Excess intersection formula

The excess intersection formula helps us accurately count intersections of geometric objects that don't intersect transversely, meaning they overlap more than just at a crisp point. When two shapes intersect with higher multiplicity—like overlapping along a line or area—the formula adjusts the count to reflect this "excess" intersection. It does so by subtracting the expected intersection count (assuming simple crossing) and adding back the "excess" intersection data, ensuring an accurate measure of how these objects truly intersect, accounting for multiplicities and overlaps.