get closest point to a line

Question

I\'d like to have a straight forward C# function to get a closest point (from a point P) to a line-segment, AB. An abstract function may look like this. I\'ve search through

Answer 1

This is the right algorythm to get nearest point of a segment from a point(Tested)(vb.net)

s2 = ClosestPointToSegment(point_x, Point_y, Segment_start_x, Segment_start_y, Segment_end_X, Segment_end_Y)

Public Shared Function DistanceTo(x1 As Double, y1 As Double, x2 As Double, y2 As Double) As Double
    Return Math.Sqrt(Math.Pow(x1 - x2, 2) + Math.Pow(y1 - y2, 2))
End Function


Public Shared Function DistanceTo(point_x As Double, point_y As Double, lineStart_x As Double, lineStart_y As Double, lineEnd_x As Double, lineEnd_y As Double) As Double
    Dim tI As Double = ((lineEnd_x - lineStart_x) * (point_x - lineStart_x) + (lineEnd_y - lineStart_y) * (point_y - lineStart_x)) / Math.Pow(DistanceTo(lineStart_x, lineStart_y, lineEnd_x, lineEnd_y), 2)
    Dim dP As Double = ((lineEnd_x - lineStart_x) * (point_y - lineStart_y) - (lineEnd_y - lineStart_y) * (point_x - lineStart_x)) / DistanceTo(lineStart_x, lineStart_y, lineEnd_x, lineEnd_y)

    If tI >= 0R AndAlso tI <= 1.0R Then
        Return Math.Abs(dP)
    Else
        Return Math.Min(DistanceTo(point_x, point_y, lineStart_x, lineStart_y), DistanceTo(point_x, point_y, lineEnd_x, lineEnd_y))
    End If
End Function
Private Shared Function ClosestPointToSegment(P_x As Double, p_y As Double, A_x As Double, a_y As Double, B_x As Double, b_y As Double) As Double()
    Dim a_to_p As PointF = New PointF(), a_to_b As PointF = New PointF()
    Dim rikthex As Double, rikthey As Double
    Dim s1(1) As Double
    Dim p1_v1_X As Double, p1_v1_y As Double, distanca1 As Double, distanca2 As Double
    a_to_p.X = P_x - A_x
    a_to_p.Y = p_y - a_y
    a_to_b.X = B_x - A_x
    a_to_b.Y = b_y - a_y
    Dim atb2 As Single = a_to_b.X * a_to_b.X + a_to_b.Y * a_to_b.Y
    Dim atp_dot_atb As Single = a_to_p.X * a_to_b.X + a_to_p.Y * a_to_b.Y
    Dim t As Single = atp_dot_atb / atb2
    rikthex = A_x + a_to_b.X * t
    rikthey = a_y + a_to_b.Y * t
    If A_x > B_x Then
        If rikthex < A_x And rikthex > B_x Then 'pika duhet ne rregulll
            If a_y > b_y Then
                If rikthey < a_y And rikthey > b_y Then 'pika duhet ne rregulll

                Else
                    distanca1 = DistanceTo(P_x, p_y, A_x, a_y)
                    distanca2 = DistanceTo(P_x, p_y, B_x, b_y)
                    If distanca1 < distanca2 Then
                        rikthex = A_x
                        rikthey = a_y
                    Else
                        rikthex = B_x
                        rikthey = b_y
                    End If

                End If
            Else
                If rikthey > a_y And rikthey < b_y Then 'pika duhet ne rregulll

                Else
                    distanca1 = DistanceTo(P_x, p_y, A_x, a_y)
                    distanca2 = DistanceTo(P_x, p_y, B_x, b_y)
                    If distanca1 < distanca2 Then
                        rikthex = A_x
                        rikthey = a_y
                    Else
                        rikthex = B_x
                        rikthey = b_y
                    End If

                End If

            End If
        Else
            distanca1 = DistanceTo(P_x, p_y, A_x, a_y)
            distanca2 = DistanceTo(P_x, p_y, B_x, b_y)
            If distanca1 < distanca2 Then
                rikthex = A_x
                rikthey = a_y
            Else
                rikthex = B_x
                rikthey = b_y
            End If
        End If
    Else
        If rikthex > A_x And rikthex < B_x Then 'pika duhet ne rregulll
            If a_y > b_y Then
                If rikthey < a_y And rikthey > b_y Then 'pika duhet ne rregulll

                Else
                    distanca1 = DistanceTo(P_x, p_y, A_x, a_y)
                    distanca2 = DistanceTo(P_x, p_y, B_x, b_y)
                    If distanca1 < distanca2 Then
                        rikthex = A_x
                        rikthey = a_y
                    Else
                        rikthex = B_x
                        rikthey = b_y
                    End If

                End If
            Else
                If rikthey > a_y And rikthey < b_y Then 'pika duhet ne rregulll

                Else
                    distanca1 = DistanceTo(P_x, p_y, A_x, a_y)
                    distanca2 = DistanceTo(P_x, p_y, B_x, b_y)
                    If distanca1 < distanca2 Then
                        rikthex = A_x
                        rikthey = a_y
                    Else
                        rikthex = B_x
                        rikthey = b_y
                    End If

                End If

            End If
        Else
            distanca1 = DistanceTo(P_x, p_y, A_x, a_y)
            distanca2 = DistanceTo(P_x, p_y, B_x, b_y)
            If distanca1 < distanca2 Then
                rikthex = A_x
                rikthey = a_y
            Else
                rikthex = B_x
                rikthey = b_y
            End If
        End If
    End If
    s1(0) = rikthex
    s1(1) = rikthey
    Return s1

End Function