## Fom VEX/OpenCl to sparse matrices

In my last blog post I wrote a bit about the possibility to (mostly) circumvent the need of using sparse matrices in Houdini and instead setting up and solving the system in VEX/OpenCl. This time, however, it’s about the other way around and how a typically VEX/OpenCl based setup could be implemented and solved in matrix form.

Pretty much everybody using Houdini has at some point done basic Laplacian smoothing on a mesh (with uniform weights), perhaps without even knowing it. It’s a widely used algorithm and fairly easy to implement by averaging the values of the 1-ring around the current point. In fact, in Houdini it’s even easier than that and we can just use the attribBlurSop. AttribBlur is using OpenCl under the hood and relies on the basic graph Laplacian to blur/smooth point data, such as P for instance. This is done by performing the smoothing/averaging step a number of times which is conveniently exposed as iteration slider in the UI of the attribBlurSop.

However, this is of course not the only way how Laplacian smoothing could be implemented. Instead of iteratively applying the smoothing step per point we could also set up a simple linear system and solve it subsequently for the final point positions. This is what I’ve done in the file below. It’s a simple example where I’m using a direct solver in Scipy which is basically solving all the equations simultaneously in one go.

In practice it doesn’t make much of a difference which method we use because both will lead to the same result in pretty much the same amount of time (at least for our example). But since Laplacian smoothing is already provided to us by the attribBlurSop it’s most probably best to just use what’s already there instead of implementing it in matrix form.

Anyways, apart from practicality I hope this simple example, together with my last post, helps to clear up some misunderstandings and the question if it’s absolutely necessary to use sparse matrix libraries in Houdini or not.

ps.: To run the example file without problems you’ll need to have Scipy installed on your system/computer.