Fastest way of converting a quad to a triangle strip?

Question

What is the fastest way of converting a quadrilateral (made up of four x,y points) to a triangle strip? I'm well aware of the general triangulation algorithms that exist, but I need a short, well optimized algorithm that deals with quadrilaterals only.

My current algorithm does this, which works for most quads but still gets the points mixed up for some:

#define fp(f) bounds.p##f

/* Sort four points in ascending order by their Y values */
point_sort4_y(&fp(1), &fp(2), &fp(3), &fp(4));

/* Bottom two */
if (fminf(-fp(1).x, -fp(2).x) == -fp(2).x)
{
    out_quad.p1 = fp(2);
    out_quad.p2 = fp(1);
}
else
{
    out_quad.p1 = fp(1);
    out_quad.p2 = fp(2);
}

/* Top two */
if (fminf(-fp(3).x, -fp(4).x) == -fp(3).x)
{
    out_quad.p3 = fp(3);
    out_quad.p4 = fp(4);
}
else
{
    out_quad.p3 = fp(4);
    out_quad.p4 = fp(3);
}

Edit: I'm asking about converting a single quad to a single triangle strip that should consist of four points.

Answer 1

Given a quad A B C D we can split it into A B C, A C D or A B D, D B C.

Compare the length of A-C and B-D and use the shorter for the splitting edge. In other words use A B C, A C D if A-C is shorter and A B D, D B C otherwise.