@ WouterH - For realtime rendering you should be looking at using a scanline polygon fill.
Basically using the bresenham algorithm you step pixel by pixel down the two sides of the polygon and draw a line between the two opposing points. This can be nicely optimized because you know the start and end X coordinates and Y is the same so rahter than filling pixel by pixel you can word fill and only special case the start an end which migt not be on a word boundary. Of course when the triangle is rotated, one of the sides ends before the other, at that point you just swtich to the next line can continue.
I have attached a primitive drawing to help explain.