Grasshopper

algorithmic modeling for Rhino

A while ago I found the remesh_planton_circles.gh script by Daniel Piker. I find this script really interesting as I am using it for my graduation and I am trying to figure out the logic behind it, which proves to be rather difficult because I have no experience with scripting whatsoever. What I (think I) understand so far is that it uses edge collapse/split based on the proximity to certain points that have been assigned certain desired length values for the Delaunay edges, based on inverse distance weighted interpolation. There is also a force that pulls the vertexes of the Delaunay to the input mesh. 
What I am not sure about is how the circle packing forces work in combination with the laplacian smoothing forces. Are the circle packing forces based on kangaroo's spring force system? Does the circle packing also use attraction or repulsion functions like the Powerlaw component does? And what is the benefit of using the laplacian smoothing forces? Are they necessary to create a tangent circle packing instead of a 'simple' circle packing that does not result in a tangent circle packing? Could anyone give me some insight as to how exactly this script works?

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Hi Denise,

The remeshing in this script is along the same lines described in this post. The combination of flip/split/collapse local operators for iterative remeshing has been around for a while, for example see this paper.

The circle packing forces in this script are not simple springs, but are based on the ideas in this paper. Essentially it is a condition on the sums of the lengths of the 4 edges around each pair of adjacent triangles, and it adjusts the lengths to meet this condition.

The Laplacian smoothing might not be necessary in this script - I just often include some amount in most types of mesh optimisation, as it is a simple way to keep meshes fairly regular.

Hello Daniel,

Thank you so much for your reply. I understand now! 

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