symm_difference_closed_polygons_xld — Compute the symmetric difference of closed polygons.
symm_difference_closed_polygons_xld calculates the
symmetric difference of the regions enclosed by the polygons
Polygons2. The boundaries of this symmetric
difference are returned in
If the individual input polygons are not closed, they are closed automatically by connecting their start and end points.
Internally, first, the regions enclosed by each set of polygons
Polygons2, respectively) are determined as
described below. Then, the symmetric difference of these two regions is
In the following, the two sets of input polygons are referred to as
boundary sets. A boundary set consists of an arbitrary number of
boundaries (the individual polygons of
Polygons2, respectively). Each boundary may be convex or concave and
self-intersecting. Internal holes may be formed by the nesting of boundaries.
The region enclosed by such a boundary set is defined by the so-called Even-Odd-Rule. Thus, it consists of all points with the following property: The line constructed by connecting the point with another reference point that lies outside of the region has an odd number of intersections with boundaries.
More descriptive, this means that a boundary defines a hole in the region enclosed by another boundary if it lies completely inside that region. Similarly, the overlapping area of two separate boundaries of one boundary set is taken as a "hole", i.e., it does not belong to the region enclosed by the two boundaries. Note that the region enclosed by a boundary does not depend on the orientation of the boundary.
A self-intersecting boundary may be split at the intersection point or it is reordered such that it touches itself at the intersection point. The resulting boundaries are treated as separate boundaries.
The resulting polygons
PolygonsDifference contain no references to
the XLD contours that are possibly referenced by
Polygons2. Hence, operators that access the contours associated with
a polygon, e.g.,
split_contours_xld will not work correctly.
Polygons enclosing the first region.
Polygons enclosing the second region.
Polygons enclosing the symmetric difference.
symm_difference_closed_polygons_xld returns TRUE if all parameters
are correct. If necessary, an exception is raised.