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Most of the time in the first chapters of a random book about rasterization and rendering techniques, I find some phrases about a triangle-based rendering system and a quad-based one.

I have never encountered a quad-based GPU or pipeline. Do I have to worry about that when dealing with OpenGL 3.0+, or is it just legacy stuff?

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No, you don't. All current-generation commodity GPUs use (and have used for some time) triangle-based rasterization methods exclusively. Even though older version of OpenGL support the GL_QUADS rendering mode, these were converted to triangles by commodity GPUs. It's likely that GL_QUADS only resulted in actual quadrilaterial-based rasterization on esoteric academic hardware or hardware used for high-end offline 3D rendering in the early 80s or 90s (I have no evidence to support this claim, I'm just postulating).

That said, looking at quadrilateral (and in general, polygon rasterization other than triangle rasterization) can still be educational, and thus useful, simply by providing a different perspective of things. The algorithms involved in doing so efficiently are interesting and sometimes still have applications beyond graphics programming. I once used a edge-walking polygon rasterization technique as a means of implementing a simplistic fake 2D water simulation, for example.

It also may help you understand why triangle rasterization is preferable, in part due to the potentially non-planar nature of polygons other than triangles and because of some of the resulting optimizations you can make with triangles.

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If you're using a rendering API, then you only need to worry about what that API tells you to worry about. OpenGL doesn't say anything about quad-based or triangle-based rendering systems. So you don't need to concern yourself with it.

In any case, all consumer-grade GPUs use triangles, not quads.

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i'm confused, so why talking about this in an OpenGL book if the OpenGL API are based on the assumption that the model is formed by triangles? –  user827992 Aug 15 '12 at 4:56
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@user827992: Don't ask me; lots of books have superfluous information in them. You never even said what "random book" you found it in. Was it actually a book about OpenGL, or was it a book about graphics that uses OpenGL? –  Nicol Bolas Aug 15 '12 at 4:57
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