【IT168技术文档】
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
