Find total overlap percent of multiple rectangles overlapping the same rectangle? - vb.net

Question

I've got a list of System.Drawing.RectangleF objects that all overlap the same RectangleF object. In my picture below, the 3 overlapping rectangles would be the pink, yellow, and red rectangles. My main rectangle in question is the light blue rectangle.
Second Image:
I know that with RectangleF objects I can use the Intersect() method that will return me another RectangleF object representing the overlap. But as far as I can tell, this only really works when comparing two rectangles.
My question is: How could I determine the TOTAL area/percentage (i.e. the combined total overlap of the red, yellow, and pink rectangles when compared to the light blue rectangle - but it would need to be smart enough to not count the area in which the red and yellow overlaps twice, and same for the pink and yellow)?
NOTE: The green lines represent the area I'm looking for, just the total area of the blue rectangle that is not visible.
UPDATE: I've added a 2nd image to further demonstrate what I'm looking for. In the second image, the presence of the burgundy rectangle should have no affect on the total percent covered because that area is already covered by the yellow and green rectangles.

Answer 1

OK I think I found a solution using a Region that seems to be working for both of my example images above:
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
This seems to be working pretty well, and is quite simple.

Answer 2

Here is my algorithm. The key point is that we are subtracting out overlaps of overlaps.
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
I amended the code to take into account tcarvin's note. However, I have not plotted out the results on graph paper to see if this is fully correct. I will look at it as soon as I have additional time. Also note that I have not included any code to handle a situation with less than 2 intersections.