subpolygons

A subpolygon is a polygon that is contained entirely within another polygon. The boundary of a subpolygon can intersect the boundary of the containing polygon at most at vertices, and it must lie strictly in the interior of the containing polygon except for these shared vertices. In simpler terms, a subpolygon is a "hole" or a region enclosed by edges within a larger polygonal area.

The concept of subpolygons is particularly relevant in computational geometry and computer graphics. For instance, in representing complex shapes, a polygon might be defined with a main outer boundary and one or more inner boundaries, each of which constitutes a subpolygon. These subpolygons define areas that are excluded from the main shape.

When performing operations on polygons, such as area calculation or point-in-polygon tests, the presence of subpolygons needs to be considered. For example, a point might be inside the outer boundary of a polygon but outside its subpolygons, thus not being considered part of the overall shape. The number and arrangement of subpolygons can affect the complexity of algorithms that process polygonal regions.

The definition of a subpolygon typically implies that it does not overlap with the boundary of the containing polygon except at shared vertices. This distinction is important for clearly defining the regions belonging to a polygon with holes.