# Swarming /& dynamic relaxation on a surface

Daniel Davis – 15 July 2010

I

have just returned from the CITA workshop in Copenhagen. One of the problems we were tackling was how to distribute elements onto a unevenly doublely curved surface. I decided to explore whether the surface could be generated from elements of the same size. The most natural solution is to draw the elements in two dimensions and try to wrap the two dimensional surface onto the three dimensional shape. However the process of wrapping a two dimensional surface onto a three dimensional shape creates so much distortion that the original properties of the surface are lost: the elements become to long or too short. To me it feels like we hit the boundary of most CAD packages, which allow you to work in Cartesian space, and provide tools to wrap/embed Cartesian space into other spaces, but they are not set up to allow you to work in the original non-Cartesian space. For a while it seemed like the easiest solution would be to laser cut the timber to fit the computer model rather than to correct the computer model. It is interesting to witness such a high-end workshop, full of nerds, struggling to overcome the limitations of CAD and in many ways giving the design over to the limitations of the software – or at-least designing within the vocabulary of the software.

The solution I came up with to this problem was to use a swarming algorithm on the surface (seen in the video above). By creating a number of random points on the surface, and then iteratively pushing these points away from each-other until they were the desired distance apart, it was possible to generate the surface from elements of the same size. I uploaded the code to do this onto openprocessing here. In the video above you will also notice that there is a Grasshopper model on the right. The processing code saves a text file of the elements and, in real time, Grasshopper turns this text file into a Rhino model that it analyses. Due to some of the code inside that model I can not release it, but you should be able to create your own version pretty fast using the Read File element in Grasshopper.

Another project from the workshop is Anders Deleuran’s exploration of the accuracy of lightweight simulation (video above). In this case he is simulating a reciprocal joint held with the bending of timber. Both of these projects were discussed by Mark Burry at the AD magazine’s 80th Birthday during his lecture on ‘The future of architecture.’ The lectures were filmed but I have yet to find them online.