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How can I get a Beizer or NURBS from curve points?

taa asked
Good every one!
    Where are the processes about beizer line and NURBS
and it should include get Beizer or NURBS form curve points, it is better if including edit functions.

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NURBS are beyond me, but bezier curves can be drawn using the PolyBezier windows GDI call. There's a nice little sample here


Here is my spline routines:

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

'=======Get cubic spline coefficients================
'inpArr - 2D array (x,y coordinates of points)
'Return True if success, False otherwise
Private Function PrepareSpline(inpArr() As Single) As Boolean
  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
  PrepareSpline = False
  On Error Resume Next
  n = UBound(inpArr, 2)
  On Error GoTo 0
  If n < 2 Then Exit Function
  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
  PrepareSpline = True
End Function

'Use above coefficients to calculate value with inter/extrapolation
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()
  If PrepareSpline(TempArr) Then
     DrawCurve Val(Text2)
     MsgBox "Unable to draw curve", vbOKOnly + vbCritical
  End If
End Sub

Private Sub Command2_Click()
  Text1 = "  X" & vbTab & "  Y" & vbCrLf & "---------------------------"
  Text2 = "1"
  ReDim TempArr(2, 1)
  bNew = True
End Sub

Private Sub Form_Load()
  Text1 = "  X" & vbTab & "  Y" & vbCrLf & "---------------------------"
  Text2 = "1"
  Caption = "Cubic Spline Interpolation"
  Label1 = "Prepare points array by clicking on PictureBox. When finished, press DrawCurve button to continue."
  Label1 = Label1 & vbCrLf & "In the TextBox below you can see your array."
  Label1 = Label1 & vbCrLf & " Default step of curve is 1 pixel. If you want to change it, type new value at TextBox near Command Button."
  Picture1.FillColor = vbRed
  Picture1.FillStyle = vbSolid
  Command1.Caption = "&DrawCurve"
  Command2.Caption = "&Clear"
  bNew = True
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 bNew Then
     n1 = 0
     bNew = False
  End If
  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

'To try this sample, place picturebox, two textboxes (1 - multiline),label and command button on form.


very interesting ark :)
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