With the understanding that at some point, all graphics have to be converted to pixels to be displayed on a monitor, would it be possible to make 3D graphics, including polygon-based objects, texture mapping and lighting effects, using vectors instead of pixels?
If it would be possible, what would be the advantages and disadvantages?
How would those differ from using vector-based graphics in a 2D game?
I’m not sure what you are asking. The use of polygonal projections and solids modeling are common in movies. Most of this is now hidden from the viewer with surface effects such as texture mapping. In the simplest display form polygonal projections are shown as a set of lines, if that’s what you mean by vectors. But except for that simplistic display mode the vectors defining the shape are just used to compute the bounds and orientation of a polygonal surface.
The advantage of 3D over 2D is that it looks better. The disadvantage is a lot more CPU time needed to compute points in 3D space, and generally a lot more storage also. Adding lighting effects and texture mapping just increases those requirements.
I also need clarification of what you mean. Virtually all 3D graphics are vectors at their core: it’s just far to expensive to manipulate every pixel independently. If my graphical dinosaur swings it’s tail, I do vector operations on the “bones” to determine the new location, which then maps to vector operations on the polygons of the “skin” to determine their new location, orientation, and lighting, and only then does texture mapping operate at the pixel level.
Most mapping and lighting effects are also at least partly vector: the texture map itself might be pixels (although vector graphics work, too), but certainly determining it’s position in space and “edges” in the projection onto the screen are vector operations.
Computer graphics tend to be either vector-based (the thing Illustrator is for) or pixel/bitmap-based (the thing Photoshop is for). I’m asking about the advantages and disadvantages of using Illustrator-type graphics as opposed to Photoshop-type graphics.
I don’t know much about Illustrator, so I have to make a lot of assumptions, but it appears to be using font definition and rendering techniques to produce images. I don’t know how much 3D capability it has, but defining stroke lines in 3D is a pretty simple adjustment from 2D. However depending on the details of how it works it may not be the best method of defining 3D shapes for animation, and rendering time may increase rapidly with the complexity of the image. If you were trying to create and animate images of soldiers you may be better off with 2D images that you call pixels. For more realistic graphics you’d need true 3D rendering which would require a lot more horsepower. If you were creative you can probably use the Illustrator images to make a nice video game, but it wouldn’t be useful for creating arbitrary shapes or graphical realism.
ETA: You linked to a very broad definition of vector graphics that includes most graphic techniques.
The 3D equivalent of vectors are nurbs, but they’re not used much anymore because working in straight polygon mode is just plain easier and now better. Like you said, it’s all coverted to and displayed as pixels on the screen. The advantage of vectors in Illustrator is that you don’t lose fidelity when scaling or printing. That is not a consideration in video games.
Some early (like early 1980s) arcade games used vector lines to create a three dimensional environment, rendered as white lines against a black background. It was remarkable for the time. Lack of texture and difficulty seeing what was what limited its appeal.
So I’m assuming you’re talking about texture maps, bump maps, and other such “skins” on the polygon mesh. As you’ve gathered, nobody uses vector art for that (although the original artwork may be–in fact probably is–vector, then converted to bitmaps at various resolutions. Artists are far more likely to work in Illustrator than Photoshop for these sorts of things).
The major advantage of vector is scaling: they stay sharp at any size or orientation. That could be an advantage (you’ve no doubt seen video games where a “mountainside” rock texture gets stretched way out and looks dorky because of a quirk of terrain), but not much of one: generally speaking, the size of a texture onscreen is pretty limited, and for the variation that does exist, mipmaps provide an easy solution.
The real downside of vector though, would come when it comes time to render them. Pretty much all the texture/skin/bump/lighting algorithms come to a point (many, many times) where they say, effectively “OK, what’s the texture value at this location in the texture?” For a bitmap, that’s basically an array lookup (i.e. very cheap). For a vector piece, it might involve lots of operations to determine if you’re inside a polygon or even a Bezier path. Think of how long a large PDF takes to render: now imagine doing that for every polygon or even every pixel of a polygon.
You don’t HAVE to use pixels. The old-school arcade games like Asteroids didn’t have pixels. They drove the electron gun in the CRT directly, drawing lines on the phosphorescent screen.
If you’re using modern hardware, you could bypass bitmapped textures by writing a shader that transforms vector graphics into screen pixels on the fly. Here’s an example: http://http.developer.nvidia.com/GPUGems3/gpugems3_ch25.html