Points (attractor?) problem

I am trying to populate this surface such that points are dense. Specifically, I want to make it so that, when I Smorph it to flat plane (like making texture image?), the points are such that they follow and are ‘attracted by’ the ridge.

In this case, the ridge is a cross, so the points on the Smorph result should look like:
1 there are dense areas and sparse areas
2 dense areas follow the cross-shape of the ridge
3 sparse areas are the not-ridge parts (four corners of the surface, in this case)

I found some resources on attractor but, in this case, I want to do this without access to the actual curves that precisely follow the ridge (e.g. the curves that might have created this surface) and purely based on the ‘ridgeness’
I know it’s easy to get such curves (e.g. split with vertical planes) but, I am running into a lot of ridge-like curves in my project, and most of them are not oriented in a way that we can easily identify the curves (or the splitting plane to create those curves)

The result I currently have is bizarre: points on the Smorph result are sparse in the non-ridge areas and actually avoids the ridges
points_problem.gh (14.6 KB)

Thanks a lot!

You can take advantage of your surface curvature data…

points_problem_re.gh (16.0 KB)

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Thanks for your help! I notice that you use curvature as a guide to take subset of points, so that we only keep points that have high gaussian value.

How can I use curvature to make it so that, I have points all over the entire surface, but denser points in these areas of high curvature, and less dense points in low-curvature areas?