基于ArcGIS Engine的任意多边形凸剖分算法
任意多边形凸剖分对于编程人员来说是经常遇到的问题，当然算法也很多，但是大多很复杂，如果从底层来编写，非常繁琐
下面介绍一种基于AE的方法，理解起来，编写起来都比较简单，供大家参考
算法思想:
1、首先找到该多边形的包罗矩形（IGeometry.Envelope）
2、然后将该多边形的顶点集合（IPointCollection）按照X坐标（或Y坐标）进行从小到大（或从大到小）排序
3、然后过排序后的多边形顶点从小到大（或从大到小）绘制竖直（或水平）的直线
4、绘制的直线与多边形边界相交，就将该多边形分割成为若干个凸多边形。
附VB.Net源码
''' <summary>
''' 得到任意多边形的剖分凸多边形集合
''' </summary>
''' <param name="pGeo">任意多边形</param>
''' <returns>剖分凸多边形集合</returns>
''' <remarks></remarks>
Private Shared Function GetSolidHatchs(ByVal pGeo As IGeometry) As IGeometryCollection
Dim pPoints As IPointCollection = pGeo
Dim pXs As New List(Of Double)
For i As Integer = 0 To pPoints.PointCount - 1
pXs.Add(pPoints.Point(i).X)
Next
'’对该多边形边界的所有点集合以X或Y为标准进行排序，用于画切割线
pXs.Sort()
Dim pGeos As IGeometryCollection = New Polygon
Dim pTopo As ITopologicalOperator = pGeo
Dim listCount As Integer = pXs.Count
Dim leftGeo As IGeometryCollection = New Polygon
Dim rightGeo As IGeometryCollection = New Polygon
For i As Integer = 0 To listCount - 1
If pTopo.Boundary.IsEmpty Then Continue For
If pXs(i) <= pTopo.Boundary.Envelope.XMin Or pXs(i) >= pTopo.Boundary.Envelope.XMax Then Continue For
Dim cutLine As IPolyline = New Polyline
Dim fromPoint As IPoint = New Point
fromPoint.PutCoords(pXs(i), pTopo.Boundary.Envelope.YMax)
Dim toPoint As IPoint = New Point
toPoint.PutCoords(pXs(i), pTopo.Boundary.Envelope.YMin)
''生成切割线
cutLine.FromPoint = fromPoint
cutLine.ToPoint = toPoint
''用切割线切割多边形
Try
pTopo.Cut(cutLine, leftGeo, rightGeo)
Catch ex As Exception
Continue For
End Try
''一条切割线切割出两个多边形，rightGeo是凸的，leftGeo继续用于切割
pTopo = leftGeo
For j As Integer = 0 To rightGeo.GeometryCount - 1
pGeos.AddGeometry(rightGeo.Geometry(j))
Next
Next
If Not rightGeo Is Nothing Then
For j As Integer = 0 To leftGeo.GeometryCount - 1
pGeos.AddGeometry(leftGeo.Geometry(j))
Next
End If
If pGeos.GeometryCount = 0 Then
For j As Integer = 0 To CType(pGeo, IGeometryCollection).GeometryCount - 1
pGeos.AddGeometry(CType(pGeo, IGeometryCollection).Geometry(j))
Next
End If
Return pGeos
End Function
通过线构造面（C# + ArcGIS Engine 9.2）
生成面之前的截图：
生成为面之后的截图：
从线生成面的方法代码：
///通过线创建面
///</summary>
///<paramname="pPolyline">线</param>
///<returns>面</returns>
IPolygonConstructPolygonFromPolyline(IPolylinepPolyline)
{
IGeometryCollectionpPolygonGeoCol=newPolygonClass();
if((pPolyline!=null)&&(!pPolyline.IsEmpty))
{
IGeometryCollectionpPolylineGeoCol=pPolylineasIGeometryCollection;
ISegmentCollectionpSegCol=newRingClass();
ISegmentpSegment=null;
objectmissing=Type.Missing;
for(inti=0;i<pPolylineGeoCol.GeometryCount;i++)
{
ISegmentCollectionpPolylineSegCol=pPolylineGeoCol.get_Geometry(i)asISegmentCollection;
for(intj=0;j<pPolylineSegCol.SegmentCount;j++)
{
pSegment=pPolylineSegCol.get_Segment(j);
pSegCol.AddSegment(pSegment,refmissing,refmissing);
}
pPolygonGeoCol.AddGeometry(pSegColasIGeometry,refmissing,refmissing);
}
}
returnpPolygonGeoColasIPolygon;
}
调用示例：
IFeatureLayerpFeatureLayer=pLayerasIFeatureLayer;
IFeatureClasspFeatureClass=pFeatureLayer.FeatureClass;
if(pFeatureClass.ShapeType==esriGeometryType.esriGeometryPolyline)
{
IFeatureCursorpFeatureCursor=pFeatureClass.Search(null,false);
IFeaturepFeature=pFeatureCursor.NextFeature();
ILayerpTargetLayer=axMapControl1.get_Layer(2);
IFeatureLayerpTargetFeatureLayer=pTargetLayerasIFeatureLayer;
IFeatureClasspTargetFeatureClass=pTargetFeatureLayer.FeatureClass;
if(pTargetFeatureClass.ShapeType==esriGeometryType.esriGeometryPolygon)
{
IPolygonpPolygon=null;
while(pFeature!=null)
{
IPolylinepPolyline=pFeature.ShapeasIPolyline;
pPolygon=ConstructPolygonFromPolyline(pPolyline);
if((pPolygon!=null)&&(!pPolygon.IsEmpty))
{
if(!pPolygon.IsClosed)
{
pPolygon.Close();
}
IFeaturepNewFeature=pTargetFeatureClass.CreateFeature();
pNewFeature.Shape=pPolygon;
pNewFeature.Store();
pFeature.Delete();
}
pFeature=pFeatureCursor.NextFeature();
}
}
}
axMapControl1.ActiveView.PartialRefresh(esriViewDrawPhase.esriViewGeography,null,null);