Ask HN: What interesting problems are you working on?

Hey, thanks for your interest! I've avoided trimmed surfaces, in part because I'm interested in doing one or another kinds of analysis on or with the parametric geometry, and trimmed surfaces are not so easy to work with for some of the finer control I want from my optimization tools. (They often cause comparability issues with export between programs as well, but that becomes more important only if somebody uses your stuff ;)

I like other methods of getting local control, or finer shape control of surfaces. In my stuff I've used truncated hierarchical B-splines (THB-splines), which are great for adding detail, but useless for changing topology. People speak highly of (analysis suitable) t-splines but I say they are complicated and subdivision may be better overall now anyway. Generally speaking, I think the whole industry will have to go to subdivision. (Among friends I'd say it may carry right down to poly meshes via differential geometry but those two representations might play well together given the right tools)

Reading recommendations:

For everything you ever wanted to know about a B-spline, including a C++ library implementation from scratch, highly documented and explained: 1.) Piegl and Tiller "The NURBS Book" This includes a tiny bit of shape control via optimization.

For an explanation of the basics of B-spline nonlinear optimization with Lagrange multipliers, focuses on ships, there is a chapter here that takes you to the state of the art, circa 1995: 2.) Nowacki, et al., Computational Geometry for Ships

3.) Tony De-Rose's book "Wavelets for Computer Graphics" actually has some good scripts getting at the basics of wavelet B-splines and some facets of hierarchical parametric geometry.

The above is a start at form parameter design for B-splines. This was okay 20 years ago. It's still importatnt as a basis for understanding optimization of parameterized shape. ---Even subdivision surfaces have control points.

Generally B-splines were found not to be flexible enough for representing local details efficiently. Further, the optimization techniques still require a lot of manual setup to get things right...

The next steps are still in development: -subdivision surfaces are a way forward for shape representation. Generally they were more problematic for computing engineering quantities of interest, especially and precisely where they "go beyond" the B-spline to allow surfaces of greater flexibility -- that is where the analysis suitability breaks down to some extent. Again, this has been patched up in the last couple of decades but still change is slow to come to the engineering industry.

I think it's well worthwhile to look at geometric optimization in computer graphics as well. See The cal-tech multi-res group, Keenan Crane at CMU (geometry collective), and tons of siggraph papers where discrete differential geometry has been leveraged to do neat things with shape. (E.g. curvature flow: https://www.cs.cmu.edu/~kmcrane/Projects/ConformalWillmoreFl... I think there is newer work building off this and adding more complicated constraints but I can't remember off hand. As is they have some already!)

Back to the point: you wanted optimization readings. Well it's mostly in the literature, and the literature is mostly kind of vague when it comes to parametric optimization of B-spline. Though the high points are mentioned, the detail is often hardly much better than you find in Nowacki, 1995. To this end, I have some really specific entry level PDFs that might help, and the first part of my stuff is written up in this paper: https://www.sciencedirect.com/science/article/abs/pii/S01678... This deals mostly with curves, but has a direct extension to surfaces. Automatic differentiation really helps here! (I never published this bit on the extension to do surfaces directly (with all their attendant properties as potential constraints) as my professor said "direct surface optimization was to expensive". Looking at the discrete differential papers as of late, I tend to disagree. )

I strongly believe that quantum field theory is at the level of tetration or pentation. The others were possible examples. Thanks for the question.

Zipline?

For the re-write?

Simply for the experience. C++ is more in demand right now, as far as I can tell, sorry to say.

Hmm, similar thoughts but less about trust and more about the psychology of personal networks.

I'm interested in what value we place on connecting people in our network. Say you meet two persons in your travels that might benefit from being connected. What value do you place on making this connection? How does it make you feel? Does it have to have an obvious personal utility?

These are the types of questions I would love to investigate further. Maybe they're kinder, calmer tools that we can build for this specific purpose.