查找與同一矩形重疊的多個矩形的總重疊百分比？

Question

我有一個System.Drawing.RectangleF對象的列表，所有對象都重疊在同一個RectangleF對象上。在下面的圖片中，3個重疊的矩形將是粉紅色，黃色和紅色矩形。我的主矩形是淺藍色的矩形。

二圖片：

我知道，與RectangleF對象我可以使用Intersect()方法將返回我代表彼此重疊RectangleF對象。但據我所知，這隻在比較兩個矩形時才起作用。

我的問題是：我怎麼能確定的總面積/百分比（即紅色，黃色和粉紅色長方形的總和重疊相比，淡藍色的長方形 - 但它需要是足夠聰明，無法計算出紅色和黃色重疊的區域兩次，粉色和黃色的區域相同）？

注意：綠線代表我正在查找的區域，只是藍色矩形的總面積不可見。

UPDATE：我已經添加了第二張圖片以進一步說明我在找什麼。在第二張圖片中，勃艮第矩形的存在不應影響總覆蓋百分比，因爲該區域已被黃色和綠色矩形覆蓋。

Answer 1

OK，我想我找到了解決辦法使用Region，這似乎是工作均高於我的例子中圖片：

Private Function TotalCoveredAreaPercent(ByVal oRectToCheck As RectangleF, ByVal oOverlappingRects As List(Of RectangleF)) As Double 

    Dim oRegion As New Region(oRectToCheck) 
    Dim dTotalVisibleArea As Double = 0 
    Dim dTotalCoveredArea As Double = 0 

    'now we need to exclude the intersection of our 
    'overlapping rectangles with our main rectangle: 
    For Each oOverlappingRect As RectangleF In oOverlappingRects 

     oRegion.Exclude(RectangleF.Intersect(oRectToCheck, oOverlappingRect)) 

    Next 

    'now we have access to the non-overlapping 
    'rectangles that make up the visible area of our main rectangle: 
    Dim oVisibleRects As RectangleF() 

    oVisibleRects = oRegion.GetRegionScans(New Drawing2D.Matrix()) 

    'add the area of the visible rectangles together 
    'to find the total visible area of our main rectangle: 
    For Each oVisibleRect As RectangleF In oVisibleRects 
     dTotalVisibleArea += AreaOf(oVisibleRect) 
    Next 

    Dim dPercentVisible As Double = dTotalVisibleArea/AreaOf(oRectToCheck) * 100 

    'percent covered is 100 - the visible percentage: 
    Return (100 - dPercentVisible) 

End Function 

這似乎是相當不錯的了，而且是相當簡單的。

Answer 2

這是我的算法。關鍵是我們正在減去重疊的重疊。

Dim baseRect As New RectangleF(10, 10, 20, 20) 
    Dim otherRectList As New List(Of RectangleF) 
    otherRectList.Add(New RectangleF(5, 5, 10, 10)) 
    otherRectList.Add(New RectangleF(20, 20, 10, 10)) 
    otherRectList.Add(New RectangleF(10, 5, 10, 10)) 

    Dim overlapRectList As New List(Of RectangleF) 
    For Each otherRect As RectangleF In otherRectList 
     If RectangleF.Intersect(otherRect, baseRect) <> RectangleF.Empty Then 
     overlapRectList.Add(RectangleF.Intersect(otherRect, baseRect)) 
     End If 
    Next 

    Dim totalArea As Single = 0 
    For Each overlapRect As RectangleF In overlapRectList 
     totalArea += overlapRect.Width * overlapRect.Height 
    Next 

    'Subtract out any overlaps that overlap each other 
    For i = 0 To overlapRectList.Count - 2 
     For j = i+1 To overlapRectList.Count - 1 
     If i <> j Then 
      If RectangleF.Intersect(overlapRectList(i), overlapRectList(j)) <> RectangleF.Empty Then 
      Dim dupeRect As RectangleF = RectangleF.Intersect(overlapRectList(i), overlapRectList(j)) 
      totalArea -= dupeRect.Width * dupeRect.Height   
      End If 
     End If 
     Next 
    Next 

我修改了代碼以考慮tcarvin的注意事項。但是，我沒有在方格紙上畫出結果，看看它是否完全正確。我會在有更多時間後儘快查看。還請注意，我沒有包含任何代碼來處理少於2個交叉點的情況。