Variable Voronoi Study

I’ve been searching for a method to study the Voronoi subdivision in order to manipulate it. There are well-known algorithms for that. But I thought it would be better if I use a projective approach just as I did in studying hyperbolic space (here). This is the metaphor of inflating balloons. However, I inflated cones instead of spheres. This way, it became possible to modify the algorithm. So I was able to develop a kind of variable Voronoi study here. Of course, it is not a real Voronoi because the edges are not straight.

Above is the regular Voronoi subdivision in 5 steps, with constantly and equally inflating points. As a result, the code is very simple and easy to use. It is a good educational experiment on the usage of projections and intersections in native Grasshopper.

The second attempt (above) shows an interpretation of the variable Voronoi study. Again I inflated points at variable distances. Curved edges are because of different cone heights. You can study linear edges by manipulating those heights to be the same.

And finally, I tried to put attractor curves, in addition to points in this algorithm. Thus I put spheres instead of cones. Look what happened;

Straight edges and variable effect from each point. Here is the working Rhino 5 Grasshopper file from 2012. This code still works in 2021. Because it was made by using the native Grasshopper components. This makes the code more durable, simple, and educational.

Here is a link that inspired me to this study. This post could be further improved by studying various components and sweeping objects along curves.