Architectural Geometry class

I'm taking an independent study in geometry next semester, and I'm looking for your advice on what are the most relevant topics to study in regards to applications of geometry/math to architecture, or digital fabrication in general. The main textbook will be Helmut Pottmann's book "Architectural Geometry", which covers many topics of interest, but I'm expecting there are many other topics worth exploring. I'll be using grasshopper/rhino to visualize some of the studies, but where this software allows us to use things like nurbs curves, hopefully the class will aimed at learning what is going on beneath the hood of rhino/GH. (ie. understanding the math behind nurbs, etc.)

The teacher is a math teacher, and he just wants me to come in once a week and teach him about architectural geometry, so the curriculum is wide open. I figured you guys would be the best source for advice on what to study here. Thanks!

Architectural Geometry, Helmut Pottmann

Replies to This Discussion

Permalink Reply by David Rutten on December 11, 2009 at 10:33am

Don't bother with Nurbs curves, it's far too difficult a starting point. The first thing to do is get comfortable with the basics of geometry: Points, Vectors, Planes, Lines, Circles etc. Important skills are that you will be able to fully understand parameter notation; how curves are defined in 2D and 3D space based on scalar parameters. For example, a line is defined as:

A + t * (B-A)

Do not venture beyond lines until you understand what the above means.

Constructs like points, vectors and planes already allow you to explore pretty complicated topics such as angles, relationships, projections and transformations.

I'd think it's far more interesting to learn about curves in general and how they can be approximated, measured and simplified than to learn about Nurbs mathematics specifically.

I've read Pottmann's book and it really only skims the surface (no pun intended). It helps you to build a lexicon of mathematical terminology but it won't be of much use if you intend to generate geometry through logic or code. It only deals with very simple cases and tells you nothing about the myriad of problems you'll encounter when you are actually dealing with real-world geometry.

--
David Rutten
david@mcneel.com
Poprad, Slovakia

Permalink Reply by Chris Wilkins on December 11, 2009 at 2:11pm

Thanks, I figured you might be the first to comment on that.

Do you have any alternate book selections? The Pottmann book does not have to be used. I definitely want to generate geometry through logic and code, so anything in that realm. Do you know any good resources on curves in general? As far as pre-reqs, I've been thru multivar calc, diff eqs, discrete math, stat and linear algebra (minoring in math and this is the final class), so I got a bit of vector stuff in linear. Saw a bit of parametric notation in calc.

-Chris

Permalink Reply by David Rutten on December 11, 2009 at 2:26pm

I've read a few books about this, but I can't recommend any of them. For me, the internet is a far more useful resource. It often provides good articles on specific algorithms, usable example code and often inspiration as well.

It seems your math skills are definitely up to snuff, which is rare enough in this day and age of MTV, Tamagotchis and Open Tip Bras. Be aware that maths on paper is very different from maths on screen. You'll have to deal with accuracies, tolerances, digit-noise, fuzz and fudge factors, insanely long computation times and limited numeric ranges.

I've always found it hard to learn something new without having a pressing need for it. Do you know what sort of project you will be working on?

--
David Rutten
david@mcneel.com
Poprad, Slovakia

Permalink Reply by Chris Wilkins on December 11, 2009 at 4:29pm

I hadn't thought about a project yet, but off the top of my head, the most interesting thing to me is modeling organic growth. I'd like to understand that type of modeling and apply it to architecture. Like use the growth models to grow buildings. I've seen a lot of people doing things like this, but I want to know the geometry behind it. Casey Mahon showed some of that type of stuff at the Cloud. I've got that book by Ernst Haeckel "Art Forms in Nature" and have been salivating over it for years now. I want to model the things in that book! Or that loofa sponge that lives in the shower.

Also, in GH I've been playing with the box morph lately, and I can imagine how/why that works in my head, but I'd have no idea of how to do it on paper or in code. That type of transformation is very interesting to me, but then I've had a hard time thinking of applications for it in building physical objects. I mean unless your using 3D printers or something.

-Chris

Permalink Reply by Richard Schaffranek on December 11, 2009 at 5:03pm

Don't know which part of the world you are coming from.
So maybe you are sitting right next to them (ETH ZURICH) but a thing I would look at is

http://www.kaisersrot.com

They are not so crazy about form but focus more on the logic side ...

http://www.kaisersrot.com/kaisersrot-02/MEDIA.html
for example the right video show's an urban plan based upon neighbourhood conditions in real time.

So it's not realy an advice on what to read or to learn but maybe you can have a look on their aproch.

But please, show us what you are doing....

maeh ein Schaf

Permalink Reply by Chris Wilkins on December 11, 2009 at 8:16pm

That picture on kaisersrot intrigued me. I'll definitely look into their approach.
-Chris

Permalink Reply by Benjamin Golder on December 11, 2009 at 10:43pm

wow! super neat!

Permalink Reply by David Rutten on December 11, 2009 at 5:47pm

A lot of so called organic shapes in Architecture are far removed from their originals. Organic shapes almost always are the result of a specific growth pattern. By aiming at specific shapes a lot of people don't seem to realise they in fact betray the underlying principles of those shapes. Shapes are never goals in nature, they are merely side-effects of processes.

A very common misconception for example is that trees make a good topology for load-bearing columns. "400 million years of evolution can't be wrong!" Trees however did not evolve to be load bearing structures, they evolved merely to carry themselves and then only within the constraints imposed by a slow growth rate. This is just one example of course, but I found that the majority of modern man-made organic shapes suffer from a similar flaw in reasoning. I think it would be exceptionally interesting to approach this entire field of architecture not from the shape point of view, but from the process point of view.

Of course along with a novel approach come many, many problems. There will be few established algorithms, few examples. You may even find that geometry like Nurbs or Meshes are totally inadequate for this kind of stuff.

But I digress. This is not what you wanted you hear, this is rather something I felt like saying.

--
David Rutten
david@mcneel.com
Poprad, Slovakia

Permalink Reply by Chris Wilkins on December 11, 2009 at 8:13pm

The process point of view is very interesting to me, but the class is under the math dept., so I have to stick to geometry. Although I love algorithms.

What if it were a sort of survey of currently useful geometries - Nurbs, Meshes, etc. An introduction to what is being used now could lead to new inquiries later.

Or a survey of shapes. I looked at Platonic and Archimedean solids in high school, and geodesics, but back then we were still doing descriptive geometry and drawing the shapes in 2D on some system called Versacad. Maybe just a look at commonly used methods like Voronoi and Delaunay, or circle packing, or attractors, or just a sort of indulgence in form.

-Chris

Permalink Reply by Benjamin Golder on December 11, 2009 at 10:37pm

Math and geometry are so broadly applied throughout architecture, so you really could go in a million directions. Can it be applied math, or are you supposed to just learn some specific abstract math?

Personally, I'm slowly becoming more and more interested in accounting for error generally, as well as the use of fuzzy logic for suitability analyses in urban design.

What about some discrete math stuff? Network topology in space trusses? Or the geometry of material deformation? Have you checked out the geometry of bending blog, by Mårten Nettelbladt? I think it would be really neat to see a research paper that thoroughly describes (and calculates) the sources of error present in the idealization of some simple structural principle applied to a specific case.
Or what about an abstract optimization problem, like the best locations for joists in a slab with non-uniform loading?

Too much neat stuff to study!

Permalink Reply by Evert Amador on December 12, 2009 at 2:44pm

Hi!

Probably you've heard or read about "On growth and form" by D'arcy Thompson which I've always found very interesting as it is about organic processes and their mathematics in terms of shape and form.

I supose it is something similar to what David is refering to, a shape given by a process in a specific time interval, beig discrete to some extent. What I found amazing about this, it's the mathematics that describe natural growth ( as in agregation of particles) taken into account phisical and chemical laws, something always forgotten in Architecture (as a bussiness) as it's perhaps too complicated or time consumming thus non profitable! so really this should be encourage at Universities.

In anycase I'd really like to keep track of you research and look forward to see the results.

Cheers!

Evert

Permalink Reply by Luis Fraguada on December 12, 2009 at 5:19am