Recent searches
Search options
I can finally work on my procedural creature parametrization again, now on a much better foundation.
After working on parametrization matrix math and custom tools for the past five weeks, the results are coming together. Here's a demo of my derived parametrization tool.
#ProcGen
A nice aspect of the math behind this, which is not conveyed in the video, is that the more high-level parameters I create, the better the results also become when rolling random creatures by setting all parameters to random values.
There's more details on the concept and the math behind it in this post from a few days ago:
https://mastodon.gamedev.place/@runevision/114213218833400674
I had a scare today when after working more on the parametrization, the matrix numbers produced by the final pseudoinverse became very large, causing the creature meshes to "explode" and even Unity to crash. (1/2)
After digging a bit online, it seems that in the singular value decomposition used as part of the pseudoinverse, it's common to set singular values below a given threshold to zero to avoid instabilities. The Math.Net pseudoinverse implementation I use doesn't provide any control, but I reimplemented the method with threshold parameter. I had to set it super large (0.01) to avoid the issues, but then it seems to work. (2/2)
It seemed like I had to set it to a larger threshold the more parameters I added, so we'll see how things progress. I must admit I don't fully understand the pseudoinverse yet, or the consequences of the large threshold I'm using. Hopefully I can keep working around the issues without the core functionality being undermined. (3/2)
Here's a video showing what I'm talking about regarding instability of the pseudoinverse and how I'm working around it. But I'd like to understand better what's going on. #math
@runevision Did you try inspecting the condition number if the original matrix?
@lisyarus Does that refer to a specific calculation, or do you just mean the same way as I did for the pseudoinverse matrix? I didn't, but given all the numbers in the original matrix are small (between 0 and 1) and given how matrix-vector multiplication works, it should be very stable, similar to how the pseudoinverse is stable once it only has small numbers.
@runevision @lisyarus I think the condition number is analogously defined for the pseudo inverse matrix A^+, so very small values in A may result in very large values in A^+ I would think.
@shanecelis @lisyarus Ok, if I understand right. The L2 norm of the input matrix, pseudoinverse matrix and the multiplication of those two norms (the condition number) are by default 0.87, 1192.46, 1040.80. If I set the two small singular values to zero, then the numbers change to 0.87, 1.45, 1.27.