A legged robot walking on uneven terrain can avoid falling only by applying contact forces with its feet on the ground that compensate for gravity without causing slip. To plan safe motions, it is necessary to test this constraint at every posture explored at each set of foot placements. Since a huge number of postures may be explored, this test must be as fast as possible. Existing approaches either search explicitly for contact forces at each posture, or precompute the support polygon and check that the robot's center of mass lies above it. This paper presents a new algorithm that is faster than either existing approach. This algorithm is an incremental method of projection, that computes only enough of the support polygon to decide whether static equilibrium is possible at each posture. It takes advantage of information gained testing previous postures in order to test subsequent postures more quickly.