Post #1757933

2026-04-22 12:05 UTC

The second problem is that the terrain patches are all separated disks which is also unnatural. That's because you can't apply a substitution to two neighbouring spheres, or it causes discontinuities. This is solvable but it is a bit tricky. You need to create an inversive limit set specifically for the overlap region between the neighbouring spheres. You then need to constrain the overlap limit set spheres in a specific way. If set A constrains sphere ids 𝑎ᵢ to its parent and child set B constraints sphere ids 𝑏ᵢ to its parent, then the overlap set needs to contrain its sphere ids 𝑎ᵢ to those on B and ids 𝑏ᵢ to those on A. Here is a basic flat icosahedral limit set with a green mountainous set on top and a brown hilly set on the left. The subtitution spheres are neighbours so the patches overlap and you can see the discontinuity between them. This happend regardless of whether you switch to the brown or green set at the overlap. (3/4)

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@TomL@mathstodon.xyz 2026-04-22 12:17

With the overlap limit set placed between them we have a continuous landscape. It also removes ambiguity of which child set has priority at the overlap. The overlap constraints leave four free spheres that can be adjusted on this overlap area, so it can look more like the brown or the green landscape if needed. Perhaps by default it should average the two sets prior to solving the dihedral angle constraints between the spheres. As far as I can work out, the smaller green disks don't need to use the overlap set against the large brown one, as they remain continuous. But you can see the green-brown overlap sets between smaller green and brown disks. The number of combinations of overlap sets between pairs of substitution sets at different orientations suggests that it would be better for them to be auto-generated as an interpolation of the two neighbouring sets, rather than being manually specified. blog: https://tglad.blogspot.com/2026/04/improving-global-landscapes.html (4/4)

Open ##1757934