Ok, this was what I found. I'll try and look for some tutorials too.

http://en.wikipedia.org/wiki/Scanline_rendering
http://en.wikipedia.org/wiki/Volume_rendering

As for the voxel tutorial, this is what I found:
http://www.advsys.net/ken/voxlap/voxlap05.htm
http://www.flipcode.com/voxtut/
https://sites.google.com/site/letsmakeavoxelengine/

Hope this helps. Also let us know what you decide to do, can't wait to see some results 

I think good speed in Axe other than maybe raycasting (unless TheMachine02's game isn't raycasting) is virtually impossible unless someone writes a 3D axiom.

well,well...
as I said before, I use a combinaison of vexel and raycasting, so I manage to have some speed, and texture, etc...
after the contest, I will try to speed it up again, to add more efficienty texturing, and Y rotation : for me, it's enough to do a good game.

So, I've looked into your links @V1mes, and didn't found anything really helpful. The Wikipedia entries only explains the main goal of the techniques and the voxels tutorial either use a 3D library or are concept-oriented.

Let's point out what I really want to do : after some researches (unsuccessful of course), it appears that I want to build a voxel engine from scratch ; not necessarily in Axe for the moment, but I want to be able to build one and then eventually to port it to Axe.

I looked for tutorials that don't use any 3D libraries and that explains the theory with examples (the exact concept of the Site Du Zéro in fact), but as you might guess I didn't found anything (but it's maybe because I don't understand English as good as I understand French ). So if you know something that can be helpful for me, just point it out.

I just programmed a simple voxel/isometric engine from scratch that works decently. As long as the world doesn't get updated a lot, it should be fast enough for calcs as well. Unfortunately, it can only show the world in a fixed isometric persfective. If you mess around with it a bit, the best you could get is isometric with 4 possible camera angles (northeast, southeast, southwest and northwest).

If you want, I can send you the algorithms.

EDIT: screenshot of how it looks on a computer:

Something like Marble Madness using something like the above would be nice. Or Final Fantasy Tactics, but that would be a huge project to take on >.<

Would such engine be fast enough for the calc to handle the golf game Kirby Bowl/Dream Course?

Actually the above by Ben_g and Materey is more Isometric it seems. But yeah a voxel engine would be nice on the z80 models. Also the animated screenshots for the 68K one is much faster than on the real calc if I remember, so maybe on a 84+ it might be a tad slow to be playable. It wouldn't hurt to try, though.

Actually the above by Ben_g and Materey is more Isometric it seems. But yeah a voxel engine would be nice on the z80 models. Also the animated screenshots for the 68K one is much faster than on the real calc if I remember, so maybe on a 84+ it might be a tad slow to be playable. It wouldn't hurt to try, though.

I do indeed use isometric sprites to display the blocks. This does limit the possible camera angles to 4, but it's way faster than a raycasting-based method, and to do raycasting with a reasonable speed, the resolution will probably be quite low as well. With the isometric technique, it's also relativly easy to add grayscale and textures.

Because of this, the best way to handle a voxel world on a z80 calc is probably isometric. (Well, at least untill TI stops putting prehistoric hardware in them)

That reminds me ben_g, were you still planning to work on your 3D engine/game for the 83+ and your computer game at one point?

Well, I am currently working on the computer game. The 3D engine is currently on hold. It's not dead, I'm going to pick the 3D engine back up when I'm tired of working on my computer game. That's how I code.