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I'm just getting started with 3D so I'm not sure what's this is called. If I move a point in a polygon out of alignment with the other points in the polygon, such that is would be on a separate plane, what do you call it? What are the implications of doing so? Should this be avoided? Does this affect CPU? rendering? Is this universally supported by hardware and WebGL?

In my example, I have essentially turned a square plane into two triangular planes, creating a "v" in the middle of a cube. It appears that both triangles belong to a single face on the cube.

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    \$\begingroup\$ Not directly related to the answer here, but definitely related to what you're doing: Most modelling tools have a way for you to indicate which way that square gets cut to make two triangles. In the case of your cube, you would switch between having a "v" cut and having a corner cut off. I've seen the terms "turn an edge" and "rotate an edge" used to refer to this. \$\endgroup\$ – Victor T. Mar 29 '17 at 19:54
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There may be a more specific term I'm not aware of, but I'd just refer to that as a non-planar polygon. You do want to avoid that for real-time rendering (not all video cards support that nicely) which is why many game engines automatically triangulate the mesh; a triangle is always planar after all.

In other words, you don't necessarily need to care about that as a 3D artist, because the code will handle it automatically.

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    \$\begingroup\$ Whatever algorithm a programmer uses to triangulate ugly data may not agree with the intend of the modeller. I suggest that you'd recommend caring about the structure as an artist unless they don't care how more complicated polygons turn out. \$\endgroup\$ – Lars Viklund Mar 30 '17 at 0:54

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