Continuity of Splines

Freya Holmér spent a year to understand continuity in splines and presented the results in a stunning youtube video. The clarity of presentation and animation shows and tells how the math of splines works. For a geometry and animation enthusiast, this is captivating. youtube author

When I worked at Spatial Technologies (which became PlanetCAD) I remember some cognitive dissonance from a conversation with one of the senior developers.

For context, I was lead developer on a team building a workflow engine to allow our customers to automate the processing of digital engineering documents. Those documents were industrial engineering models and bills-of-material for all kinds of things. Prospective customers included Black&Decker, Freightliner, and similar manufacturers.

People are familiar with supply chains for manufacturing (especially after the pandemic disrupted them). Well, those same businesses have a similar sort of problem when designing the things they manufacture. The companies need to transfer three-dimensional models of systems and subsystems to their suppliers for design and manufacture. But the companies in that exchange generally use different CAD tools. So conversion of the models into different model formats is a constant source of friction. Our workflow engine was aiming to help orchestrate the conversions.

Back to the conversation. I was feeling a bit intimidated and impressed at the mathematical depth of the senior developers who were working on the three-dimensional modeling kernel that was the core of the original business. I always fancied myself as good at math and especially geometry and three-dimensional space. But listening to these guys talk to each other it was clear I was way out of my league.

So I was enormously flattered and surprised when this particular member of that team said something like "the stuff we're doing is much easier. You systems guys have the hard problems."

At that time I didn't know I was a systems guy.

Anyway, I asked him what was an example of the kind of hard problems he was working on. He described how the math and modeling gets difficult where three dimensional surfaces have discontinuities. There was a combination of geometric constraint solving and dealing with floating point numbers at these points of discontinuity that required a lot of innovative heuristics and algorithms to protect the integrity of the mathematical models and related computations.

I think this video visualizes exactly the kind of problems he and his teammates were wrestling with.

In the many years since that conversation I've learned that he was gesturing at the inherent complexity of distributed systems. Now I can understand how my problems at the time were worthy of his respect.