A few months ago I spent some time trying to come up with a straight skeleton curve solution for houdini.
Here you have some theoretical background about this topic:
http://visgraph.cse.ust.hk/projects/skeleton/skeleton_sig08.pdf [visgraph.cse.ust.hk]
https://www.cse.wustl.edu/~taoju/lliu/paper/pgcc/pgcc.html [www.cse.wustl.edu]
https://houdinigubbins.wordpress.com/2017/07/22/fiedler-vector-and-the-medial-axis/ [houdinigubbins.wordpress.com]
I trid to select the mosts relevant papers I found, IMO..
Challenges I faced:
1. Performance
Initially I tried to use the Smooth SOP(curvature mode) or Voronoi Fracture SOP with some acceptable results but unfortunately these solutions are extremely slow with dense meshes and they are not working very well with triangulated meshes. Then I decided to try VDB Advection against surface gradient with much better results.
2. Curve resampling
My technique uses a remeshed version of the original mesh, so the problem here is that during thinning process you need more resolution for elongated poligons. The solution here was to simply use a Resample SOP node.
3. Curve detection
Advection along VDB medial axis is cool, but it's not stopping until all points are contracted to the VDB's B-tree center nodes.
So, I had to come up with some kind of “curve detection” algorithm. Accidentally I discovered that you can do this easily using a VDB dilation followed by a medial VDB smooth and another dilation
4 Noise
Dealing with surface noise is a very sensitive problem. In reality, a 3D straight skeleton is more like a surface and very branchy. In order to solve this problem we have to use VDBSmooth SOP(medial smoothing mode) and make sure that advection is done with Fourth-Order Runge-Kutta method. Also, if the original mesh is very noisy you can use Paint SOP followed by a Smooth SOP to locally smooth the mesh and eliminate potential unwanted branches.
5. Remeshing & partitioning
This problem is relatively simple once you have the skeleton. You can use a voronoi fracture against the original mesh and as control points you can use the a resampled and refined version of your skeleton polycurve.
Also here you can do skeleton curve partitioning based on curve branching or angle/curvature and then transfer back these attrbutes to the original mesh points. Very useful for mesh partitioning, limb detection, bone automatic positining and even quad remeshing.
In combination with Convex Decomposition SOP(appliend to the shrinked mesh) you can get some kind of branch based decomposition.
So, here are some results:
