Someone recently asked about determining if a point resides within a polyline using VBA. There are a few ways to achieve this, some being more complex than others, each with their own advantages. However, there is one way that is particularly simple within the AutoCAD® environment, as we are able to use built in features such as the IntersectWith method.
The concept for finding out if a point is within a polyline is this – if we were to draw a line from the point in any direction to infinity, the number of intersections the line would have with the polyline would be an odd number. Think about it – if it was a square, it would cross the polyline once. For irregular shapes where the line crosses it many times, it firstly has to exit the shape – any re-entry to the shape must have a corresponding exit – so if the point is within the polyline, any line eminating from it to infinity must cross the boundary an odd number of times. And for the same reason, any point outside the boundary must cross the boundary an even number of times.
So, armed with this knowledge, we need a way to actually achieve this in AutoCAD®. And what better way of doing so is there than to simply draw a Ray in any direction, and find out how many intersections with the boundary there are? Well, that’s exactly what this code does:
Option Explicit Sub main() Dim selPolyline As AcadLWPolyline Dim selPoint As AcadPoint Dim pnt As Variant Randomize 'Initialise random number generator ThisDrawing.Utility.GetEntity selPolyline, pnt, "Pick polyline" ThisDrawing.Utility.GetEntity selPoint, pnt, "Pick point" If isPointInPolyline(selPolyline, selPoint) Then ThisDrawing.Utility.Prompt "The point resides within the polyline" Else ThisDrawing.Utility.Prompt "The point resides outside the polyline" End If End Sub Function isPointInPolyline(pl As AcadLWPolyline, pnt As AcadPoint) As Boolean Dim p1 As Variant Dim p2 As Variant Dim ray As AcadRay Dim arr As Variant Dim upperbound As Long Dim IntersectionCount As Long p1 = pnt.Coordinates p2 = p1 ' edit on 03/12/2010 for increased reliability ' horizontal ray exchanged for a ray with a random direction p2(0) = p2(0) + 1 - Rnd * 2 'offset x coordinate for secondary point in Ray by random amount p2(1) = p2(1) + 1 - Rnd * 2 'offset y coordinate for secondary point in Ray by random amount ' end of edit Set ray = thisSpace.AddRay(p1, p2) arr = ray.IntersectWith(pl, acExtendNone) upperbound = UBound(arr) If upperbound = -1 Then ' No intersections - the point must not be inside the polyline ' Assumes no elevation isPointInPolyline = False Else IntersectionCount = (upperbound + 1) / 3 'number of elements in array is equal to the upperbound + 1 because of element zero 'we divide by 3 to find the number of individual intersections because each has '3 coordinates - X, Y and Z If IntersectionCount Mod 2 = 0 Then 'There are an even number of intersections - it cannot be inside the polyline isPointInPolyline = False Else 'There are an odd number of intersections - it must be inside the polyline isPointInPolyline = True End If End If ray.Delete End Function Function thisSpace() As AcadBlock If ThisDrawing.ActiveSpace = acModelSpace Then Set thisSpace = ThisDrawing.ModelSpace Else Set thisSpace = ThisDrawing.PaperSpace End If End Function
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