[RESOLVED] Linear regression

[InertiaM]

Has anyone done any linear regression algorithms in VB.NET?

I have a laser sensor which streams distance measurements via TCP. The minimum dimension is 700mm and the maximum is 3000mm. It takes measurements every 0.25degrees, from 55 degrees to 125 degrees - a total of 70 degrees => 280 measurements per scan. Sometimes the laser will not take a true reading, and will return 0mm.

When the laser has performed its scan, I need to evaluate all the measurements to find two "edges" which are perpendicular to each other. Once I have found these lines and proved that they are perpendicular, I can calculate the X and Y offset, and rotation, of the two edges. This information will then be passed by serial to a robot to perform a pick-and-place operation.

The point where the two "edges" meet will always (in theory) be the closest point to the laser centre.

Here's a totally stripped down version - the sample set of measurements is in the next post. A screenshot (with lines removed) is also attached.

The problem I have is that I am not sure how to do the linear regression lines without including some of the obviously invalid points. This is where I could do with some help (which would be GREATLY appreciated )

Option Explicit On
Option Strict On

Imports System.Drawing.Drawing2D

Public Class Form1

    Structure MEASUREDVALUE
        Public Distance As Integer
        Public X As Integer
        Public Y As Integer
    End Structure

    Public MeasuredPoints(280) As MEASUREDVALUE

    Private iSmallestMeasurementFromLeft As Integer = Integer.MaxValue
    Private iSmallestMeasurementScanNumberLeft As Integer = 0

    Private iSmallestMeasurementFromRight As Integer = Integer.MaxValue
    Private iSmallestMeasurementScanNumberRight As Integer = 0

    Public Sub New()

        ' This call is required by the Windows Form Designer.
        InitializeComponent()

        ' Add any initialization after the InitializeComponent() call.
        Me.SetStyle(ControlStyles.OptimizedDoubleBuffer, True)
        Me.SetStyle(ControlStyles.UserPaint, True)
        Me.SetStyle(ControlStyles.AllPaintingInWmPaint, True)

        Me.WindowState = FormWindowState.Maximized

        For i As Integer = 1 To 280
            MeasuredPoints(i).Distance = 0
            MeasuredPoints(i).X = 0
            MeasuredPoints(i).Y = 0
        Next

        SetupSampleData()

    End Sub

    Private Sub SetupSampleData()
         'see next post
    End Sub

    Private Sub Form1_Paint(ByVal sender As Object, ByVal e As System.Windows.Forms.PaintEventArgs) Handles Me.Paint
        With e.Graphics
            Dim mYFlip As Matrix = New Matrix(1, 0, 0, -1, 0, 0)

            .Transform = mYFlip

            .TranslateTransform(CSng(Me.ClientRectangle.Width / 2), 0 - (Me.ClientRectangle.Height - 100))
            .ScaleTransform(0.2, 0.2)

            .DrawEllipse(Pens.Black, -25, -25, 50, 50)

            .DrawLine(Pens.Black, CSng(0 + (700 * Math.Cos(DTR(90 + 35)))), CSng(0 + (700 * Math.Sin(DTR(90 + 35)))), CSng(0 + (3000 * Math.Cos(DTR(90 + 35)))), CSng(0 + (3000 * Math.Sin(DTR(90 + 35)))))
            .DrawLine(Pens.Black, CSng(0 - (700 * Math.Cos(DTR(90 + 35)))), CSng(0 + (700 * Math.Sin(DTR(90 + 35)))), CSng(0 - (3000 * Math.Cos(DTR(90 + 35)))), CSng(0 + (3000 * Math.Sin(DTR(90 + 35)))))

            .DrawArc(Pens.Black, 0 - 3000S, 0 - 3000S, 3000S * 2, 3000S * 2, 90 - 35, 70)
            .DrawArc(Pens.Black, 0 - 700S, 0 - 700S, 700S * 2, 700S * 2, 90 - 35, 70)

            Dim Angle As Single = 0
            For i As Integer = 1 To UBound(MeasuredPoints)
                Angle = CSng((140 - i) * 0.25)
                If MeasuredPoints(i).Distance >= 700 AndAlso MeasuredPoints(i).Distance <= 3000 Then
                    .DrawLine(Pens.Black, CSng(0 - (MeasuredPoints(i).Distance * Math.Cos(DTR(90 - Angle)))), CSng(0 + (MeasuredPoints(i).Distance * Math.Sin(DTR(90 - Angle)))), CSng(0 - (MeasuredPoints(i).Distance * Math.Cos(DTR(90 - Angle)))), CSng(0 + (MeasuredPoints(i).Distance * Math.Sin(DTR(90 - Angle)))) + 1)
                End If

                'if you want to identify a measured point, add a NumericUpDown control
                'and set its minimum value to 1 and its maximum value to 280
                If i = NumericUpDown1.Value Then
                    If MeasuredPoints(i).Distance >= 700 AndAlso MeasuredPoints(i).Distance <= 3000 Then
                        .DrawLine(Pens.Red, 0, 0, CSng(0 - (MeasuredPoints(i).Distance * Math.Cos(DTR(90 - Angle)))), CSng(0 + (MeasuredPoints(i).Distance * Math.Sin(DTR(90 - Angle)))) + 1)
                    Else
                        .DrawLine(Pens.Red, 0, 0, CSng(0 - (3000 * Math.Cos(DTR(90 - Angle)))), CSng(0 + (3000 * Math.Sin(DTR(90 - Angle)))) + 1)
                    End If
                End If
            Next

            'find the smallest measurement working from left to right
            iSmallestMeasurementFromLeft = Integer.MaxValue
            iSmallestMeasurementScanNumberLeft = 0
            For i As Integer = 1 To 280
                If MeasuredPoints(i).Distance >= 700 AndAlso MeasuredPoints(i).Distance <= 3000 AndAlso MeasuredPoints(i).Distance < iSmallestMeasurementFromLeft Then
                    iSmallestMeasurementFromLeft = MeasuredPoints(i).Distance
                    iSmallestMeasurementScanNumberLeft = i
                End If
            Next
            Angle = CSng((140 - iSmallestMeasurementScanNumberLeft) * 0.25)
            .DrawLine(Pens.Green, 0, 0, CSng(0 - (MeasuredPoints(iSmallestMeasurementScanNumberLeft).Distance * Math.Cos(DTR(90 - Angle)))), CSng(0 + (MeasuredPoints(iSmallestMeasurementScanNumberLeft).Distance * Math.Sin(DTR(90 - Angle)))) + 1)

            'TODO: calculate the linear regression line to the left


            'find the smallest measurement working from left to right
            iSmallestMeasurementFromRight = Integer.MaxValue
            iSmallestMeasurementScanNumberRight = 0
            For i As Integer = 280 To 1 Step -1
                If MeasuredPoints(i).Distance >= 700 AndAlso MeasuredPoints(i).Distance <= 3000 AndAlso MeasuredPoints(i).Distance < iSmallestMeasurementFromRight Then
                    iSmallestMeasurementFromRight = MeasuredPoints(i).Distance
                    iSmallestMeasurementScanNumberRight = i
                End If
            Next
            Angle = CSng((140 - iSmallestMeasurementScanNumberRight) * 0.25)
            .DrawLine(Pens.Green, 0, 0, CSng(0 - (MeasuredPoints(iSmallestMeasurementScanNumberRight).Distance * Math.Cos(DTR(90 - Angle)))), CSng(0 + (MeasuredPoints(iSmallestMeasurementScanNumberRight).Distance * Math.Sin(DTR(90 - Angle)))) + 1)

            'TODO: calculate the linear regression line to the right

        End With
    End Sub

    Private Function DTR(ByVal whatDegrees As Double) As Double
        DTR = (whatDegrees * Math.PI) / 180
    End Function

    Private Function RTD(ByVal whatRadians As Double) As Double
        RTD = (whatRadians * 180) / Math.PI
    End Function

    Private Sub NumericUpDown1_ValueChanged(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles NumericUpDown1.ValueChanged
        Me.Invalidate()
    End Sub

End Class