Since vector-based topological map overlay operations involve overlaying the point, line, or polygon features of one layer on the polygon features of another layer, the three following processing algorithms are fundamental:

Point-in-Polygon
Line-in-Polygon
Polygon-on-Polygon (ie. Polygon Overlay)

Note: As polygons are made up of line segments, Polygon-on-Polygon processing uses essentially the same algorithm as Line-in-Polygon processing. Therefore, the Point-in-Polygon and Line-in-Polygon algorithms are worked through in detail.

Point in Polygon
Step through the Point in Polygon processing algorithm used in vector based GIS
Line in Polygon
Step through the Line in Polygon processing algorithm used in vector based GIS