Gradient Flow on Mesh

Here a different use of Gradient Flow.
I have a Voronoi pattern that needed to be printed with just one path

Of the idea is to offset it, make a Spanning tree that links the cells

And then bridge the cells

Lets say I put a weight of 100 of the red dot and 0 at all others places. And then I smooth the weights. I could also use geodesic distance or heat flow.

Gradient Flow of the weight gives that




Weight Smoothing Cotan Weight Method


Weight Smoothing Edge Length Method/Uniform method