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I'm experimenting with adding modelling techniques, one being attaching edges that don't have the same vertex count (for example so I can model hands with more detail than the arms to which they attach). I've made two simple meshes to experiment on:

enter image description here

I've tried various ways of connecting them and have so far come up with the following:

enter image description here

Whilst these work for basic flat planes, there's a couple of issues:

  • The version with 2x vertices in one edge introduces triangles
  • The version with 2x vertices introduces poles with 5 edges meeting at a vertex
  • The version with 3x vertices introduces poles with 6 edges meeting at a vertex

I expect that there's no way to eliminate all of the above issues, but are there ways to minimise them? Is there a recommended technique for doing this in the general case (connecting edges with an arbitrary number of vertices?)

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This is what I'd recommend:

enter image description here

There are no triangles, and no 6 poles. There are, however, 3 poles and 5 poles.

Notice another thing: your left attempt has degenerate quads, quads with 3 collinear vertices. Triangulation can create zero-area faces which wreak havoc on the interpolation of smooth-shaded normals. It's easily enough fixed, just wanted to make sure you were thinking of it.

There are a number of issues with vertex connections like this. Undesirable poles cannot be completely eliminated. There is no way to connect an odd number of verts to an even number of verts without making triangles. For character animation, you frequently screw up your edge flow or topology chosen to hold volume at joints, and those are more important than your strict vertex count-- you're better off adding or deleting edge loops than you are trying to use joining techniques.

The way to work with the poles is to minimize their impact. Place them on the most planar part of the mesh that you can-- even a thousand=pole is fine when all of its neighbor faces are coplanar! You don't have to drop the whole 2:1 over a single edge loop; you can use multiple edge loops, dropping 2 or 4 verts each one, so that you can place your poles more carefully.

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That's about it, the technique on the right is the one that is usually recommended because it consists of quads. Check out this guide, search for "Optimal edge loop reduction flow" https://topologyguides.com/ Also you can use one more 'level' of edge loop reduction to reduce the instances of 6 edges meeting at a vertex. Check out the answer to this question: How do i connect two meshes together without ruining the topology

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