تحديد مركز الدائرة فى صورة - نسخة قابلة للطباعة

كود :
   'Find a circle through the three points.

    Private Sub FindCircle(ByVal a As PointF, ByVal b As PointF, ByVal c As PointF, ByRef center As PointF, ByRef radius As Single)

        ' Get the perpendicular bisector of (x1, y1) and (x2, y2).

        Dim x1 As Single = (b.X + a.X) / 2

        Dim y1 As Single = (b.Y + a.Y) / 2

        Dim dy1 As Single = b.X - a.X

        Dim dx1 As Single = -(b.Y - a.Y)



        ' Get the perpendicular bisector of (x2, y2) and (x3, y3).

        Dim x2 As Single = (c.X + b.X) / 2

        Dim y2 As Single = (c.Y + b.Y) / 2

        Dim dy2 As Single = c.X - b.X

        Dim dx2 As Single = -(c.Y - b.Y)



        ' See where the lines intersect.

        Dim lines_intersect, segments_intersect As Boolean

        Dim intersection, close1, close2 As PointF

        FindIntersection(New PointF(x1, y1), New PointF(x1 + dx1, y1 + dy1), New PointF(x2, y2), New PointF(x2 + dx2, y2 + dy2), lines_intersect, segments_intersect, intersection, close1, close2)

        If Not lines_intersect Then

            MessageBox.Show("The points are colinear")

            center = New PointF(0, 0)

            radius = 0

        Else

            center = intersection

            Dim dx As Single = center.X - a.X

            Dim dy As Single = center.Y - a.Y

            radius = CSng(Math.Sqrt(dx * dx + dy * dy))

        End If

    End Sub

    ' Find the point of intersection between the lines p1 --> p2 and p3 --> p4.

    Private Sub FindIntersection(ByVal p1 As PointF, ByVal p2 As PointF, ByVal p3 As PointF, ByVal p4 As PointF, ByRef lines_intersect As Boolean, ByRef segments_intersect As Boolean, ByRef intersection As PointF, ByRef close_p1 As PointF, ByRef close_p2 As PointF)

        ' Get the segments' parameters.

        Dim dx12 As Single = p2.X - p1.X

        Dim dy12 As Single = p2.Y - p1.Y

        Dim dx34 As Single = p4.X - p3.X

        Dim dy34 As Single = p4.Y - p3.Y



        ' Solve for t1 and t2

        Dim denominator As Single = (dy12 * dx34 - dx12 * dy34)



        Dim t1 As Single = ((p1.X - p3.X) * dy34 + (p3.Y - p1.Y) * dx34) / denominator

        If Single.IsInfinity(t1) Then

            ' The lines are parallel (or close enough to it).

            lines_intersect = False

            segments_intersect = False

            intersection = New PointF(Single.NaN, Single.NaN)

            close_p1 = New PointF(Single.NaN, Single.NaN)

            close_p2 = New PointF(Single.NaN, Single.NaN)

            Return

        End If

        lines_intersect = True



        Dim t2 As Single = ((p3.X - p1.X) * dy12 + (p1.Y - p3.Y) * dx12) / -denominator



        ' Find the point of intersection.

        intersection = New PointF(p1.X + dx12 * t1, p1.Y + dy12 * t1)



        ' The segments intersect if t1 and t2 are between 0 and 1.

        segments_intersect = ((t1 >= 0) AndAlso (t1 <= 1) AndAlso (t2 >= 0) AndAlso (t2 <= 1))



        ' Find the closest points on the segments.

        If t1 < 0 Then

            t1 = 0

        ElseIf t1 > 1 Then

            t1 = 1

        End If



        If t2 < 0 Then

            t2 = 0

        ElseIf t2 > 1 Then

            t2 = 1

        End If



        close_p1 = New PointF(p1.X + dx12 * t1, p1.Y + dy12 * t1)

        close_p2 = New PointF(p3.X + dx34 * t2, p3.Y + dy34 * t2)

    End Sub