Actually, if you want to produce an image without aliasing, you need to evaluate multiple geometry samples per pixel.
e.g. if the edge of some geometry cut a 2D line through a pixel's bounding box, so that only 40% of the pixel is filled with that geometry, then to produce a correct image you need to find out which geometry fills the other 60% of the pixel.

I don't see how this will be a problem. It will find an intersection with accuracy equal to how many times you want to repeat the intersection finding process.
And yes I know what ray tracing is, just not a whole lot about it. I usually hear it described as just moving in a fixed step from a to b looking for a ray-polygon intersection, so I assumed what I described was different.

The above quote is assuming that your ray-collision algorithm is not all all affected by the amount of objects in the scene or visible to the camera

I was thinking of the time it takes to find a collision being equal to the time it would take to to march from point a to point b in the smallest interval you allow it to use. But now that I think about it, if you add objects in the scene, you have to check each object per ray movement, so it would add up time. But without any objects and just rendering a height field, wouldn't there be a maximum time it could take per pixel?

I found another hole in my method though. When moving along the ray at a large interval, you could potentially miss the first intersection of the geometry and find another intersection and think it is the first.
But my methods for doing this aren't really the point in this post. I honestly don't know a lot about this stuff. I just wanted to see if a "one vertex per pixel" algorithm has been made, or even something similar, because I find it very interesting.

Actually, if you want to produce an image without aliasing, you need to evaluate multiple geometry samples per pixel.
e.g. if the edge of some geometry cut a 2D line through a pixel's bounding box, so that only 40% of the pixel is filled with that geometry, then to produce a correct image you need to find out which geometry fills the other 60% of the pixel.

I don't see how this will be a problem. It will find an intersection with accuracy equal to how many times you want to repeat the intersection finding process.
And yes I know what ray tracing is, just not a whole lot about it. I usually hear it described as just moving in a fixed step from a to b looking for a ray-polygon intersection, so I assumed what I described was different.

The above quote is assuming that your ray-collision algorithm is not all all affected by the amount of objects in the scene or visible to the camera

I was thinking of the time it takes to find a collision being equal to the time it would take to to march from point a to point b in the smallest interval you allow it to use. But now that I think about it, if you add objects in the scene, you have to check each object per ray movement, so it would add up time. But without any objects and just rendering a height field, wouldn't there be a maximum time it could take per pixel?