#delaunay-triangulation

Boris Nikolayevich Delaunay was a Russian mathematician and mountain climber. He developed the Delaunay triangulation, which is a method in computational geometry. It is a triangulation of a set of points such that no point is inside the circumcircle of any triangle formed by the points. It’s widely used in computer graphics and mesh generation. In 2013, I made the brute force code in Rhino Python which is a slow solution to this problem. It used to be a nice…

This is a useful tip both to solve some of the problems with custom surface subdivisions, and to explain the uses of parametric surface evaluations (the U, V, W thing) and the practical use of data lists. Step 1: Put your points inside 0,0,0 and 1,1,0 so that the resulting coordinates can easily be converted to U and Vs. In the example, we are putting some random points between 0,0 and 1,1 using the Populate2d component. Step 2: Then make whatever you…

This is the final Grasshopper sketch of our graduate studio conducted together with Fulya Akipek at Yıldız Technical University Computational Design Unit. The project was about designing parametric “Landscape Extensions” at Kabataş Park in İstanbul. I hope I’ll be able to post the actual student works and the material system, but now; only the final result of the digital sketch we’ve developed together with students is presented here. This was a kind of “sketchy” definition that came up as an…

After becoming a ready-made component in Grasshopper, the Delaunay triangulation lost its popularity quickly. It used to be a nice problem of computational geometry for designers obsessed with scripting.  Last month, Benay reminded me of the method of circle checking. She showed her Rhinoscript that creates circles from point triplets and checks if a point is inside or not. Today I studied this in Grasshopper to see if I can handle the required point combinations quickly. However, my first attempt…