Summary

The curve geometry classes are MgCurveString, MgMultiCurveString, MgCurvePolygon, and MgMultiCurvePolygon.

A provider may not support the construction of curve geometries or may not support their construction in all coordinate systems.

The fundamental building block of the curve geometries is the curve segment. MgCurveSegment is the abstract base class, and MgLinearSegment and MgArcSegment are two concrete classes.

These two classes are classified as geometry components; they are not geometries but are used to construct geometries. The coordinates defining an MgLinearSegment are interpolated linearly. The three coordinates (start, end, and control) defining an MgArcSegment belong to a circle.

An MgCurveString is composed of a collection of connected curve segments, which is not closed. The ending coordinate of one segment is the starting coordinate of the next segment in the sequence. The ending coordinate of the last segment is not the starting coordinate of the first segment. The curve string as a whole cannot be self-intersecting.
An MgMultiCurveString is a geometry constructed from a collection of MgCurveString objects.
An MgCurveRing is also a geometry component. It is used to construct an MgCurvePolygon geometry. Like the MgCurveString, it is composed of a collection of connected curve segments. But unlike the MgCurveString, it is closed. That is, the ending coordinate of the last segment is the starting coordinate of the first segment.

An MgCurveRing can be constructed using a collection of curve segments containing only one member. An MgArcSegment can have a starting coordinate that is the same as the ending coordinate. This case places a special condition on the control point; it is taken to be the point diametrically opposed to the starting point.
An MgCurvePolygon consists of an exterior boundary defined by an MgCurveRing and an optional collection of inner boundaries ("holes").
An MgMultiCurvePolygon is a geometry constructed from a collection of MgCurvePolygon objects.