## Coreform Short-Course

In February, Coreform held its second short-course, which I attended. It was fairly similar to the last short-course, though a bit more polished. The biggest difference, however, was the unveiling of their beta version of *Flex* preprocessing software — which is built on the Trelis meshing software they obtained through their acquisition of CSimSoft. Inspired by one of my work colleagues, I made a video of their stress-testing of one of the tutorial problems.

## Planar Spring

After the short-course I began developing a strategy to build a simulation model of the planar spring in Flex. I ran into a few bugs, but was able to work with Coreform to get some fixes. Namely I was trying to construct a U-Spline on the mesh shown in figure there was an infinite loop happening in their algorithm to apply creases along one of my boundary conditions.

Caleb and Florian were able to quickly troubleshoot the error and get a fix pushed to their master branch. Now I’m just waiting to get a new build of Flex so that I can run the simulation on the working U-Spline. As you can see in figure 2, it’s still not perfect, but this will be an important milestone for me: building an entire simulation from scratch using only Coreform’s software stack.

## U-Spline vs. B-Spline

Another thing I worked on with another graduate student was coming up with a simple example demonstrating the difference between a traditional B-Spline and a U-Spline — in 2-D. Remember that a traditional B-Spline is a basis-spline constructed via the Cox de Boor recursion algorithm in 1-D and then expanding to higher-dimensions via tensor products. The figure below shows an unstructured spline topology and demonstrates a quadratic spline basis function with maximal continuity, B-Splines on the left and U-Splines on the right. Notice that the B-Spline basis is and has to be constructed via three carefully parameterized B-Spline tensor product surfaces. In practice (i.e. moden CAD) this basis wouldn’t even be continuous, but rather . The U-Spline, on the otherhand, is constructed as a single entity and is able to acheive continuity, except at the extraordinary point though I’m told this isn’t a theoretical limitation, but rather that Coreform hasn’t yet implemented smooth extraordinary points. Later I’ll talk about the far-reaching implications this may have for constructing watertight-CAD models.

That’s it for February, hopefully March proves to be another fruitful month!