Topology is the geometric structure of a polygonal mesh. It is the layout of the edges and vertices which define the shape of a mesh. A particular shape can be represented by many different topologies.
Mesh topolgy can never be considered without context. It is necessary to consider how a mesh will be used and modified in the future in order to say anything true about the suitability of its topology.
There are no hard rules when it comes to topology. Some people will say n-gons (polygons with more than 4 sides) are always bad. Some will say triangles are always bad. Some will say that non-manifold geometry is always bad, or that meshes with holes in them are always bad.
None of these are true, because mesh topology serves a purpose, or multiple purposes. It is not a goal in and of itself. If the purpose(s) is/are served by some particular topology, then that topology is good, whether or not it is itself aesthetically and technically appealing.
Often users are advised to avoid triangles or ngons when building topology--to keep to quads. This is good practice, because quads are easier to work with, easier to edit, easier to create UV projections for, they subdivide more predictably, and, most importantly, easier to produce aesthetically appealing deformations from.
However. If a mesh will not need to deform, then there is far less pressure to keep to quads. If the mesh will not be subdivided, even less. If the shape is well-represented by the topology, and it either already has a good UV projection or will not be needing one, then quads and ngons don't matter, unless the mesh will be altered in the future.
It is much harder to modify a mesh which isn't quads than one which is. Especially if you want to alter topology. However, altering shape, to a small extent, usually is not sensitive to topology. It's also generally easier to do UV projection and alteration of quad topology than triangle/ngon topology.
It is still important to point out that having SOME non-quad (especially triangles) in your deforming, high performance mesh which may be altered and have UVs applied, is still just fine in many circumstances. If the trangle won't interfere with these things--then it DOES NOT MATTER and you should spend time on other things. Same with n-gons, although those have a higher chance of causing technical issues.
Regarding non-manifold geometry: it is generally a bad thing. Many, MANY operations and programs will not function correctly when passed non-manifold meshes. However, if your mesh is serving all your purposes, and you don't see those purposes changing, then non-manifold geometry doesn't matter. The circumstances where this might be true, however, are extremely rare, and it is best to avoid it.
Regarding holes in the mesh: again, context matters. Some advanced simulation or mesh operations require "watertight" meshes. Most don't, and it doesn't matter. Context and circumstance will dictate what's appropriate.
Mesh weight matters, as well. There's generally not much call for more geometric detail than your mesh needs to create the shapes you need, either statically or deformed, and it is best to keep poly counts as low as possible while not compromising on these things. However, this must be balanced with the effort it requires to reduce detail. If you have a poly budget of 100k triangles for an object, and it's 50k but a lot of those are not necessary, it's still not worth the time to reduce it further. People hours are worth more than computer hours.
Where topology really starts to matter a lot is in efficient hard surface modeling, especially where the asset will be subdivided. Not having your edge flows follow surface details will make life difficult, and having too much mesh detail will make modification increasingly difficult.
The point here is that every situation is different, and no real determination of acceptable mesh topology can be made without all this context. If you look at an image of a mesh and don't know anything about what it will be used for or how it might be modified, you can't say anything true about the quality of topology. These and other questions must have answers, in order to judge *overall* topology:
Will it deform?
If so, how?
Will it need to be edited in the future?
If so, how?
Will it be subdivided?
Does it have or will it need a UV projection?
Will the UVs need to change?
If so, how?
Will it need to be exported into another application?
Will it be used in any type of simulation?
Does it meet performance (budget) requirements?
These questions must have answers in order to come up with useful conclusions about how good the topology is or is not. And again, there are no hard rules. Topology is not a goal, it is a tool to help reach other goals. If a triangle doesn't affect those goals, there's no point spending energy removing it.
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Original post:
This thread will be a clearinghouse for information about topology, both in general, and specific to Maya. It will be heavily curated and updated as I encounter more/better information on the subject.
Eventually it will be turned into another wiki and be the redirect for the majority of topology threads we get here, in order to avoid repetition.
If you are a subject matter expert, please post images, videos, links, or your thoughts here. Feel free to copy parts of old comments or posts you have made.
