I had planned on asking this eventually, but a comment by one of my bosses is causing me to post it sooner. The comment my boss had was on the following:
He initially stated that the circled polygons were bad because they were non-planar faces (but on further investigation via Maya's cleanup, 99% of my mesh is non-planar faces), and needed to be fixed (ie. made planar). This is my first question, how relevant are non-planar faces to modeling in the industry? Should I try to maintain planar faces?
Besides that I have a question of my own. How essential is it to maintain circular edgeloops when dealing with odd or complicated meshes? For instance the above shot was taken from my in progress reconstruction of our company's heart model. The mesh is starting to get very complex, and since in its finished version the interior will also be contiguous with the exterior...it will be very complicated. I have maintained an entirely quad mesh (save for one triangle that I haven't figured out how to remove), but the problem is that most of my edgeloops cross each other, or form t-junctions, instead of just forming a neat loop like you see on most character models. I am unsure of how much this should perturb me, or how much I should fix it, or how relevant it is to take into consideration when going forward.
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Being non-planar faces is not a cause of being bad. Your boss needs to actually come up with a reason they are bad- right now it sounds as if they are bad because he decided they are bad.
My gut feeling is that when/if you can uncover his rationale it'll be full of holes.
He might be thinking those are 5 sided and therefore "wrong"? Or maybe he sees two triangles with an edge missing and doesn't realize its a quad?
Have him read this...
http://www.subdivisionmodeling.com/page4.htm#limit
Hopefully he misspoke and hadn't had his morning cup of brain fuel. If not, you need a new boss, your companies health depends on it. It sucks having to explain simple terms to your boss and encourage them to use them correctly...
What is the reasoning behind wanting to keep perfect edge loops? If it's just meant to be for ease of editing when modelling, then actually trying to keep quads everywhere can be WORSE than just accepting that you will be able to use triangles and n-gons, and leave an easily editable model with edge loops where necessary.
What is the "destination" of the model? Is it going into a game engine? If so, it's all going to be triangulated anyway, so then you need to worry more about the triangulation than the quadrangulation. If it's going to be rendered, or subdivided, then all you should care about is how it looks when smoothed or subdivided, without the wireframe.
Are these meshes going to be animated at all? Quads are easier to predict in deformation, if you have n-gons they may deform in strange ways. If they're not going to be animated then you don't need to worry so much.
Pretty much its going to be used for everything from realtime animation/viewing and realtime interaction (via interactive surgery or even haptics based interaction), to traditional video style animations and renders, even single frame beauty still images. Its going to have to be a base for a zbrush sculpt, its going to have to be editable in the future to show cross-sectional cuts. Its probably going to have to do things which I have no idea about at the current moment. The shelf life of our last heart model apparently was 5 years, this will probably have to persist for nearly the same amount of time. Which is why I'm asking so many questions in reference to it...
To answer the edge-loop/quad question, its so that it can subdivide well for regular rendered video animations and zbrush, but also be low-poly enough that not much has to be done to it to bring it into a realtime engine...
I'd ask your boss about it in as nice a way as you can.