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 Jon Malkovich on December 14, 2009 at 3:56am

I see, is a general expression so.
Can you suggest any good books about differential geometry of curves and surfaces maybe with some fundamentals of computational geometry?

Permalink Reply by Luis Fraguada on December 14, 2009 at 4:20am

Hey Chris,

I think from what has been discussed, the Institute for Lightweight Structures publications called "IL" will definitely have examples of applied mathematical processes on architecture and engineering. There are many investigations into biology and how those systems can be studied and applied in different scales and purposes.

Another book you might want to take a look at is 'La Sagrada Familia: De Gaudi al CAD' (Publisher: Edicions UPC, Universitat Politecnica de Catalunya (1996)) - Unfortunately out of print, but it can still be found. Now there is a sort of 'sequel' to that one called 'Sagrada Familia s.XXI' (same publisher 2008) which speaks more about the mathematical / geometric language which Gaudi focused on intensely prior to his death in order to leave behind some kind of logic to complete the works. The connection to fabrication here is also quite intense as you can track the how eventually the manual templates the modelmakers and masons were using and inventing for stonework were transformed into CAM versions.

Permalink Reply by Chris Wilkins on December 14, 2009 at 6:36am

Yes. The connection to fabrication is a good place to linger. I saw Mark Burry speak last year about the Sagrada project, and how they are using parametric tools to do what Gaudi was doing with hanging chains and models. The cutting of the masonry was awesome. I was not aware of how the hyperboloid of one sheet worked until looking at Gaudi's stuff.

This thread has turned up a lot of good resources and ideas. Thanks to all. The Grasshopper forum rocks. (not trying to close discussion! just voicing appreciation)