Question

我在这里重新使用了sijipie的代码：https://www.mrexcel.com/forum/excel-questions/713005-does-point-fall-within-polygon-visual-basic-applications-function.html

我需要做的是确定一条线是否在多边形内。

不可否认，这有点懒，因为我没有测试线与每一边的交点，因为我迭代线的中点并测试它们作为内点。

我想知道是否有更快的方法来做到这一点。

以下VBA代码：

Function PolyLineIntersect(lXY As Range, polyXY As Range) As Boolean
    Dim i As Integer, j As Integer, a As Integer, polySides As Integer
    Dim Result As Boolean
    Dim x As Double, y As Double
    Dim aXY As Variant
    Dim mXY(1 To 5, 1 To 2) As Integer
    Dim tXY(1 To 5) As Boolean

    x = lXY.Cells.value2(1, 1)
    y = lXY.Cells.value2(1, 2)
    xb = lXY.Cells.value2(1, 3)
    yb = lXY.Cells.value2(1, 4)

    mXY(1, 1) = x
    mXY(1, 2) = y
    mXY(2, 1) = xb
    mXY(2, 2) = yb
    mXY(3, 1) = (xb + x) / 2
    mXY(3, 2) = (yb + y) / 2
    mXY(4, 1) = (xb + mx1) / 2
    mXY(4, 2) = (yb + my1) / 2
    mXY(5, 1) = (xb + mx1) / 2
    mXY(5, 2) = (yb + my1) / 2

    Result = False

    aXY = polyXY.Value

    polySides = polyXY.Rows.Count
    j = polySides - 1
    For a = 1 To 5                
      x = mXY(a, 1)
      y = mXY(a, 2)                
      For i = 1 To polySides                     
        If (((aXY(i, 2) < y And aXY(j, 2) >= y) _
         Or (aXY(j, 2) < y And aXY(i, 2) >= y)) _
         And (aXY(i, 1) <= x Or aXY(j, 1) <= x)) Then                  
          Result = Result Xor (aXY(i, 1) + (y - aXY(i, 2)) / (aXY(j, 2) - aXY(i, 2)) * (aXY(j, 1) - aXY(i, 1)) < x)                            
        End If
        j = i        
      Next i
    Next a
    PolyLineIntersect = Result

End Function

Answer 1

使用cross product检查所有多边形顶点是否位于相对于给定线的同一半平面（左侧或右侧）中。如果是，则线不与多边形相交。

Side = Sign(CrossProduct(L2-L1, P[i] - L1))
where L1, L2 are points defining the line, P[i] is i-th polygon vertex

算法在线性时间O（N）中工作，其中N是多边形顶点计数。请注意，对于凸多边形，可以使用二分搜索在O（logN）时间推导出结果。

线是否与多边形相交？

1 个答案: