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Thread: Tangent to a Curve

  1. #1

    Tangent to a Curve

    this example can be used for demonstrations in the calculus lessons in the secondary schools.
    this is the tangent and the normal
    Click image for larger version. 

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    look for explanation:
    https://www.siyavula.com/maths/grade...s-04.cnxmlplus

    to find a tangent is to find a derivative at that point (one of the Calculus lessons), the best place to find the derivative is wolfram alpha, such as to find the derivative of y = Sin(x) go to
    http://www.wolframalpha.com/input/?i...tive+of+sin(x)
    and it will give you Cos(x)
    the derivative of x^2 is 2*x
    look at the folowing curve and its tangent, at the newTurn of the curve it seems to slow down because there is a lot of points there (condensed).

    i have used a box to represent the tangent, because i find tbgl_Cylinder rotate around one of its sides and not from its center, (useful for tree branches generation).
    if i use tbgl_cylinder instead of the tbgl_box like this way:
    TBGL_Translate x,y,0
              'TBGL_Rotate 0,0,slope
              TBGL_Rotate slope,0,0
              TBGL_Rotate -90,0,0  
              TBGL_Cylinder 0.1,0.1,1
    
    then at the newTurn of the curve it will not stay like the classical tangent.

    curve y = x^2 press Space to move the tangent over the curve
    Uses "TBGL", "Math" 
    Begin Const
      %listPoints = 1
    End Const
    
    Dim FrameRate  As Double
    Local hWnd As DWord
    
    hWnd = TBGL_CreateWindowEx("curve tangent .... press 'Space' to move the Tangent line over the curve", 800, 600, 32, %TBGL_WS_WINDOWED Or %TBGL_WS_CLOSEBOX) 
    TBGL_ShowWindow 
    
    
    TBGL_BackColor(255,255,255) 
    
    TBGL_ResetKeyState() 
    
    Global  x,y As Single
    ' catch the data and store it to %listPoints
    TBGL_NewList %listPoints
          TBGL_Color(0,0,0)
          TBGL_PointSize 3 
          For x = -2.5 To 2.5 Step 0.01
              y = x^2 - 3  ' just to shift down the curve   
              
              TBGL_BeginPoly(%GL_POINTS) 
                   TBGL_Color(150, 150, 255 )
                   TBGL_Vertex(x,y)
              TBGL_EndPoly
             
          Next
            
    TBGL_EndList
    
    TBGL_ResetKeyState() 
    x = -2.5: y = 0
    Global slope, slopeAngle As Single
    
    While TBGL_IsWindow(hWnd)
         
        FrameRate = TBGL_GetFrameRate
        
        TBGL_ClearFrame 
    
          TBGL_RenderMatrix2D( -5, -5, 5, 5 ) 
                                             
          TBGL_CallList %listPoints
          
              If TBGL_GetWindowKeyState( hWnd, %VK_SPACE) Then 
              x + 0.01
              y = x^2 - 3 ' just to shift down the curve 
            
              slope = 2*x ' This is the derivative of f(y)=x^2
              slopeAngle = RadToDeg(Atn(slope)) 'find the angle correspend to slope and convert it to degrees
              'slopeAngle = (Atn(slope))*180/Pi 'find the angle correspend to slope and convert it to degrees
              End If
              TBGL_Translate x,y,0
              TBGL_Rotate slopeAngle,0,0
              TBGL_Color(255, 0, 0 )
              TBGL_Box 1, 0.05, 0.2
              TBGL_Rotate 180,0,0 
              TBGL_Cylinder 0.02,0.02,0.5
              
        TBGL_DrawFrame 
    
        If TBGL_GetWindowKeyState(hWnd, %VK_ESCAPE) Then Exit While
            
    Wend
    
    TBGL_DestroyWindow
    
    Curve y = Sin(x)
    Uses "TBGL", "Math" 
    Begin Const
      %listPoints = 1
    End Const
    
    Dim FrameRate  As Double
    ' Handle for our window
    Local hWnd As DWord
    
    hWnd = TBGL_CreateWindowEx("curve tangent .... press 'Space' to move the Tangent line over the curve", 800, 600, 32, %TBGL_WS_WINDOWED Or %TBGL_WS_CLOSEBOX) 
    TBGL_ShowWindow 
      
    ' Set background  to white
    TBGL_BackColor(255,255,255) 
    
    TBGL_ResetKeyState() 
    
    Global  x,y As Single
    ' catch the data and store it to %listPoints
    TBGL_NewList %listPoints
          TBGL_Color(0,0,0)
          TBGL_PointSize 3 
          For x = -5 To 5 Step 0.01
              y = Sin(x)   
              
              TBGL_BeginPoly(%GL_POINTS) 
                   TBGL_Color(150, 150, 255 )
                   TBGL_Vertex(x,y)
              TBGL_EndPoly
              
          Next
            
    TBGL_EndList
    
    TBGL_ResetKeyState() 
    x = -5: y = 0
    Global slope, slopeAngle As Single
    
    While TBGL_IsWindow(hWnd)
         
        FrameRate = TBGL_GetFrameRate
        
        TBGL_ClearFrame 
    
          TBGL_RenderMatrix2D( -5, -5, 5, 5 ) 
                                             
          TBGL_CallList %listPoints
           
              If TBGL_GetWindowKeyState( hWnd, %VK_SPACE) Then 
              x + 0.01
              y = Sin(x)
            
              slope = Cos(x) ' This is the derivative of f(y)=Sine(x)
              slopeAngle = RadToDeg(Atn(slope)) 'find the angle correspend to slope and convert it to degrees
              'slopeAngle = (Atn(slope))*180/Pi 'find the angle correspend to slope and convert it to degrees
              End If
              TBGL_Translate x,y,0
              TBGL_Rotate slopeAngle,0,0
              TBGL_Color(255, 0, 0 )
              TBGL_Box 1, 0.05, 0.2
              TBGL_Cylinder 0.02,0.02,0.5
              'TBGL_Box 0.1, 1, 0.1
              
         TBGL_DrawFrame 
    
        If TBGL_GetWindowKeyState(hWnd, %VK_ESCAPE) Then Exit While
            
    Wend
    
    TBGL_DestroyWindow
    
    Click image for larger version. 

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    Last edited by primo; 16-07-2017 at 09:45.

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