problem set 02

Get started working parametrically in Grasshopper, and start thinking about alternative approaches to manipulating tiled systems.

At the end of our last session together, we discussed projective geometry.   Produce a grasshopper model which combines two kinds of projection together:  First, a spherical projection, which projects a given set of curves (not polycurves) onto the surface of a sphere.  Next, create a stereographic projection which takes as an input the results of the spherical projection.  For clarification, see the screenshots below.  While these screenshots show a simple hexagonal tiling system, you should define your own custom pattern.

In addition, complete the reading which I have attached via email, and be prepared to discuss.

deliverables

* a single grasshopper definition which performs the projections described above, uploaded into your dropbox folder.

* three screenshots of distorted tile systems which you find compelling or which contain potential for future development.

The spherical projection – this grid of hexagons is being projected unto the surface of a sphere…

… resulting in a distorted hexagonal tiling.  Try moving the sphere relative to the initial geometry, and see what kind of effects you can achieve.

Next, perform a stereographic projection.  Here, the curves which resulted from our previous projection are projected from an arbitrary point in space back onto a flat plane. 

Can you figure out where to position this point in order to return these distorted hexagons back to their previous state?  Can you find more interesting or more useful kinds of distortion using this technique?