I'm not quite sure whether you understood the sutherland-hodgman algorithm correctly (or at least I didn't get your example). Thus I will prove here, that it doesn't make any difference whether clipping happens before or after the perspective divide. The proof is only shown for one plane (clipping has to be done against all 6 planes), since applying multiple such clipping operations after each other makes not difference here.
Let's assume we have two points (as you described) R' and S' in clip space. And we have a clipping plane P given in hessian normal form [n, p] (if we take the left plane this is [1,0,0,1]).
If we would be calculating in pure 3d space (R^3), then checking whether a line crosses this plane would be done by calculating the signed distance of both points to the plane and checking if the sign is different. The signed distance for a point X = [x/w,y/w,z/w] is given by
D = dot(n, X) + p
Let's write down the actual equation we have (including the perspective divide):
d = n_x * x/w + n_y * y/w + n_z * z/w + p
In order to find the exact intersection point, we would, again in R^3 space, calculate for both points (A = R'/R'w, B = S'/S'w) the distance to the plane (da, db) and perform a linear interpolation (I will only write the equations for the x-coordinate here since y and z are working similar):
x = A_x * (1 - da/(da - db)) + A_y * (da/(da-db))
x = R'x/R'w * (1 - da/(da - db)) + S'x/S'w * (da/(da-db))
And w = 1 (since we interpolate between two points both having w = 1)
Now we already know from the previous discussion, that clipping has to happen before the perspective divide, thus we have to adapt this equation. This means, that for each point, the clipping cube has a different scaling w. Lt's see what happens when we try to perform the the same operations in P^3 (before the perspective divide):
First, we "revert" the perspective divide to get to X=[x,y,z,w] for which the distance to the plane is given by
d = n_x * x/w + n_y * y/w + n_z * z/w + p
d = (n_x * x + n_y * y + n_z * z) / w + p
d * w = n_x * x + n_y * y + n_z * z + p * w
d * w = dot([n, p], [x,y,z,w])
d * w = dot(P, X)
Since we are only interested in the sign of the whole calculation, which we haven't changed by our operations, we can compare the D*ws and get the same inside-out result as in R^3.
For the two points R' and S', the calculated distances in P^3 are dr = da * R'w and ds = db * S'w. When we now use the same interpolation equation as above but for R' and S' we get for x:
x' = R'x * (1 - (da * R'w)/(da * R'w - db * S'w)) + S'x * (da * R'w)/(da * R'w - db * S'w)
On the first view this looks rather different from the result we got in R^3, but since we are still in P^3 (thus x'), we still have to do the perspective divide on the result (this is allowed here, since the interpolated point will always be at the border of the view-frustum and thus dividing by w will not introduce any problems). The interpolated w component is given as:
w' = R'w * (1 - (da * R'w)/(da * R'w - db * S'w)) + S'w * (da * R'w)/(da * R'w - db * S'w)
And when calculating x/w we get
x = x' / w';
x = R'x/R'w * (1 - da/(da - db)) + S'x/S'w * (da/(da-db))
which is exactly the same result as when calculating everything in R^3.
Conclusion: The interpolation gives the same result, no matter if we perform the perspective divide first and interpolation afterwards or interpolating first and dividing then. But with the second variant we avoid the problem with points flipping from behind the viewer to the front since we are only dividing points that are guaranteed to be inside (or on the border) of the viewing frustum.
winstead of 1. Everything else works completely similar. – Pantsuit