[Blinn78] describes how clipping can be done in 4D homogeneous space (Figure 5.29). After the perspective divide, points inside the view frustum are in normalized device coordinates and bounded as follows:
That is, the points are bounded by the simple 4D planes:
Left: w = −x
Right: w = x
Bottom: w = −y
Top: w = y
Near: z = 0 Far:
z = w Once we know the frustum plane equations in homogeneous space, we can apply a clipping algorithm (such as Sutherland-Hodgeman). Note that the mathematics of the segment/plane intersection test generalizes to , so we can do the test with 4D points
and the 4D planes in homogeneous clip space.