Saturn was maxed out in the first games with virtua fighter remix and other games that I won't name to avoid unnecessary debates
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No it wasn't, this is just comedy now. Even stuff like the 3D stage in Sonic Jam or titles like Bulk Slash show otherwise.
I don't understand 2d but I realize that even without the cartridge the Sega Saturn can get animated backgrounds and vdp2 effects like 2d fog. I believe that the second sh2 influences or perhaps it is the ps1's limitation of making 4,096 sprites through triangles and storing it in the 1mb vram, the Saturn can access an additional 0.5mb of vdp2's vram.
PS1 has its own strength in 2d, its texturing capabilities, lighting and other effects associated with 3D are extra strength over Saturn in this requirement.
Street Fighter Alpha 3 is the best of both, as much as Sega Saturn fans insist on denying it, the PlayStation version is efficient while Saturn's 3d does not . that's the difference.
The PS1 is better at 2D than people give it credit for, agreed.
However, you're underselling the Saturn's 2D advantages. VDP2 could draw effectively infinitely-sized (technically 4096 x 4096 IIRC, which was massive back in the mid '90s) background planes with full Mode 7-style scrolling, which could take off a lot of polygon-crunching load from the GPU. On PS1, making similar planes required dedicating tons of polygons. FWIW, the PS1's GTE is very powerful and actually limited in its cap by the CPU if anything, but due to that it would potentially have an issue with background planes as large or detailed as Saturn's in a game using a mix of 2D & 3D.
Not that it wouldn't be able to do it; the PS1 definitely could. I just think it'd be a bit more taxing so less left over for polygonal processes or CPU-bound logic. But that's why I used the specific example of 2D/3D game hybrids, and it was mostly impractical at the time because most devs were leaning to 3D. For whatever 2D elements they used in games, it was mainly character sprites or different special effects, or HUD elements. In all those cases, PS1 had no issues keeping up with the Saturn.
So we'd have to be talking about a very specific type of 2D/3D hybrid game also requiring vast open fields and areas, lots of sprites, and a similar polygon & sprite budgets on both platforms while achieving the same frame rate for both systems.
But I think this kind of example is unfair because it would likely put the PS1 at a bigger handicap in terms of cutting off its polygonal budget, even if the Saturn would also be somewhat less handicapped by not pushing VDP2 to
its absolute max..
We indeed know for a fact that there is a lot of texture wobbling on PS1, and this does not affect Saturn. So yes, there are many PS1 games where it looks pretty bad. This is due to the fact that it uses triangles and lacks perspective correction, which is not an issue on quads. So at least that makes one argument in favor of quads, as well as having to push less polygons to draw the same amount of visuals. So that's a second argument as well.
Texture warping on the borders of the screen happen for both consoles.
FWIW, neither console supported floating point, only fixed-integer math. That's the reason for texture distortion on PS1, but there are some instances of supposed texture distortion that's actually deliberate texture being moved across polygon surfaces.
I think the main reason texture distortion happened less on Saturn was because of both the use of quads, and hard-mapping textures to quadratic surfaces. But that came with drawbacks which would happen when trying to fold two points to form a triangular polygonal surface, and also for transparency in 3D games (which is why Saturn relied so much on dithered meshes & CRT blending to give the illusion of transparent shadows).