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Gaming Beauty Is Only Pixel Deep
Thanks to NTSC-uk for its feature discussing what the new pixel and vertex shaders mean to this generation of videogames. The piece laments: "Looking back at the past few years, games have looked incredibly similar. And this is the main reason why: they all used the same tools", before going on to explain: "The hardware previously contained logic circuits to simply perform the operations needed by Gouraud and Flat shading, but now the fully Programmable Pipeline has introduced a whole new world of graphical effects for us all, limited only by the programmers' time and creativity", referencing "the water effects used in Super Mario Sunshine, cel shading effects used in Zelda, or the rippling water effects on Dead or Alive 3."
The Gamecube doesn't have a programmable function pipleline for graphics effects - it has a very robust fixed function pipeline. The effects the author emphasizes in those three Gamecube Games were more than likely done on the CPU and not with a programmable GPU. While that doesn't diminish the look or technical achievement of those games it does throw water on the author's assertion that games all looked alike before GPUs because all fixed function pipelines give the same look to their output.
It could mean less stress is on the CPU, meaning the physics can be more realistic and funner and the AI can be smarter, giving a better gaming experience.
^_^
Even though I haven't thought of that when I wrote my comment, this is a very interesting thing.
In old games, to get to a high place, you need to find the correct set of crates/ledges that just "happen to be there" if such existed, or click a specific button that will let you eradicate your enemies fast.
In new games, they just put reasonable world features in a way that you can CLIMB on them and get where you want to go, even if the game designers didn't think going there could help. Or just place some barrels somewhere and u could shoot/push them and expect them to roll down on your enemies.
It becomes so that there is more than one way to achieve your goal.
It's funner to see your char doesn't need to find a teleporter to go over a 0.5meter ledge (doom2, lvl2) but do what YOU as the player would like to do at that situation.
Ofcourse the devs need to make sure you don't go to places you shouldn't go to if the storyline dictates, but not thru stupid things like tiny wall that a human could easily pass.
^_^
Games aren't going to use the standard fixed-function pipeline any more- they're all going to use the same shader programs. There's only one "best" way to implement character model normal mapping, and that's polybump, which virtually everyone is using for upcoming games. There are only 2 ways to do shadows, shadow buffers or stenciling, and both of those are very common. The only exceptions are going to be games making really unusual style choices like Jet Set Radio Future. What's really going to differentiate games in the future is going to have to be something other than graphics and physics, as those fields tend to converge onto a single "one true implementation" as they evolve (for graphics it's photorealism, for physics it's something like Havok which is available for anyone to just drop into their games).
This is what a typical Metroid game already gives you. You can spend a lot of time just trying to get somewhere you aren't really supposed to and sometimes it works... you can even bypass large sections of the game if you work at it.
Picking three examples that use 2 simplistic effects doesn't do justice to the breadth of graphical wizardry that has come about and been *enhanced* because of a programmable pipeline. Note the word "enhanced"-all of those effects were achievable on a CPU. It just wouldn't be good for game performance to do them that way.
I stand by all my points; though I'll only address the mathematical point:
The proof you indicated is a proof of triangulation. Triangulation only applies to closed 2D polygons. We're dealing with 3-space polygons who's cartesian projection does not always form a polygon or set of polygons. Subsequently the statement inquestion is indeed false.
On the subject of triangulation, there are many finite polygons who's triangulation requires an infinite number of triangles to construct. Subsequently, realtime 3D polygon based applications restrict what polygons can be presented and often incorporate failure cases.
The point is that treatments of mathematical subjects, including computer graphics and the article in question, should be presented with at least a minimal degree of rigor. I wouldn't expect proofs, but I do expect at least accurate and fairly precise statements.