Planarization implemention behind Kangaroo CoPlanar

[samwilcock]

I’m hoping that @DanielPiker may get chance to respond to this, but posting here for everyone’s benefit:

While responding to a paper review, I’m trying to understand how Kangaroo’s CoPlanar goals work. Are they analagous to VTPI? I note your comment in a previous post about disliking the tangential plane intersection methods. Would you be able to share roughly what approach is taken?

@DanielPiker

I’ve never really liked the methods which assign these directions essentially arbitrarily (which includes all the examples of tangent plane intersection method, and agent based approaches I’ve seen), as I find the resulting cells rather ugly where the regions clash.

I think the only way to make all nicely shaped planar hexagons on surfaces with multiple saddle regions would be to systematically create some non hexagonal faces at key points, and control the alignment of the ‘bowties’ in different regions and where they meet. That’s a big challenge though, as it is closely related to generating a perfect curvature aligned mesh and ideal singularity placement on arbitrary surfaces, which is still an unsolved problem and topic of ongoing research.

I’ve searched through previous posts but couldn’t quite see an exact answer (although I see someone else asked similar)

@marinellacontestabil

I have a curiosity: when we use Kangaroo 2 for planarization, in general besides this case, which methodoloy we rely on to reach planarity?

Kind regards!
Sam

[samwilcock]

Just to get my thoughts out… My assumption so far is that it follows a similar procedure from ShapeOp*, that attempts to keep vertices still and projects faces onto the closest local planes, and then moving vertices towards these planes. I suppose it seems a little analagous to a VTPI approach to me.

@DanielPiker

Since version 2, Kangaroo doesn’t actually use the classical form of DR, but a new form where instead of summing accelerations, it combines projections onto the zero energy state of each goal. This draws on conversations I had with the LGG group at EPFL, during the development of their ‘Projective Dynamics’ paper (though the method used in Kangaroo is not exactly the same as the one described in that paper, and incorporates a different approach to the damping to accelerate convergence). I later also learned that this method of combining projections actually dates back much further than the LGG work, and can be seen as a form of the alternating direction method of multipliers (ADMM).

*(Mario Deuss, Anders Holden Deleuran, Sofien Bouaziz, Bailin Deng, Daniel Piker, and Mark Pauly. 2015. ShapeOp - A Robust and Extensible Geometric Modelling Paradigm. Design Modelling Symposium)