I’m happy to see this discussion as I think it is an important topic.

Making and understanding good quad patch layouts does get easier with practice, and I think it is a valuable skill to learn - not only for relaxing meshes in Kangaroo - many of the same principles are often useful when working with SubD and NURBS.

By ‘higher valence points’ I mean vertices of the quad mesh which are surrounded by more than 4 faces.

When we talk about a ‘nice’ quad mesh, we usually think of one where *most* of the internal vertices are regular with valence=4, i.e. they are surrounded by 4 faces (and connected by 4 edges to 4 surrounding vertices).

The shapes we can make from quad meshes of *all* regular valence without highly distorting the size and shape of the quads are quite limited though - a bit like trying to tailor a well fitting suit from a single sheet of fabric without cutting or stitching it - wrapping it onto forms much more complex than an extrusion would result in lots of stretching and bunching.

So we often need to include a few special points in the mesh (sometimes called irregular vertices/singular vertices/singularities) where the valence does not equal 4.

We can change the density or number of faces of the mesh by subdividing quads, which adds lots of new valence 4 vertices, but leaves the arrangement of irregular vertices unchanged.

The shapes and edge lengths can also change during the relaxation, so usually the precise geometry of the starting mesh also isn’t important, just its topology.

So when creating a starting mesh all we need to focus on is creating the right irregular vertices, usually with only a very small number of faces, and subdivision and relaxation takes care of the rest.

In my example above, I started with something like this and reflected it and subdivided (similar to what @martynjhogg shows, but with valence 6 vertices, not valence 5) :

Valence 2 and 3 vertices are useful for forming dome or bowl shaped regions (positive Gaussian curvature), while valence 5 and 6 vertices are useful for saddle shaped regions (negative Gaussian curvature).

(also, because a valence 2 vertex is ‘missing’ 2 quads compared to a regular vertex, it can be replaced by a pair of valence 3s (each of which is ‘missing’ 1 quad) without changing the surrounding region.

Similarly, a valence 6 vertex can be replaced by a pair of valence 5s.)

The aim with Kangaroo is that by seeing and experimenting with how meshes of different topology relax, you build up some intuition for the relationship between starting topology and relaxed shape, in the same way you get a feel for working with a particular material after working with it for a while.

QuadRemesh is a wonderful tool, but unfortunately not often suitable for this application because when making a mesh in a flat boundary it does not know your intent for which regions should be domes/saddles/supports in the 3d shape it is going to relax into.

See my answer in this thread.

A mesh can have planar faces, but that alone doesn’t guarantee it can be offset without twisting in the beams connecting the edges of the 2 layers.

Making the mesh conical can be the difference between nodes like these