I seem to frequently find myself with an odd number of edge loops needing to connect to an even number of them. Using the 'standard' 5-3, 4-2 or 3-1 reductions ultimately leads to needing a 2-1 reduction. I know I could add/remove an edge loop, but suppose I didn't want to change the existing topology. Is a 2-1, with its triangle really that bad? If subdivided, it winds up all quads, and if not subdivided I don't see any artifacting. If 2-1, with it's triangle, is considered taboo, and would get you fired, what can be done without adding or reducing existing topology?
| "what can be done without adding or reducing existing topology?"
Nothing.
It really depends on the situation whether the Triangle is bad or not. Triangles aren't taboo! And they cannot always be avoided.
In non-deforming, flat surfaces they can do very little to no harm, as long as they are not directly at the edge of that flat surface.
On curved surfaces, they can cause pinching, when Subdivided, but even then you can sometimes get away with it.
You're not going to get fired over a triangle, so not to worry. Ngons and triangles are fine, given they don't disrupt anything, produce any pinching or whatever else, you can use them to your advantage. There can be that feeling of being a purist, but that is OCD or overall nonsense. If you can get away with all quads without any effort or even with effort, then more power to you, but it's not a must, you don't have to loose lots of energy over it.
You know what it is like, when your parents made you obey all the dinner table rules as a kid, you had to use napkins on your lap, the spoon is for this, this kind of fork is for that, the other kind of fork is for this, the knife always with the left hand, in this situation on the right hand, don't slurp your food, blah blah blah, etc, etc, etc. Then you grow up, get your own place and you're like wait, I can totally do what I want and nothing bad happens, I can drink out of the juice box, I can grab the food with my hands, I don't have to use a napkin and use one fork for everything and not even use a knife, this is life baby yeah!
Thanks very much for your responses. Being somewhat new to the whole 'optimal topology/retopology' process, the great Google oracle has been unable to find an answer like 'nothing', even though I suspected that to be the case; so thanks for that Martin. And Omar, I greatly appreciate your reply. Although my OCD and finely honed ability to 'over think' everything will likely persist, I can at least put this to rest and move on to something else inconsequential to worry about. ^^