Polygon with holes
From Wikipedia, the free encyclopedia
In geometry, a polygon with holes is an area-connected planar polygon with one external boundary and one or more interior boundaries (holes).[1] Polygons with holes can be dissected into multiple polygons by adding new edges, so they are not frequently needed.
An ordinary polygon can be called simply-connected, while a polygon-with-holes is multiply-connected. An H-holed-polygon is H-connected.[2]
Degenerate cases may be considered, but a well-formed holed-polygon must have no contact between exterior and interior boundaries, or between interior boundaries. Nondegenerate holes should have 3 or more sides, excluding internal point boundaries (monogons) and single edge boundaries (digons).
Boundary orientation
Area fill algorithms in computational lists the external boundary vertices can be listed in counter-clockwise order, and interior boundaries clockwise. This allows the interior area to be defined as left of each edge.[3]
Conversion to ordinary polygon
A polygons with holes can be transformed into an ordinary unicursal boundary path by adding (degenerate) connecting double-edges between boundaries, or by dissecting or triangulating it into 2 or more simple polygons.
Example conversion of a single-holed polygon by connecting edges, or dissection
