AutoCAD Map 3D 2009 Geospatial Platform Reference

Remarks:

Class	Boundary
MgPoint, MgMultiPoint	Empty set.
MgLineString, MgCurveString	If closed: empty set. If not closed: 2 end points.
MgMultiLineString, MgMultiCurveString	Points that are in the boundaries of the element curves after application of the 'Mod 2' union rule (see below).
MgPolygon, MgCurvePolygon	Its set of Rings.
MgMultiPolygon, MgMultiCurvePolygon	The set of Rings of its polygons.
MgMultiGeometry	Points that are in the boundaries of the heterogenous element geometries after application of the 'Mod 2' union rule (see below).

Returns:

An MgGeometry that represents this geometric entity's boundary.

'Mod 2' Union Rule

[OGC99-049 ] references [OGC96-015R1 ] for the definition of this rule. In section 3.12.3.2 [OGC96-015R1] states the following:
"For complex geometries, we take the 'mod 2' union of the components. That means that a point is in the boundary of a complex object (represented as disjoint representational geometries) if it is in an odd number of the boundaries of its component simple geometries."

The following illustrations are inspired by the discussion in section 8.2.5 of [JTS1.4 ].

Case	Boundary
1	a, b, c, d
2	a, b, c, d
3	a, d
4	a, b, e, d
5	b, c, polygon((d, e, f, g))
6	b, (polygon((d, e, f, g)) - c)