A MultiPolygon is a geometric collection whose elements
are polygons. The interiors of any two polygons in a
MultiPolygon may not intersect. The boundaries of any two
elements in a MultiPolygon may intersect at most at a
finite number of points.
The assertions for MultiPolygons are:
1. The interiors of 2 Polygons that are elements of a
MultiPolygon may not intersect. ∀ M ∈ MultiPolygon, ∀ Pi,
Pj ∈ M.Geometries(), i≠j, Interior(Pi) ∩ Interior(Pj) = ∅
2. The Boundaries of any 2 Polygons that are elements of
a MultiPolygon may not ‘cross’ and may touch at only a
finite number of points. (Note that crossing is prevented
by assertion 1 above). ∀ M ∈ MultiPolygon, ∀ Pi,
Pj ∈ M.Geometries(), ∀ ci ∈ Pi.Boundaries(),
cj ∈ Pj.Boundaries() ci ∩ cj = {p1, ….., pk | pi ∈ Point,
1 <= i <= k}
3. A MultiPolygon is defined as topologically closed.
4. A MultiPolygon may not have cut lines, spikes or punctures,
a MultiPolygon is a Regular, Closed point set:
∀ M ∈ MultiPolygon, M = Closure(Interior(M))
5. The interior of a MultiPolygon with more than 1 Polygon
is not connected, the number of connected components of the
interior of a MultiPolygon is equal to the number of Polygons
in the MultiPolygon.
The boundary of a MultiPolygon is a set of closed curves
(LinearRings) corresponding to the boundaries of
its element Polygons. Each Curve in the boundary of the
MultiPolygon is in the boundary of exactly 1 element Polygon,
and every Curve in the boundary of an element Polygon is in
the boundary of the MultiPolygon.
Inheritance Hierarchy
Namespace: ArtDatabanken.WebService.DataAssembly: ArtDatabanken.WebService.Data (in ArtDatabanken.WebService.Data.dll) Version: 1.3.0.0 (1.3.0.0)
Syntax public class WebMultiPolygon : WebData
Public Class WebMultiPolygon
Inherits WebData
public ref class WebMultiPolygon : public WebData
type WebMultiPolygon =
class
inherit WebData
end
The WebMultiPolygon type exposes the following members.
Constructors Properties
| Name | Description |
---|
| Polygons |
Polygons that defines the multi polygon.
|
TopSee Also