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When are tris appropriate to use on a model and where are they usually seen?

For example, this image of a popcorn container (from turbosquid), uses tris for the top half circles and the edge corners on the bottom. Is this use of tris appropriate for this kind of model?

Why are triangles added at the bottom corners?

popcorn container with triangles

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In terms of quality I suggest you to model in quads. The simplest reason is:

The flexibility to soften and sharpen edges is key to build high quality models.

enter image description here

Example geometry with a soft edge on the left side and more sharp edge on the right

The best way to achieve this, is to build consistent topology to be fast in selecting Alt+Shift+RMB and creating edge loops Ctrl+R, which depends on quads.

enter image description here

Create edge loop issue

For the picture of your question, I assume that automatic algorithms (e.g. bevel modifiers) have been applied to improve the edges. A side effect of such algorithms is that unwanted edges appear (triangles at the corners), but I can't really see if there is a reason for this.

For sure there are exceptions to use triangles.

In terms of speed artists often use modifiers on simple geometry to build complex shapes - side effect can be a geometry of triangles. For the crumpled paper I could also imagine that here some kind of modifier on a icosphere was used.

But it really depends on what do you want to achieve.

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Tris are very important for exporting to other applications, especially game engines, as those very often work with tris internally.
But as poor says, model in quads and let the exporter handle the conversion. It's usually easiest.

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Although your question was answered long ago, for future readers here are some ideas to consider.

Tris are appropriate for:

  • Low-poly game assets, as long as deformation still looks acceptable (if applicable)
  • Areas of a mesh that will not be seen (inside nostrils, ears, etc)
  • Dynamic Topology - DynTopo sculpting would not be possible with an all-quads restriction
  • Cases where you know the final product will not require such exactness

What I mean by this last one is, if you're building a movie set don't fuss over parts you know will never be in the shot, or you may not make the deadline. The same principle applies to modeling.

Relevant YouTube video: "Is Good Topology Overrated?"

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For starters, game engines themselves only use triangle geometry. I think it is because it's the only geometry it can read, but I am not sure about that.

People (Like myself) stress a lot about the use of triangles, because you generally want to avoid them. Triangles aren't totally bad, but can deliver problems.

1 - You want a clean topology as best as possible, but tri's break your topology. 2 - tri's can deliver shading problems and with some modifiers like subsurface division. 3 - if you want to make an animation, it could deliver nasty deformations you don't want.

What you want to ask yourself is;

  • Is it a hardsurface object or rather an organic object?
  • Am I going to make an animation for my object?
  • Can the player see the specific surface well?

Tri's are an effective way to reduce vertices count, but you can not place them willy nilly all around your model. There needs to be a logical reason to place it and not because you didn't see any other solution or it was easier that way.

I hoped that helped a little bit.

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