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Have a question thats gets me confused sometimes.

For game models, do modelers try to keep models as one piece, or have have multiple objects throughout a model. I'm trying to model something knowing that in real life it's one single object, but modeling it as one piece gives me weird topology, should I just make it two separate objects and then just clip the models where they would natural be?

For example, the mug in pic related to keep things simple, you could easily model the handle as part of mugs geometry. But you can could make the mug and handle different geometry, and clip them through to make the final coffee mug.

Is there pros and cons to that technique? This question pertains to hard surface game modeling.
For game models there's no real downside to modularity unless each component is loaded in discreetly, in which case you do increase your overhead slightly.
For smaller models, it all depends on what the aim of the modularity is. If you plan on being able to mix and match pieces, then you can make them separately, but the issue is that you won't get a catch light where the two join together unless you do some trickery with vertex normals.
I've seen models which contained both discreet chunks and chamfered edges, because each gives a different impression of how the surfaces connect, so there's no reason you can't use both methods for aesthetic reasons.
one piece unless you meed multiple.
smoother running physics that way.
i'm acknowledging the spelling error.
What you're talking about is often called "Floating Geometry"
If iit's static: make it one object
If it's animated (the separate meshes can move on their own) it's usually simpler just to have floating geo
To help you with your google searches; "multiple objects" is not what you are talking about.

You're talking about intersecting meshes. And that's completely fine as long as it looks good. No downsides to doing that.
Ultimately you're going to do a mix of both. If you made the handle separate and then just clipped it into your model (or were able to align it to the nearest face via built in software features), it would look unnatural and you wouldn't be able to use a Sub Division modifier.

Real world objects tend to have a visible weld point or seam where something was joined to something else (whether via melting the two things together via literal irl welding, or glue, or joining two pieces of clay or glass), it's extremely rare to just have two objects perfectly joined together.
Even when you have a shape that's been cast in a mold, some of the material is going to seep into the surrounding space.

HOWEVER, if you have something that's covering the attachment point, it's perfectly fine and natural to have it be floating geometry. You'll drive yourself crazy trying to extrude every single detail on something, and likely to no real benefit.
When it comes to hard surface stuff in particular, you're often going to want to be able to change things easily, recombine things you've already used ("kitbashing"), and generate shapes, curves, contours, and depressions via booleans.

Even when you want everything joined together, for purposes of say fluid simulation or 3d printing, that just means you'll need to clean up any "non-manifold geometry" that results from loose geometry being joined to the main mesh.
I think you might be describing a level of detail that OP will never need, anon...

OP here, no he's giving me good answers. It's that sometimes when modeling something with in mind how it was made can be daunting and sometimes not workable, hence why I'm asking for those more difficult to model, when I have to option to use floating geometry, should I?

what requires more polys/edges/vertices?

i almost never try to keep something one object unless i'm trying to get a very smooth transition, like a slight weld or highlight a curvature.

and you have to do multiple pieces if you want higher detail on a single model, i.e., more than one UVW map.

btw, i should add that rendering triangles has gotten so efficient, you don't really need to fret over poly count, it should be obvious where to draw the line of reason.
Just think about how it was made in real life, were the two pieces welded together? Or do they attach with a screw or bolt? Just think about that and you get your answer usually.
That's great advice for HP topo.

For the LP, it depends. Intersecting geo might be easier to make, and easier to make LODs with. The downsides are seams (if they're in a place where it would matter), and wasting some of the UV space where part of the texture is covered by another piece (this doesn't matter for small things such as screws, for anything bigger consider removing the "hidden" faces.

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