Relaxation of points / meshes constrained to a surface (circle packing)

In response to some requests, here are a couple of simple examples of distributing points on a surface.

In both examples the points are constrained to a predefined surface using the PullToSurf force (The PullToMesh force could also be used).

The first one treats the points as hard spheres, and uses springs with cutoffs to simulate collisions stopping them overlapping.

Switching on the mesh spheres component at the end allows you to see this. By finding the normal of the point on the surface you can also show circles oriented to it at each of the points.

There is a weak attraction force between the spheres, so if they do not fill the surface they will gather together and form a packing .

If you want to completely fill the surface, you can adjust the radius of the spheres with the slider.

If you want to then find a mesh on the surface you can use the Delaunay component, (provided it can be projected flat). I have also shown how you can use my new dual component (which you can get here: http://www.grasshopper3d.com/forum/topics/skeletal-mesh?commentId=2...) to turn the triangles into hexagons (with the occasional pentagon and heptagon - which are what allow it to fit a curved surface)

In the second example, I show how you can start with a set of curves or a mesh on a surface and relax them so their edge lengths become more equal. ( I have used curves generated by the first example). You can choose between the triangles or the dual. With the triangles they even out a bit, but it is not possible for all the edge lengths to become equal, whereas with the dual, the edges can become exactly* the same length.

*(actually to within 0.00000000000005%, but I think that's probably close enough for most practical purposes!)

Attachments:

mesh_on_surf_example1.gh, 11 KB
mesh_on_surf_example2.gh, 186 KB

Replies to This Discussion

Permalink Reply by Luis Fraguada on March 24, 2012 at 7:41am

Nice examples Daniel. Will these be added to the examples page or were you going to attach them to this post?

Permalink Reply by Daniel Piker on March 24, 2012 at 8:10am

oops! sorry about that. Files now attached to the post. Thanks Luis

Permalink Reply by guillermo gago doreste on November 18, 2014 at 6:47am

thanks for this examples!

but I have a problem with a missing component called "MeshDual"

did you know where i can found it?

Permalink Reply by guillermo gago doreste on November 18, 2014 at 7:50am

by the way for the first example i found something interesting

if you reaplace the "inter" component in the power law for a "delaunay edges" componet, you will save time and the result for bigger numbers of components will fit better

Attachments: