TOPOLOGY OPTIMIZATION

Just an old experiment I did using ToPy in Houdini. ToPy is written by William Hunter and it is the Python implementation and 3D extension of Ole Sigmund’s famous 99 line topology optimization code in Matlab. Since ToPy is written entirely in Python, it’s easy to use in Houdini. Preparing and converting the input and output files worked pretty flawless by using the Python VTK library.

 

 

For more about topology optimization, check out the following links:
https://github.com/williamhunter/topy
http://www.topopt.dtu.dk/
http://www.topopt.dtu.dk/files/matlab.pdf

 

BALANCING 3D SHAPES

3D printing became rather popular over the last years and many people started to print their own models. The technology is great and the workflow generally quite hassle-free: Just do the design in your favourite 3D software, save the file and then send it to manufacturing.
There is one problem, though (apart from the necessity to have a watertight model): It’s easy to forget about the laws of physics, or more precisely, to forget about gravity. Consequently, the printed model which is intended to stand, simply doesn’t. The reason for this is most probably because it’s unbalanced and thus just tuple down. However, a great solution to this problem is provided in the excellent paper “Make It Stand: Balancing Shapes for 3D Fabrication” published by the igl Zürich. The authors propose a two-step balance optimization algorithm which works by firstly modifying the volume of the object and secondly, by deforming the original shape. Since I like 3D printing and have first-hand experience with the “it doesn’t stand” problem I thought an implementation of the paper might be worth a try.

The method described in the paper basically works as follows:

  • Define support polygons of the shape
  • Calculate center of mass
  • Carve out inner void based on computed center point
  • Calculate new center point and check if its projection along gravity is on support polygons
  • If center point isn’t on support polygons, furthermore deform original shape to ensure stability

Computing the center of mass (not to be confused with the centroid) is easy. It can be done quite efficiently by using the divergence theorem. It’s described in the paper but in case you are interested in details, check out the link. For the mass carving part Houdini already has the perfect toolset, namely VDBs. After converting the mesh to a VDB I used vdbReshapeSdf to compute the overall offset of the surface. The final inner volume is then computed iteratively during optimization in a volumeWrangle based on a mask. For the shape deformation I used on an old custom SOP based on laplace editing. And finally, the overall minimization problem was solved in Scipy within a SopSolver. Even though this setup was quite inefficient since all matrices have to be rebuild in every iteration, it worked surprisingly well. Of course, there is much room for improvements but tbh. I was more interested in the general method than in the exact implementation of the paper.

 

 

R. Prèvost, E. Whiting, S. Lefebvre, O. Sorkine-Hornung: Make It Stand: Balancing Shapes for 3D Fabrication