Function to fill a triangle defined by points p1, p2 and p3 using their barycentric coordinates. The functions are made in Javascript, but the porting any language is easily.

FillTriangle.js

function f_ab(x, y, pa, pb)
{
  return (pa.y - pb.y) * x + (pb.x - pa.x) * y + pa.x*pb.y - pb.x*pa.y;
}

/// @param context the context of the canvas
/// @param p1, p2, p3 The three points of the triangle
function drawTriangle(context, p1, p2, p3)
{
  var bbox = {  top: {x: Math.min(p1.x, p2.x, p3.x), y:Math.min(p1.y, p2.y, p3.y)}, 
              right: {x: Math.max(p1.x, p2.x, p3.x), y:Math.max(p1.y, p2.y, p3.y)}};
  var x,y;
  for (y = bbox.top.y; y <= bbox.right.y; y++)
  {
    for (x = bbox.top.x; x <= bbox.right.x; x++)
    {
      var alpha = f_ab(x, y, p2, p3) / f_ab(p1.x, p1.y, p2, p3);
      var theta = f_ab(x, y, p3, p1) / f_ab(p2.x, p2.y, p3, p1);
      var gamma = f_ab(x, y, p1, p2) / f_ab(p3.x, p3.y, p1, p2);
      if(alpha >= 0 &&  alpha <= 1 && theta >= 0 &&  theta <= 1 && gamma >= 0 &&  gamma <= 1)
        setPixel(context, x, y, 240,190,0,1);
    }
  }
}