[Download link at the bottom]

In geometry, trilateration is the process of determining absolute or relative locations of points by measurement of distances, using the geometry of circles, spheres or triangles. It has practical applications in surveying and navigation, including global positioning systems (GPS). In contrast to triangulation, it does not involve the measurement of angles. [Wikipedia]

Given 3 points in space and 3 corresponding radiuses the component determines the intersection point(s) - usually 2, in particular cases 1. If no intersection occurs outputs are null.

We developed this component to simulate rigid folding of triangles without recurring to iterative processes or boolean intersections. You can see it in action here, while reproducing Aedas Al Bahr towers façade folding components:

Installation: go to File > Special Folders > User Object folder and copy the user object there. Restart Grasshopper. It should appear in the Extra tab, under the Co-de-iT sub-tab.

You can check the code by double-clicking the user object. It is based on the wikipedia page implementation: http://en.wikipedia.org/wiki/Trilateration
I have included also a Python version in the Grasshopper definition.

It's a little feature, but we hope it could be implemented as a standard component in the next version of Grasshopper.

Download link: Trilateration.zip

You can also find it in our Grasshopper code page.

Hope you find it useful.

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Alessio Erioli - Co-de-iT

http://www.co-de-it.com