s Cellular Automata city providing an 3d Printed infrastructure for the people
Diana Raican's Fractal City on the rising sea provides protection from Tsunami and a gradation between private and communal spaces.
Diana Raican’s Fractal City on the rising sea provides protection from Tsunami and a gradation between private and communal spaces.
Garius Iu's inflatable curved origami city recycles the ocean's plastic patches while providing a playful shelter on the rising seas.
Garius Iu’s inflatable curved origami city recycles the ocean’s plastic patches while providing a playful shelter on the rising seas.
Diana Raican's Fractal City on the rising sea provides protection from Tsunami and a gradation between private and communal spaces.
Diana Raican’s Fractal City on the rising sea provides protection from Tsunami and a gradation between private and communal spaces.
Lianne clarke's growing pixel city offers reduced rent for advertisement campaigns and provides LED clad cubes connected together with a plug-in cross system.
Lianne clarke’s growing pixel city offers reduced rent for advertisement campaigns and provides LED clad cubes connected together with a plug-in cross system.
Diana Raican's Fractal City on the rising sea provides protection from Tsunami and a gradation between private and communal spaces.
Diana Raican’s Fractal City on the rising sea provides protection from Tsunami and a gradation between private and communal spaces.
Lianne clarke's growing pixel city offers reduced rent for advertisement campaigns and provides LED clad cubes connected together with a plug-in cross system.
Lianne clarke’s growing pixel city offers reduced rent for advertisement campaigns and provides LED clad cubes connected together with a plug-in cross system.
Vlad Ignatescu is terra-forming mars with 3d printing robots that solidify sand dunes using giant fresnel lenses.
Vlad Ignatescu is terra-forming mars with 3d printing robots that solidify sand dunes using giant fresnel lenses.

 

 

WikiVault

A computer render of the WikiVault system at night
A computer render of the WikiVault system at night
WikiVault is my proposal in response to Brief 02_Template (the details of which can be found under brief). It utilises a reciprocal frame structure created from flat sheet material that can be assembled rapidly on site with only the aid of a jig for lifting. The system is a very efficient use of material particularly owing to the fact that no formwork is necessary in the assembly of the vaulting structure. In addition, the use of a flat sheet material means that it can be easily and accurately pre-fabricated offsite using either CNC machines or laser cutters depending on the scale required. This has the added benefit of easy transportation to the site.
System development summary diagram
System development summary diagram
The structural logic for the system evolved from the mandala reciprocal roof structure and Joseph Abeille’s vault, a solid ashlar floor construction from the seventeenth century.
Software Variations
Software Variations
The value of an open source construction set is that it is easy to use and adapt by anyone. With this in mind I developed a software plug-in for Grasshopper and Rhino that simplifies the system into easily changeable parameters. A series of sliders and any input surface determine the final form of the vault system. I hope to make this plug in available for Grasshopper users as an open-source software once further testing and bug fixes have been resolved.
Physical Model
Physical Model
As part of the continuing development of the WikiVault system I have started to develop a component based library including floors, stairs and modular wall elements to increase the versatility of the system. One obvious flaw is the shelter from the weather of the interior space. In order to address this I have also begun to develop two composite systems utilising a tensile membrane in the first instance and heavy earth construction in the second.
Full details of the initial research and subsequent development of my proposal can be found in the two research documents at the bottom of the page however the gallery below shows some of the key features and images of the system.
The video below shows a timelapse of the physical model assembly without the aid of formwork showing how the vault self-supports as it grows in size.

Brief 01:Test_Research and Development Document

Brief 02:Template_Research and Development Document

Wikihouse at TED London

Designer Alastair Parvin is the Co-creator of Wikihouse, an open-source construction set. He argues in this short presentation, that there is an economics to architecture that we don’t think about, and realizing this can be a game changer.

It is interesting to look at the simple drivers for the Wikihouse project and see some of the constraints set for the project, such as ease of fabrication, material availability and transportability. For more information see the Wikihouse website: http://www.wikihouse.cc/

The Tragedy of Planned Obsolescence

Technology today is designed to fail. Products are made so that you will buy a new one after a pre-determined time. This is called planned obsolescence and is a widely accepted commercial concept within industrial companies.

The Phoebus Kartel  was a cartel of, among others, Osram, Philips and General Electricfrom December 23, 1924 until 1939 that controlled the manufacture and sale of light bulbs. It decided that it would limit the lifetime of a lightbulb to 1000 hours. Before this arbitrary and profit-driven decision, light bulbs could last for a very long time, a solid proof for that is the Livermore’s Centennial Lightbulb which shines since 1890. The 1000 hours rule was the beginning of an imposed large-scale planned obsolescence.

Above: The Livermore’s Centennial Lightbulb’s webcam

After the great depression, Bernard London thought that imposing planned obsolescence by law would bring prosperity to Americans.

The american designer Brook Stevens gave many conferences on the advantage of planned obsolescence. His products would always look newer, better than the existing one. By his definition, planned obsolescence was “Instilling in the buyer the desire to own something a little newer, a little better, a little sooner than is necessary.”

Above: The toastalator by Brook Stevens

Without planned obsolescence, shopping malls would probably not exits and economic growth would not be as crucial as it it today to the economy.  In essence, economic growth does not attempt to make human life better, it just tries to grow for the sake of it. This growth is based on debt and on consuming products that are not necessary. As the economist and system theorist Kenneth Boulding once said: “Someone who believes that an economy that constantly grows on a planet that is finite is either mad or an economist, the problem is that we are all economists now.”

The Waste Makers, published in 1960 by Vance Packard is the first book on the topic.

Apple, largest public company in the U.S., gave a clear notice to its reseller when the IPOD battery would fail: “buy a new ipod“.  Apple was sued for that by consumers, the case was called Wesley vs. Apple. Apple lost the case and was forced to extend the warranty on the battery. Apple has no environmental policy for its products and tries to sell as many products as possible, not products that will last.

Image courtesy of Stay Free Magazine.

Epson adds microchips in some of their printers that counts the amount  of prints and breaks the printer after reaching a pre-determined printer. In fact, some freewares help you to reset the count so that you can use your printers more.

Electronic products that could have lasted much longer end up in illegal dump site in countries such as Ghana and Nigeria (have a look at the Agbogbloshie dump site on this BBC documentary).

Above: kid looking for copper on the Agbogbloshie illegal E-Waste dump site, Ghana

The idea of creating “Open-Source” buildings from simple materials that can be made and improved by anyone and based on home-grown or widely accessible products is DS10’s answer to the tragedy of planned obsolescence. Similarly to open source software that can always be updated and maintained by the end user, the makers will not be at the sole mercy of a proprietary vendor. We will also look into temples, timeless monuments for spirituality and best counter example for modernist buildings, a theory which emerged around the same time as the Phoebus Kartel.

Sources:

-This post is based on the documentary “The Light Bulb Conspiracy” by Cosima Dannoritzen.

-http://www.apfelkraut.org/2011/03/the-untold-story-of-planned-obsolescence/

-http://quiet-environmentalist.com/is-the-earth-doomed-due-to-planned-obsolescence/

-http://www.amazon.com/Made-Break-Technology-Obsolescence-America/dp/0674022033

-http://www.amazon.co.uk/Planned-Obsolescence-Publishing-Technology-Academy/dp/0814727883

A Year of Grasshopper Experiments with DS10

It has almost been already a year that Toby and I started tutoring DS10 at Westminster. One of our main ambitions was to link physical and digital experiments so that one feeds the other.

Physical reality is much more than surfaces on a screen therefore students created complex parametric models working as systems linked to many forces (gravity, environment, structure…etc…) and not just finished objects. These very precise digital models allow students to implement what they learn from their physical models, to simulate even more design options and further understand the rules behind them.

To do so, they used Grasshopper and its numerous plugins provided by generous developers. Grasshopper is a graphical algorithm editor integrated with Rhinoceros 3D modelling tool and a 18,000 strong community exchanging ideas and helping each other on the Grasshopper3d.com forum.

Below are most of the printscreens that I used to help the students with their journey into parametric modelling which is based on help that I also received previously. I hope that this will help others to design amazing things! If you have any questions on one of the images, please do not hesitate to ask.

Below is my favourite image: packing balloons on a surface using Kangaroo (with Emma Whitehead)