? B4XTurtle - Examples for teachers and parents

[Erel]

The sine function has a very interesting characteristic - its second derivative equals to -sine(x).
With this knowledge we can draw it with very simple code and without using any trigonometric function.

Sub Turtle_Start
    Turtle.RabbitMode.SetPenColor(xui.Color_Blue).SetPenSize(1)
    Dim YZero As Float = 100
    Turtle.SetY(YZero).SetX(10).SetAngle(-45)
    For i = 1 To 600
        Dim value As Float = Turtle.GetY - YZero 'f(x)
        Turtle.TurnLeft(value * 0.01).MoveForward(1) 'TurnLeft = f''(x) * constant
    Next
End Sub

It will only work in rabbit mode as we need to get the current position before executing the next command.

 

[Johan Schoeman]

Using the Fourier Series.....

sin((2n−1)*x)/(2n−1)

.... to generate a square wave.

#Region Project Attributes
    #MainFormWidth: 1000
    #MainFormHeight: 650
#End Region

#Region Form Preperation
'Template version 1.00
Sub Process_Globals
    Private fx As JFX
    Private MainForm As Form
    Private xui As XUI 'ignore
    Private Turtle As B4XTurtle
    Dim zerox, zeroy, offset As Float
    
    Private Spinner1 As Spinner
End Sub

Sub AppStart (Form1 As Form, Args() As String)
    MainForm = Form1
    MainForm.RootPane.LoadLayout("Main")
    MainForm.Show
    Spinner1.SetNumericItems(1, 150, 1, 1)

End Sub

#End Region

'B4XTurtle examples: https://www.b4x.com/android/forum/threads/examples-for-teachers-and-parents.116979
Sub Turtle_Start
    
    turtle_prep
    
End Sub

Private Sub btnDraw_Click
    
    Dim val As Int = Spinner1.Value
    
    Dim x As Float = 0
    Dim y As Float = 0
    
    Turtle.SetPenColor(xui.Color_ARGB(255, Rnd(0, 255), Rnd(0, 255), Rnd(0, 255)))
    For i = -720 To 720
        x = offset + (2 * zerox / (2 * cPI)) * ((i+720)/1440) * 2 * cPI            'add the offset to the calculated x position
        y=0
        For n = 1 To val                                                        'Fourier series for a square wave
            y = y + (Sin((2*n-1) * i * 2 * cPI/360)/(2*n-1))
        Next
        
        y = offset + (y * -1 * zeroy) + zeroy

        If i = -720 Then
            Turtle.SetX(x)
            Turtle.SetY(y)
        End If
        Turtle.MoveTo(x,y)
    Next
    
End Sub

Private Sub btnClear_Click
    
    Turtle.SetPenColor(xui.Color_Black)
    Turtle.ClearScreen
    turtle_prep
    
End Sub

Sub turtle_prep
    
    offset = 25  'leave a gap of 25 at the top and bottom as well as on the left and right of the X and Y axis
    zerox = (Turtle.Width - 2 * offset ) / 2
    zeroy = (Turtle.Height - 2 * offset) / 2

    Turtle.SetSpeedFactor(10)
    Turtle.mBase.Color = xui.Color_LightGray                  'set the Turtle background color
    Turtle.PenUp
    Turtle.SetX(zerox + offset)
    Turtle.SetY(0 + offset)
    Turtle.PenDown
    Turtle.MoveTo(zerox + offset, 2 * zeroy + offset)          'Draw the y-axis
    Turtle.SetX(0 + offset)
    Turtle.SetY(zeroy + offset)
    Turtle.MoveTo(2 * zerox + offset , zeroy + offset)         'Draw the x-axis
    
End Sub