Finding the Centroid of a Room Boundary

It‘s been a while since my last post and I‘m sure most of you were like... "Where the hell is Don!".... it‘s ok! I‘m still around. I‘ve been busy working on stuff I can‘t talk about. Don‘t worry though, I‘m not a good secret keeper.
So this post is going to explain something that a bunch of folks have issues with that involves finding the actual centroid of a polygon, or in this case a Room element. Now let‘s be careful not to confuse a centroid with a pair of midpoints taken from the furthest X and Y planes... a centroid is more closely described as the center of mass within a polygon.

Now this is done by taking a series of 2D points and running some tricky math on them and dividing the points by 6x the area of the polygon. So to make it simple for you guys, I‘ve taken the liberty of sharing a couple of functions that makes this all possible. The samples here are in Revit 2011 format.
First you‘ll need a function that iterates through the boundary segments of a Room Element and builds up a series of 2D points taken from either endpoints of each segment (no need to worry about curved segments since they usually wont effect the centroid too much, or you can add the midpoint of the curve arc to get it closer).
This little Function will return a list of 2D PointF from a boundary of a Room element.

‘‘‘ <summary>    ‘‘‘ Extract a List of 2D Points from a Room‘s Boundary    ‘‘‘ </summary>    ‘‘‘ <param name="p_room"></param>    ‘‘‘ <remarks></remarks>    Private Sub ExtractBoundaryPointsFromRoom(p_room As Room)        ‘ The Points List        Dim m_pts As New List(Of PointF)        ‘ The Z Height        Dim m_z As Double = 0        ‘ Work with the Boundary        Dim m_bsaa As Autodesk.Revit.DB.Architecture.BoundarySegmentArrayArray = m_room.Boundary        ‘ Segment Array at Floor Level        For Each bsa As Autodesk.Revit.DB.Architecture.BoundarySegmentArray In m_bsaa            Try                For Each bs As Autodesk.Revit.DB.Architecture.BoundarySegment In bsa                    Dim m_c As Curve = bs.Curve                    ‘ First Endpoint                    Dim m_EndPoint1 As XYZ = m_c.EndPoint(0)                    Dim m_PointF1 As New PointF(m_EndPoint1(0), m_EndPoint1(1))                    m_pts.Add(m_PointF1)                    ‘ Second Endpoint                    Dim m_EndPoint2 As XYZ = m_c.EndPoint(1)                    Dim m_PointF2 As New PointF(m_EndPoint2(0), m_EndPoint2(1))                    m_pts.Add(m_PointF2)                    ‘ The Height                    m_z = m_EndPoint1(2)                Next            Catch ex As Exception            End Try        Next        ‘ Return the 2D Centroid        Dim m_2Dcentroid As PointF = FindCentroid(m_pts.ToArray, m_room.Area)        ‘ Add the Floor Level of Boundary for Z Elevation        InsertionPoint = New XYZ(m_2Dcentroid.X, m_2Dcentroid.Y, m_z)    End Sub

‘‘‘ <summary>    ‘‘‘ Find 2D Centroid    ‘‘‘ </summary>    ‘‘‘ <param name="pts">Collection of Points Describing the Polygon</param>    ‘‘‘ <param name="p_rmArea">The Area of the Polygon</param>    ‘‘‘ <returns>2D Point (Pointf)</returns>    ‘‘‘ <remarks>This Function Kicks Ass</remarks>    Private Function FindCentroid(ByVal pts() As PointF, p_rmArea As Single) As PointF        ‘ Add the First PT to the End of the Array (full circulation)        ReDim Preserve pts(pts.Length)        pts(pts.Length - 1) = New PointF(pts(0).X, pts(0).Y)        ‘ Get the Centroid        Dim X As Single = 0        Dim Y As Single = 0        Dim m_sf As Single        ‘ This is Where the Magic Happens        For i As Integer = 0 To pts.Length - 2            m_sf = pts(i).X * pts(i + 1).Y - pts(i + 1).X * pts(i).Y            X += (pts(i).X + pts(i + 1).X) * m_sf            Y += (pts(i).Y + pts(i + 1).Y) * m_sf        Next i        ‘ Divide by 6X the Are of the Polygon        X /= (6 * p_rmArea)        Y /= (6 * p_rmArea)        ‘ This is the Final Result        Return New PointF(X, Y)    End Function