#graphics folks, I have a feeling I've asked this before, but it never hurts to ask again :)
Are there some good (preferably free) materials/courses/books on modern GPU hardware from a graphics perspective? Like all those registers, caches, wavefronts, occupacy stuff, etc
Say you're making hex tiles with roads (like in Civ 5), but some of the tile variations are just rotations/reflections of others. How many unique tiles do you need? Why, obviously (2⁶ + 2⋅2 + 2⋅2² + 2³ + 3⋅2³ + 3⋅2⁴) / 12 = 13.
Let me tell you about Burnside's lemma. (1/n)
The lemma is a beautiful result from group theory that talks specifically about enumerating things that are specified up to some transformations. But do we really need some cryptic lemma for that? On the image above I've easily managed to figure out all 13 cases. (2/n)
Truth be told, I did this after already knowing there are 13 of them (we'll check this by hand later in the thread). Even in such a small example it is very easy to miss some cases or introduce duplicates. The lemma also has an extra benefit that we'll discuss later. (3/n)