Public Class Form1
    'this is a trochoid curve 
    Dim x(10000) As Integer
    Dim y(10000) As Integer 'these are points on curve
    Const xs As Integer = 650
    Const ys As Integer = 675 'start point at bottom of page
    Dim n As Integer 'the timer count
    Dim gonow As Integer
    Dim fast As Integer
    Dim xi As Integer
    Dim yi As Integer 'inner circle ellipse box
    Dim ri As Integer = 165 'inner circle defining points
    Dim cpen As New System.Drawing.Pen(System.Drawing.Color.Green, 1) 'start green
    Dim col As Integer = 0

    Private Sub Timer1_Tick(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Timer1.Tick
        Dim g As Graphics = CreateGraphics()
        If gonow = 1 And fast = 0 Then
            g.DrawEllipse(Pens.White, xi, yi, 2 * ri, 2 * ri) 'erase previous red inner
            calc()
            g.DrawEllipse(Pens.Cyan, xi, yi, 2 * ri, 2 * ri) 'rotates anticlock from the bottom
            For i = 1 To n
                g.DrawLine(cpen, x(i - 1), y(i - 1), x(i), y(i))
                'this draws entire curve so white does not erase
            Next
            x(n) = x(n + 1)
            y(n) = y(n + 1)
            n = n + 1
            If n = 10000 Then
                gonow = 0 'used up x,y array
                MsgBox("You can see how the curve is going. See final curve or start over", 0)
            End If
        End If
    End Sub

    Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
        gonow = 1 'start drawing
        x(0) = xs
        y(0) = ys 'first point on curve
        xi = 450 + ri
        yi = 675 - 2 * ri 'first point in centre of inner
        n = 0 'first count
    End Sub

    Private Sub Button2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button2.Click
        Invalidate() 'clear existing page of drawing
        gonow = 0 'start a new graph
        fast = 0 'clear all buttons
        n = 0 'set all start values
    End Sub

    Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load

    End Sub

    Private Function calc() 'the next point in the curve
        Const rpc As Double = 2 * Math.PI
        Dim angstep As Double 'angle outer moves
        Dim inang As Double 'angle inner moves
        angstep = (n * rpc) / 360 'the rotation angle of outer wheel
        inang = angstep * 325 / ri 'inner circle angle
        xi = (325 - ri) * Math.Sin(angstep) + (650 - 2 * ri)
        yi = (325 - ri) * Math.Cos(angstep) + (350 - 2 * ri) 'this is the centre of the inner circle
        xi = xi + ri
        yi = yi + ri 'start x,y of draw.ellipse
        x(n + 1) = ri * Math.Sin(inang) + xi + ri
        y(n + 1) = ri * Math.Cos(inang) + yi + ri 'next point on curve
        Return xi
        Return yi
        Return x(n + 1)
        Return y(n + 1)
    End Function

    Private Sub Form1_Paint(ByVal sender As Object, ByVal e As System.Windows.Forms.PaintEventArgs) Handles Me.Paint
        Dim g As Graphics = CreateGraphics()
        g.DrawRectangle(Pens.Blue, 320, 20, 660, 660) 'a border
        g.FillRectangle(Brushes.White, 321, 21, 659, 659)
        g.DrawEllipse(Pens.Cyan, 323, 23, 655, 655) 'this is outer circle
    End Sub

    Private Sub Button3_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button3.Click
        fast = 1 'lets go fast
        Const rpc As Double = 2 * Math.PI
        Dim angstep As Double 'angle outer moves
        Dim inang As Double 'angle inner moves
        Dim xf As Integer = xs
        Dim yf As Integer = ys 'start of curve
        Dim xn As Integer
        Dim yn As Integer 'nextpoint on curve
        Dim g As Graphics = CreateGraphics()
        n = 1 'next point
        For i = 1 To 60000
            angstep = (n * rpc) / 360 'the rotation angle of outer wheel
            inang = angstep * 325 / ri 'inner circle angle
            xi = (325 - ri) * Math.Sin(angstep) + (650 - 2 * ri)
            yi = (325 - ri) * Math.Cos(angstep) + (350 - 2 * ri) 'this is the centre of the inner circle
            xi = xi + ri
            yi = yi + ri 'start x,y of draw.ellipse
            xn = ri * Math.Sin(inang) + xi + ri
            yn = ri * Math.Cos(inang) + yi + ri 'next point on curve
            g.DrawLine(cpen, xf, yf, xn, yn)
            n = n + 1
            xf = xn
            yf = yn 'next point
        Next
    End Sub

    Private Sub RadioButton1_CheckedChanged(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles RadioButton1.CheckedChanged
        cpen.Color = Color.Green
    End Sub

    Private Sub RadioButton2_CheckedChanged(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles RadioButton2.CheckedChanged
        cpen.Color = Color.Red
    End Sub

    Private Sub RadioButton3_CheckedChanged(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles RadioButton3.CheckedChanged
        cpen.Color = Color.Blue
    End Sub

    Private Sub Button4_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button4.Click
        Dim radius As String
        Dim noerr As Integer = 0
        For i = 10 To 315
            radius = i
            If radius = TextBox1.Text Then
                ri = radius
                noerr = 1
            End If
        Next
        If noerr = 0 Then
            MsgBox("radius must be a number between 10 and 315", 16)
        End If
    End Sub
End Class