If you need a way for a creature to go from node to node in your 2D world at any angle, or need a patrol path then this simple code is for you. I have functions for 1D as well as 2D to do this. Now commonly when you google up code for linear interpolation, you tend to see this function, which is one dimensional:

Vertex = (X_Start * (1 - mu) + X_End * mu)

where mu is anywhere between 0 and 1. 0 is the starting point and 1 is the ending point and anywhere in between is the sprite moving from that point to the other. However I feel it goes beyond that. First of all, how can you determine the speed of how fast the sprite is moving from that point to the other accurately? Or how bout this. How bout the 2D version of the code! Its hard to find and I have managed to pull off all these unanswered questions and also will be blending it in my Bosskillers game I'm currently working on. This code is in VB6, however its very easy to convert to VB.Net, C#, and C++ or any other language you are working with. Enjoy the code:

vb Code:
  1. Option Explicit

  2.  
  3. Private Type Vector2D

  4.     

  5.     X As Single

  6.     Y As Single

  7.  
  8. End Type

  9.  
  10. Private Const PI As Single = 3.14159265358979 'Atn(1) * 4

  11.  
  12. Private Vector As Vector2D

  13.  
  14. Private Starting(3) As Vector2D

  15. Private Ending(3) As Vector2D

  16.  
  17. Private Running As Boolean

  18. Private mu As Single

  19. Private mu2 As Vector2D

  20. Private Speed As Single

  21. Private Current_Path As Long

  22.  
  23. Private Function Linear_Interpolation_1D(ByVal Vertex As Single, ByVal X_Start As Single, ByVal X_End As Single, ByRef mu As Single, ByVal Speed) As Boolean

  24.  
  25.     If (X_End >= X_Start) Then

  26.         mu = mu + Convert_Speed_To_MU(Speed, X_Start, X_End)

  27.     Else

  28.         mu = mu + Convert_Speed_To_MU(-Speed, X_Start, X_End)

  29.     End If

  30.     

  31.     If mu <= 0 Then mu = 0

  32.     If mu >= 1 Then

  33.         mu = 1

  34.         Linear_Interpolation_1D = True

  35.     End If

  36.     

  37.    Vertex = (X_Start * (1 - mu) + X_End * mu)

  38.  
  39. End Function

  40.  
  41. Private Function Linear_Interpolation_2D(ByRef Vector As Vector2D, ByVal X_Start As Single, ByVal Y_Start As Single, ByVal X_End As Single, ByVal Y_End As Single, ByRef mu As Vector2D, ByVal Speed As Single) As Boolean

  42.     

  43.     Dim Radian As Single

  44.     

  45.     Radian = Get_Radian(X_Start, Y_Start, X_End, Y_End)

  46.     

  47.     mu.X = mu.X + Convert_Speed_To_MU(Speed, X_Start, X_End) * Cos(Radian)

  48.     mu.Y = mu.Y + Convert_Speed_To_MU(Speed, Y_Start, Y_End) * Sin(Radian)

  49.     

  50.     If mu.X <= 0 Then mu.X = 0

  51.     If mu.X >= 1 Then mu.X = 1

  52.  
  53.     If mu.Y <= 0 Then mu.Y = 0

  54.     If mu.Y >= 1 Then mu.Y = 1

  55.     

  56.     If mu.X = 1 Or mu.Y = 1 Then Linear_Interpolation_2D = True

  57.     

  58.     Vector.X = (X_Start * (1 - mu.X) + X_End * mu.X)

  59.     Vector.Y = (Y_Start * (1 - mu.Y) + Y_End * mu.Y)

  60.     

  61. End Function

  62.  
  63. Private Function Convert_Speed_To_MU(ByVal Speed As Single, ByVal X_Start As Single, ByVal X_End As Single) As Single

  64.     

  65.     If (X_End - X_Start) <> 0 Then Convert_Speed_To_MU = Speed / (X_End - X_Start)

  66.  
  67. End Function

  68.  
  69. Private Function Get_Radian(X1 As Single, Y1 As Single, X2 As Single, Y2 As Single) As Single

  70.  
  71.     Dim DX As Single, DY As Single

  72.     Dim Angle As Single

  73.  
  74.         DX = X2 - X1

  75.         DY = Y2 - Y1

  76.         

  77.         Angle = 0

  78.  
  79.         If DX = 0 Then

  80.             If DY = 0 Then

  81.                 Angle = 0

  82.             ElseIf DY > 0 Then

  83.                 Angle = PI / 2

  84.             Else

  85.                 Angle = PI * 3 / 2

  86.             End If

  87.         ElseIf DY = 0 Then

  88.             If DX > 0 Then

  89.                 Angle = 0

  90.             Else

  91.                 Angle = PI

  92.             End If

  93.         Else

  94.             If DX < 0 Then

  95.                 Angle = Atn(DY / DX) + PI

  96.             ElseIf DY < 0 Then

  97.                 Angle = Atn(DY / DX) + (2 * PI)

  98.             Else

  99.                 Angle = Atn(DY / DX)

  100.             End If

  101.         End If

  102.         Get_Radian = Angle

  103.  
  104. End Function

  105.  
  106. Private Function Draw_Rectangle(ByVal X As Single, ByVal Y As Single, ByVal Width As Single, ByVal Height As Single, ByVal Color As Long)

  107.  
  108.     Me.Line (X, Y)-(X + Width, Y + Height), Color, B

  109.     

  110. End Function

  111.  
  112. Private Sub Form_Load()

  113.     

  114.     Me.Show

  115.     Me.ScaleMode = vbPixels

  116.     Me.BackColor = RGB(0, 0, 0)

  117.     Me.AutoRedraw = True

  118.     

  119.     Starting(0).X = 10: Starting(0).Y = 10: Ending(0).X = 100: Ending(0).Y = 10

  120.     Starting(1).X = 100: Starting(1).Y = 10: Ending(1).X = 100: Ending(1).Y = 100

  121.     Starting(2).X = 100: Starting(2).Y = 100: Ending(2).X = 10: Ending(2).Y = 100

  122.     Starting(3).X = 10: Starting(3).Y = 100: Ending(3).X = 10: Ending(3).Y = 10

  123.     

  124.     Vector.X = Starting(0).X: Vector.Y = Starting(0).Y

  125.     

  126.     Running = True

  127.     

  128.     Do While Running = True

  129.         Cls

  130.         If Linear_Interpolation_2D(Vector, Starting(Current_Path).X, Starting(Current_Path).Y, Ending(Current_Path).X, Ending(Current_Path).Y, mu2, 1) = True Then

  131.             If Current_Path <> UBound(Starting) Then

  132.                 Current_Path = Current_Path + 1

  133.                 mu2.X = 0

  134.                 mu2.Y = 0

  135.             Else

  136.                 Current_Path = UBound(Starting)

  137.                     

  138.                 'To have it repeat, Comment out the line above and use these instead:

  139.                     'Current_Path = 0

  140.                     'mu2.X = 0

  141.                     'mu2.Y = 0

  142.             End If

  143.         End If

  144.             

  145.         Draw_Rectangle Vector.X, Vector.Y, 20, 20, RGB(255, 255, 255)

  146.         DoEvents

  147.     Loop

  148.         

  149. End Sub

  150.  
  151. Private Sub Form_Unload(Cancel As Integer)

  152.  
  153.     Running = False

  154.     Unload Me

  155.  
  156. End Sub