How does mode 7 work? What do the registers do? Is there a formula that I need to use?

Abonetochew

You're asking a very big question. So, I'll just give a quick over view.

Normal backgrounds are like maps that can be shifted horizontally or vertically on the screen. The one background in Mode7 however can do more than just shifting, you can scale/rotate/warp it however you want with matrix operations.

How does the PPU know which pixel to display where? It puts the (x1,y1) coordinates of the pixel on the screen into the equation below. Which tells it what pixel (x2,y2) to take from the 'BG map'.

There are registers to allow you to set all the values in this matrix equation (a,b,c,d,x0,y0).

from the nintendo documentation:

		/ x2 \   / a b \ / x1-x0 \   / x0 \
		|    | = |     | |       | + |    |
		\ y2 /   \ c d / \ y1-y0 /   \ y0 /

		x0&y0: center coordinate
		x1&y1: display coordinate
		x2&y2: coordinate before calculation

an example matrix transformation from nintendo:
	to scale and rotate the picture -       

	a=cos(gamma)*(1/alpha), b=sin(gamma)*(1/alpha)
	c=-sin(gamma)*(1/beta), d=cos(gamma)*(1/beta)

  	gamma: rotation angle
  	alpha: reduction rates for x(h)
  	beta : reduction rates for y(v)

Is the NES capable of these operations, and thus, Mode 7?

Curse you, evil RF shielding! CURSE YOU, I SAY!
-MM007, the novice console case modder

It should be possible through software on the NES, by using bankswitching with extra CHR-RAM for the whole screen. I've never tried anything like that, but I imagine calculating stuff for every pixel involves major CPU usage. But it would be cool to see.

How hard would it be to make a demo of that for an NES emu?

Curse you, evil RF shielding! CURSE YOU, I SAY!
-MM007, the novice console case modder

An IRQ should be able to do trigger CHR-switching while the CPU is busy. But then we need a mapper that has more than 8KB of CHR-RAM, only Videomation and the Maxicart design have enough. And I don't think Videomation has an IRQ..

But 8KB could handle about half of the screen (which would go easier on the CPU, too).

So it doesn't look too hard really, just requires lots of math operations (something I have little experience with), that need to be done as quickly as possible. Kinda hard for me (I suck at math :P ), but it would be good for me to learn sometime. I always wanted to make a 3D demo for NES too, but never got around to figuring that out either. (but my 3D test program did make some neat-o patterns, heheh)

So how hard would it be to make a Mode 7 game, ex: an RPG, with 2-D characters for sprites and buildings? (Imagine if the original Final Fantasy used Mode 7! I get all drolly thinking about it!) Also, if Mode 7 games would be impossible, would isometric games work?

Curse you, evil RF shielding! CURSE YOU, I SAY!
-MM007, the novice console case modder

That's an interesting idea. While not impossible, it would probably be too slow or choppy to be good for an NES game. Plus the attribute tables would be pretty much unusable, so this mode on NES would be 4-colors, while SNES's mode 7 has 256 colors (one byte per pixel!)

I believe isometric games are tile-based by their nature, so that's suitable for the NES (look at Solstice, for example).

would isometric games work? I'd like to see an isometric RPG(maybe 8-bit theatre? ^^ That would rock) sometime. Heck, I'd buy it if it were on cart!

Curse you, evil RF shielding! CURSE YOU, I SAY!
-MM007, the novice console case modder

> I'd like to see an isometric RPG sometime.
What, like Super Mario RPG?

--
Quietust
P.S. If you don't get this note, let me know and I'll write you another.

More along the lines of Final Fantasy-type story if possible, like FF, FF V, or FF VII, if possible.

Oh! Did you hear that square is FINALLY gonna make a FF VII-2 for the PS2? I'd buy it. ^^

Curse you, evil RF shielding! CURSE YOU, I SAY!
-MM007, the novice console case modder