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spline cubic rutine with VB5

Posted on 2000-05-12
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Last Modified: 2008-02-26
I need a VB5.0 function able to do a smoth curve since a several datas from 2d array using spline cubic method
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Question by:rsilva
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bhess1 earned 5 total points
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Expert Comment

by:Ark
Comment Utility
Hi
1. Do you need local (3 points) or global (all points) spline?
2. Do you need interpolation or extrapolation too?
3. I'm afraid you forgot to add some zeroes to points value <smile>
Cheers
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Author Comment

by:rsilva
Comment Utility
1. all points
2. interpolation
3. I lost my points because I put the
questions first in a wrong topic area
sorry, but I don't have more points
availables :(
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LVL 27

Expert Comment

by:Ark
Comment Utility
Hi
just one more question - plz, describe your 2d array - is this A(n,2) or A(2,n) dimension, is it zero or 1 bazed. Or you have 2 one-dim arrays?
for example:
A(0,0) = X(0)
A(0,1) = Y(0)
A(1,0) = X(1)
etc...
Cheers
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Expert Comment

by:Ark
Comment Utility
Ok, here it is.
I assume, you have 1 based 2dim array,like this:
A(1,1) = X(1)
A(1,2) = X(2)
A(1,3) = X(3)
A(2,1) = Y(1)
A(2,2) = Y(2)
A(2,3) = Y(3)
If not, I specially work with X() and Y() arrays so you can change code.
Place PictureBox, command button and TextBox (multiline) on form. Form code:

Option Explicit
Option Base 1
Dim M() As Single
Dim X() As Single, Y() As Single
Dim TempArr() As Single

Private Sub PrepareSpline(inpArr() As Single)
  Dim n As Integer, i As Integer
  Dim L() As Single, R() As Single, S() As Single
  Dim D As Single, E As Single, F As Single, H As Single, P As Single
  n = UBound(inpArr, 2)
  If n < 2 Then Exit Sub
  ReDim M(n), X(n), Y(n), L(n), R(n), S(n)
  For i = 1 To n
      X(i) = inpArr(1, i)
      Y(i) = inpArr(2, i)
  Next i
  D = X(2) - X(1):  E = (Y(2) - Y(1)) / D
  For i = 2 To n - 1
      H = D: D = X(i + 1) - X(i)
      If D = 0 Then D = 0.0001
      F = E: E = (Y(i + 1) - Y(i)) / D
      L(i) = D / (D + H)
      R(i) = 1 - L(i)
      S(i) = 6 * (E - F) / (D + H)
  Next i
  For i = 2 To n - 1
      P = 1 / (R(i) * L(i - 1) + 2)
      L(i) = -L(i) * P
      S(i) = (S(i) - R(i) * S(i - 1)) * P
  Next i
  M(n) = 0: L(n - 1) = S(n - 1): M(n - 1) = L(n - 1)
  For i = n - 2 To 1 Step -1
      L(i) = L(i) * L(i + 1) + S(i)
      M(i) = L(i)
  Next i
End Sub

Private Function CalcValue(arg As Single) As Single
  Dim ret As Single, i As Integer, n As Integer
  Dim D As Single, H As Single, P As Single, R As Single
  n = UBound(X)
  For i = 1 To n
      If arg < X(i) Then Exit For
  Next i
  Select Case i
     Case 1    ' arg less then x(1) -> Extrapolation
       D = X(2) - X(1)
       If D = 0 Then D = 0.0001
       ret = -D * M(2) / 6 + (Y(2) - Y(1)) / D
       ret = ret * (arg - X(1)) + Y(1)
     Case n + 1 ' arg greater then x(n) -> Extrapolation
       D = X(n) - X(n - 1)
       If D = 0 Then D = 0.0001
       ret = D * M(n - 1) / 6 + (Y(n) - Y(n - 1)) / D
       ret = ret * (arg - X(n)) + Y(n)
     Case Else  'interpolation
       D = X(i) - X(i - 1): H = arg - X(i - 1)
       R = X(i) - arg: P = D * D / 6
       ret = (M(i - 1) * R ^ 3 + M(i) * H ^ 3) / (6 * D)
       ret = ret + ((Y(i - 1) - M(i - 1) * P) * R + (Y(i) - M(i) * P) * H) / D
  End Select
  CalcValue = ret
End Function

Private Sub Command1_Click()
  PrepareSpline TempArr
  DrawCurve 1
End Sub

Private Sub Form_Load()
  Text1 = ""
  Picture1.FillColor = vbRed
  Picture1.FillStyle = vbSolid
End Sub

Private Sub Picture1_MouseDown(Button As Integer, Shift As Integer, X As Single, Y As Single)
  Dim i As Integer
  Static n1 As Integer
  If Button = 1 Then
     n1 = n1 + 1
     ReDim Preserve TempArr(2, n1)
     TempArr(1, n1) = X
     TempArr(2, n1) = Y
     Text1 = Text1 & vbCrLf & TempArr(1, n1) & vbTab & TempArr(2, n1)
     Picture1.Circle (X, Y), 50
  End If
End Sub

Private Sub DrawCurve(iStep As Integer)
  Dim i As Integer
  Picture1.PSet (X(LBound(X)), CalcValue(X(LBound(X))))
  For i = X(LBound(X)) + iStep To X(UBound(X)) Step iStep
      Picture1.Line -(i, CalcValue(CSng(i)))
  Next i
End Sub

' click on picturebox to draw points, then press command button
' sometimes you can received overflow or division by zero - it's depend on array value. You can fixed this yourself. (I've already spend 3 hours for coding and have no more time). Or I'll fix it after weekend.

Cheers

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Author Comment

by:rsilva
Comment Utility
Thanks for help me, the rutines
works perfect..!!
regards,
Ricardo
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