基于ArcGIS Engine的任意多边形凸剖分算法

文章出处：http://www.cnblogs.com/wall/archive/2008/04/10/1147220.html

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