Grading algorithms used in some commercial civil engineering products employ a simple method of ray projection. A ray is simply projected from the footprint at the given criteria to find the intersection with the surface. This method does not fully resolve situations where the grading intersects itself in 3D, such as in a tight inside corner, or where the grading is projecting past the radius of the footprint, as shown in figure 8.
Figure 8: Projecting past the radius of a footprint
Figure 8 shows an example where the footprint has a rounded corner with a radius of 50 feet. Gradings are projected out 100 feet to the surface, and the gradings along two adjacent sides intersect far from the corner. The region of intersection can be quite complicated if the two segments have different footprint elevations or slope projections, resulting in ambiguous elevations where they meet.