List Coordinates of Pixels Inside a Triangle

I'm making a game in C# and XNA, and I was trying to come up with a method to render massive terrains without using a tremendous amount of memory or passing the poly limit hard-coded into XNA.

My solution so far is to create a massive heightmap, and that heightmap is loaded into memory at the beginning of th开发者_StackOverflowe game in the initialization phase. Then, terrain is only generated nearest to the camera. This is accomplished by projecting a triangle whose vertex is the character and the other two endpoints extend to the sides of the character's viewing area. Then, all the pixels inside that triangle on the heightmap are rendered and drawn into the game, thus only rendering what is seen.

The problem is, I've successfully found (I think, can't test until I get terrain rendering) the three vertices of the triangle. Now I need to find a list of the coordinates for every single pixel inside that triangle - whole numbers only, because I just need a list of pixels to render.

I know it sounds a little confusing, so here's the gist of it:

I have an image, and I project a triangle onto that image. The only thing I know about that triangle are the three vertices. I need a list of the pixels inside that triangle.

I've been Googling around for maybe 20 minutes now, and I figured I midas well go ahead and post something here due to the fact that what I'm trying to do isn't all that common. If I find an answer, I'll be sure to post it here.

But until then, can anyone tell me how to accomplish this?

Edit: A formula, please. If you can provide a formula or algorithm, and an explanation, that would be just perfect.

Edit: I've posted a new question, as I've ditched this method of rendering large terrains. The question is here.

---

Start here:

http://mathworld.wolfram.com/TriangleInterior.html

One of the non-trivial problems, not mentioned there, that you have to deal with is the pixelization along the boundary.