Nurbs Relaxation Rhino Script

'Version december 3rd 2004

'Routines developed and copyrighted by Gelfling '04 aka. David Rutten
'Parts of these routines were developed while I was a intern at Prat-SA, Toulouse, France
'Surface relaxation using FDM (force density method) and VR(vibration reduction)
'(This method was written specifically for Rhinoceros 3.x and it's scripting engine.
'However only the interface section of the source code *requires* RhinoScript methods...)

'Internal mesh definitions differ from those required by the Rhinoceros 3.x Scripting engine.
'Instead of faces these routines use edges. Translation from one definition to the other
'will have to be performed prior to and after relaxation. Since only the coordinates
 'of mesh vertices (or nodes) will be altered, this should be fairly straightforward.

'Furthermore in these routines vector objects play an important role. Vectors are arrays
'of 2 3D point definitions:
' Dim vecExample(1)
' vecExample(0) = Array(0,0,0) 'Starting point of vector
' vecExample(1) = Array(1,0,1) 'Ending point of vector
'Vector variables may be bigger than these dimensions but not smaller. They always need at
'least an x, y and z component.

Option Explicit

'This function performs a number of relaxation steps on the nodes of a mesh-definition.
'arrNodes is an array of 3D-points identifying the node coordinates in euclidian space
'arrConnections is an array of arrays containing information about connections between nodes
' Every index in the array is another array containing 2 numeric values:
' 0 = the index of the node where the connection links to
' 1 = the tension of the connection.
'  Note that arrNodes and arrConnections must have the same size (every index describes a single  node)
' Also note that if connections link to non-existent nodes an overflow error will occur.
' Then note that every node needs at least one connection, although logically 2 is the absolute  minimum.
' Nodes can be connected to themselves, but this makes no sense so try to avoid it.
'arrConstrains is an array that describes the constrains a node can have in space.
' Every entry describes a single node. It can have the following values:
' Non-UUID string = the point is free to move in space if there is no object that has an ID   which is identical
'     to the supplied string. Using zero length strings to make  sure nodes are free.
' UUID-String = the point is locked to an object (can be curve, surface or polysurface) by  ClosestPoint
'    (ClosestPoint routines are not included in this routine. Instead  native Rhino 3.x script
'    methods are called. If you intend to run this script on alternate  platform you'll have to
'    translate these calls into native methods. Also if other platforms  use different object
'    identifyers (instead of strings), you should make further  alterations).
'Damping = a real number controlling the damping of the relaxation routine. Numbers higher than one
' will accelerate the relaxation, likely causing instable results. This however can be  combatted by
' limiting the maximum distance nodes are allowed to travel. Numbers between zero and one will  deccelerate
' the relaxation thus preventing bouncing solutions, but more steps will be required to reach a  stable solution
' within tolerance. Negative numbers should be avoided.
'Limit = a real number controlling the distance every node is allowed to move during each iteration.
'Summary will be filled with an array of data regarding the details of the entire relaxation process
' it will be filled with the following values:
' 0 = The sum-total of distances of all node translations
' 1 = The biggest resultant vector in the set
'The return value of the function is an array identical to arrNodes but with different coordinates
Private Function RelaxMeshNodes(ByRef arrNodes, ByRef arrConnections, ByRef arrConstraints, ByVal Damping, ByVal Limit, ByRef Summary)

        Dim i, j
 Dim arrV(), resV
 Dim newNodes
 Dim ptCP

 Dim maxResVec, curResVec
 Dim sumNodeTrans

 maxResVec = 0.0
 sumNodeTrans = 0.0

 newNodes = arrNodes
 For i = 0 To UBound(newNodes)
  If arrConstraints(i) <> "FIXED" Then
   Erase arrV
   ReDim arrV(UBound(arrConnections(i)))
   For j = 0 To UBound(arrV)
    arrV(j) = MultiplyVector(Array(newNodes(i),  newNodes(arrConnections(i)(j)(0))), _
           arrConnections(i)(j)(1))
   Next
   resV = ResultantVector(arrV)
   resV = MultiplyVector(resV, Damping)
   resV = LimitVector(resV, Limit)

   If Rhino.IsObject(arrConstraints(i)) Then
    If Rhino.IsCurve(arrConstraints(i)) Then
     ptCP = Rhino.EvaluateCurve(arrConstraints(i),  Rhino.CurveClosestPoint(arrConstraints(i), resV(1)))
    ElseIf Rhino.IsBREP(arrConstraints(i)) Then
     ptCP = Rhino.BrepClosestPoint(arrConstraints(i), resV(1))(0)
    End If

    If IsArray(ptCP) Then
     newNodes(i) = ptCP
      curResVec = PointPointDistance(newNodes(i),  arrNodes(i))
      If curResVec > maxResVec Then maxResVec = curResVec
      sumNodeTrans = sumNodeTrans + curResVec
    Else
     newNodes(i) = resV(1)
      curResVec = PointPointDistance(newNodes(i),  arrNodes(i))
      If curResVec > maxResVec Then maxResVec = curResVec
      sumNodeTrans = sumNodeTrans + curResVec
    End If
   Else
    newNodes(i) = resV(1)
      curResVec = PointPointDistance(newNodes(i), arrNodes(i))
     If curResVec > maxResVec Then maxResVec = curResVec
     sumNodeTrans = sumNodeTrans + curResVec
   End If
  End If
 Next

 Summary = Array(sumNodeTrans, maxResVec)
 RelaxMeshNodes = newNodes
End Function

Private Function PointPointDistance(ByRef arrPoint1, ByRef arrPoint2)
 PointPointDistance = (arrPoint1(0)-arrPoint2(0)) * (arrPoint1(0)-arrPoint2(0)) + _
      (arrPoint1(1)-arrPoint2(1)) *  (arrPoint1(1)-arrPoint2(1)) + _
      (arrPoint1(2)-arrPoint2(2)) *  (arrPoint1(2)-arrPoint2(2))
 PointPointDistance = Sqr(PointPointDistance)
End Function

'This function calculates the resultant vector of an array of vectors.
'The starting point of the first vector in the array will be used as grip
'for the resultant vector, if an invalid vector array is passed an error will occur
Private Function ResultantVector(ByRef arrVectors)
 Dim i
 Dim divX, divY, divZ
 Dim resX, resY, resZ
 Dim ptT(2), ptH(2)

 resX = 0.0
 resY = 0.0
 resZ = 0.0
 For i = 0 To UBound(arrVectors)
  divX = arrVectors(i)(1)(0) - arrVectors(i)(0)(0)
  divY = arrVectors(i)(1)(1) - arrVectors(i)(0)(1)
  divZ = arrVectors(i)(1)(2) - arrVectors(i)(0)(2)
  resX = resX + divX
  resY = resY + divY
  resZ = resZ + divZ
 Next
 ptT(0) = arrVectors(0)(0)(0)
 ptT(1) = arrVectors(0)(0)(1)
 ptT(2) = arrVectors(0)(0)(2)
 ptH(0) = ptT(0) + resX
 ptH(1) = ptT(1) + resY
 ptH(2) = ptT(2) + resZ

 ResultantVector = Array(ptT, ptH)
End Function

'This function will limit a vectorlength to a certain value
'vectors smaller than the specified length will remain untouched.
'Note that it is unhealthy to use negative numbers or zero for dblMaxLength
Private Function LimitVector(ByVal vecIn, ByVal dblLimitation)
 Dim vecOut(1)
 Dim l

 vecOut(0) = vecIn(0)
 vecOut(1) = vecIn(1)
 l = PointPointDistance(vecIn(0), vecIn(1))

 If l > dblLimitation Then
  vecOut(1)(0) = vecOut(0)(0) + ((vecOut(1)(0)-vecOut(0)(0)) / l) * dblLimitation
  vecOut(1)(1) = vecOut(0)(1) + ((vecOut(1)(1)-vecOut(0)(1)) / l) * dblLimitation
  vecOut(1)(2) = vecOut(0)(2) + ((vecOut(1)(2)-vecOut(0)(2)) / l) * dblLimitation
 End If
 LimitVector = vecOut
End Function

'This function will multiply a vectorlength by a specified factor.
Private Function MultiplyVector(ByVal vecIn, ByVal dblFactor)
 Dim vecOut(1)
 vecOut(0) = vecIn(0)
 vecOut(1) = vecIn(1)
 vecOut(1)(0) = vecOut(0)(0) + (vecOut(1)(0) - vecOut(0)(0)) * dblFactor
 vecOut(1)(1) = vecOut(0)(1) + (vecOut(1)(1) - vecOut(0)(1)) * dblFactor
 vecOut(1)(2) = vecOut(0)(2) + (vecOut(1)(2) - vecOut(0)(2)) * dblFactor
 MultiplyVector = vecOut
End Function

'----------------------------------------------------------------------------------------------
'----------------------------------------------------------------------------------------------
'----------------------------------------------------------------------------------------------
'---------------------Thus ends the mesh relaxation source code...-----------------------------
'--------------Below you will find an subroutine which implements the above  routine-----------
'------------and also adds interface code.  (This subroutine requires Rhinoceros  3.x)---------
'----------------------------------------------------------------------------------------------
'----------------------------------------------------------------------------------------------
'----------------------------------------------------------------------------------------------

'This function translates a Rhino Nurbs Surface definition into an FDM Mesh definition
'idSurface = The ID of the surface to convert. If the ID is invalid, Null will be returned
'   If the surface is a non-compatible FDM object, Null will be returned
'   Surface that are closed or periodic in the v-direction should not be used.  Trims will be ignored.
'arrNodes = Points to a Variant variable that will recieve the Mesh Node data
'arrConnections = Points to a Variant variable that will recieve the Mesh Connectivity data
'arrConstraints = Points to a Variant variable that will recieve the Mesh Constraint data
'WarpTension = A double representing the tension of the fabric in Warp direction (U)
'WeftTension = A double representing the tension of the fabric in Weft direction (V)
'EdgeTension = An Array containing tension factor for all 4 surface edges 0=umin; 1=umax; 2=vmin;  3=vmax
'EdgeLinks = An Array containing constraint information for all four edges. Values can be:
' "FIXED" = Fixed edge
' objID = Linked edge
'  = Free edge. String that are not "FIXED" and do not represent an object are  automatically treated as free.
'     Use "FREE" to skip a few steps in the relaxation loop
'TipLinks = An Array containing constraint information for all four tips. Values can be identical to  EdgeLinks
'   0=umin,vmin; 1=umax,vmin; 2=umin,vmax; 3=umax,vmax
'If the function succeeds True will be returned, if the function fails Null will be returned.
Private Function NURBS2FDM(ByVal idSurface, ByRef arrNodes, ByRef arrFaces, _
         ByRef arrConnections, ByRef arrConstraints, _
         ByVal WarpTension, ByVal WeftTension, ByVal  EdgeTension, _
         ByVal EdgeLinks, ByVal TipLinks)
 NURBS2FDM = Null

 Dim u, v, N, M
 Dim arrN(), arrF(), arrC(), arrL()
 Dim rhPoints
 Dim uCount, vCount
 Dim uDegree, vDegree
 Dim strChoice

 rhPoints = Rhino.SurfacePoints(idSurface)
 uCount = Rhino.SurfacePointCount(idSurface)(0)
 vCount = Rhino.SurfacePointCount(idSurface)(1)
 uDegree = Rhino.SurfaceDegree(idSurface, 0)
 vDegree = Rhino.SurfaceDegree(idSurface, 1)

 If Rhino.IsSurfacePeriodic(idSurface, 0) Then 'periodic in u-direction
   'Set mesh nodes
  ReDim arrN(vCount * (uCount-uDegree) - 1)
  N = 0
  For u = 0 To uCount - uDegree - 1
  For v = 0 To vCount - 1
   arrN(N) = rhPoints((u*vCount)+v)
   N = N+1
  Next
  Next

  ReDim arrF((vCount-1)*(uCount-uDegree)-1)
  ReDim arrC(UBound(arrN))
  ReDim arrL(UBound(arrN))
  'Set mesh faces
  N = 0
  For u = 0 To uCount-uDegree-1
  For v = 0 To vCount-2
   arrF(N) = Array((u*vCount)+v, _
       ((u*vCount)+v+vCount) Mod  ((uCount-uDegree)*vCount), _
       ((u*vCount)+v+vCount+1) Mod  ((uCount-uDegree)*vCount), _
       (u*vCount)+v+1)
   N = N+1
  Next
  Next

  'Set fabric
  For u = 0 To uCount-uDegree-1
  For v = 1 To vCount-2
   N = (u*vCount)+v
   arrC(N) = Array(Array(N+1, WeftTension), _
       Array(N-1, WeftTension), _
       Array(((N-vCount)+((uCount-uDegree)*vCount))  Mod ((uCount-uDegree)*vCount), WarpTension), _
       Array((N+vCount) Mod  ((uCount-uDegree)*vCount), WarpTension))
   arrL(N) = "FREE"
  Next
  Next

  'Set u-border edges
  For u = 0 To (uCount-uDegree-1)*vCount Step vCount
   N = u
   arrC(N) = Array(Array((N+vCount) Mod ((uCount-uDegree)*vCount),  EdgeTension(0)), _
       Array((N-vCount+((uCount-uDegree)*vCount))  Mod ((uCount-uDegree)*vCount), EdgeTension(0)), _
       Array(N+1, WeftTension))
   arrL(N) = EdgeLinks(0)

   N = u+vCount-1
   arrC(N) = Array(Array((N+vCount+((uCount-uDegree)*vCount)) Mod  ((uCount-uDegree)*vCount), EdgeTension(1)), _
       Array((N-vCount+((uCount-uDegree)*vCount))  Mod ((uCount-uDegree)*vCount), EdgeTension(1)), _
       Array(N-1, WeftTension))
   arrL(N) = EdgeLinks(1)
  Next
 ElseIf Rhino.IsSurfaceClosed(idSurface, 0) Then  'closed in u direction
  'Set mesh nodes
  ReDim arrN(vCount * (uCount-1) - 1)
  N = 0
  For u = 0 To uCount - 2
  For v = 0 To vCount - 1
   arrN(N) = rhPoints((u*vCount)+v)
   N = N+1
  Next
  Next

  ReDim arrF((vCount-1)*(uCount-1)-1)
  ReDim arrC(UBound(arrN))
  ReDim arrL(UBound(arrN))
  'Set mesh faces
  N = 0
  For u = 0 To uCount-2
  For v = 0 To vCount-2
   arrF(N) = Array((u*vCount)+v, _
       ((u*vCount)+v+vCount) Mod  ((uCount-1)*vCount), _
       ((u*vCount)+v+vCount+1) Mod  ((uCount-1)*vCount), _
       (u*vCount)+v+1)
   N = N+1
  Next
  Next

  'Set fabric
  For u = 0 To uCount-2
  For v = 1 To vCount-2
   N = (u*vCount)+v
   arrC(N) = Array(Array(N+1, WeftTension), _
       Array(N-1, WeftTension), _
       Array(((N-vCount)+((uCount-1)*vCount)) Mod  ((uCount-1)*vCount), WarpTension), _
       Array((N+vCount) Mod ((uCount-1)*vCount),  WarpTension))
   arrL(N) = "FREE"
  Next
   Next

  'Set u-border edges
  For u = 0 To (uCount-2)*vCount Step vCount
   N = u
   arrC(N) = Array(Array((N+vCount) Mod ((uCount-1)*vCount), EdgeTension(0)), _
       Array((N-vCount+((uCount-1)*vCount)) Mod  ((uCount-1)*vCount), EdgeTension(0)), _
       Array(N+1, WeftTension))
   arrL(N) = EdgeLinks(0)

   N = u+vCount-1
   arrC(N) = Array(Array((N+vCount+((uCount-1)*vCount)) Mod ((uCount-1)*vCount),  EdgeTension(1)), _
       Array((N-vCount+((uCount-1)*vCount)) Mod  ((uCount-1)*vCount), EdgeTension(1)), _
       Array(N-1, WeftTension))
   arrL(N) = EdgeLinks(1)
  Next
 Else 'rectangular patch
  'Set mesh nodes
  ReDim arrN(UBound(rhPoints))
  For N = 0 To UBound(rhPoints)
   arrN(N) = rhPoints(N)
  Next
  'Set mesh faces
  ReDim arrF((uCount-1)*(vCount-1)-1)
  N = 0
  For u = 0 To uCount-2
  For v = 0 To vCount-2
   arrF(N) = Array((u*vCount)+v, (u*vCount)+v+vCount, (u*vCount)+v+1+vCount,  (u*vCount)+v+1)
   N = N+1
  Next
  Next
  'Set connections and link-constraints
  ReDim arrC(UBound(arrN))
  ReDim arrL(UBound(arrN))

  For N = 0 To UBound(arrN)
   arrC(N) = Array(Array(N+1, WeftTension), Array(N-1, WeftTension), _
       Array(N-vCount, WarpTension), Array(N+vCount,  WarpTension))
   arrL(N) = "FREE"
  Next
   'Set u-border edge cables
  For N = 0 To vCount*(uCount-1) Step vCount
   arrC(N) = Array(Array(N+vCount, EdgeTension(0)), Array(N-vCount,  EdgeTension(0)), Array(N+1, WeftTension))
   arrL(N) = EdgeLinks(0)
   M = N+vCount-1
   arrC(M) = Array(Array(M+vCount, EdgeTension(1)), Array(M-vCount,  EdgeTension(1)), Array(M-1, WeftTension))
   arrL(M) = EdgeLinks(1)
  Next
  'Set v-border edge cables
  For N = 0 To vCount-1
   arrC(N) = Array(Array(N+vCount, WarpTension), Array(N+1, EdgeTension(2)),  Array(N-1, EdgeTension(2)))
   arrL(N) = EdgeLinks(2)
   M = N + (uCount-1)*vCount
    arrC(M) = Array(Array(M-vCount, WarpTension), Array(M-1, EdgeTension(3)),  Array(M+1, EdgeTension(3)))
   arrL(M) = EdgeLinks(3)
  Next
  'Set tips
  arrC(0) = Array(Array(1,EdgeTension(2)), Array(uCount, EdgeTension(0)))
  arrL(0) = TipLinks(0)
  arrC(vCount-1) = Array(Array(vCount-2, EdgeTension(2)), Array(2*vCount-1,  EdgeTension(1)))
  arrL(vCount-1) = TipLinks(2)
  arrC(vCount*(uCount-1)) = Array(Array(vCount*(uCount-1)+1, EdgeTension(3)),  Array(vCount*(uCount-2), EdgeTension(0)))
  arrL(vCount*(uCount-1)) = TipLinks(1)
  arrC(vCount*uCount-1) = Array(Array(vCount*uCount-2, EdgeTension(3)),  Array(vCount*(uCount-1)-1, EdgeTension(1)))
  arrL(vCount*uCount-1) = TipLinks(3)
 End If

 arrNodes = arrN
 arrFaces = arrF
 arrConnections = arrC
 arrConstraints = arrL
 NURBS2FDM = True
End Function

Private Function RecreateFDMSurface(idSurface, arrNodes)
 Dim newNodes()
 Dim u, v, N, index
 Dim Nu, Nv, Du

 Nu = Rhino.SurfacePointCount(idSurface)(0)
 Nv = Rhino.SurfacePointCount(idSurface)(1)
 Du = Rhino.SurfaceDegree(idSurface, 0)
 ReDim newNodes(Nu*Nv-1)

 If Rhino.IsSurfacePeriodic(idSurface, 0) Then
  N = 0
  For u = 0 To Nu-1
  For v = 0 To Nv-1
   index = (u*Nv+v) Mod ((Nu-Du)*Nv)
   newNodes(N) = arrNodes(index)
   N = N+1
  Next
  Next
 ElseIf Rhino.IsSurfaceClosed(idSurface, 0) Then
  N = 0
  For u = 0 To Nu-1
  For v = 0 To Nv-1
   index = (u*Nv+v) Mod ((Nu-1)*Nv)
   newNodes(N) = arrNodes(index)
   N = N+1
  Next
  Next
 Else
  For N = 0 To UBound(arrNodes)
   newNodes(N) = arrNodes(N)
  Next
 End If
 RecreateFDMSurface = Rhino.AddNurbsSurface(Rhino.SurfacePointCount(idSurface), _
             newNodes, _
             Rhino.SurfaceKnots(idSurface)(0), _
             Rhino.SurfaceKnots(idSurface)(1), _
             Rhino.SurfaceDegree(idSurface), _
             Rhino.SurfaceWeights(idSurface))
End Function

'This function displays a message at the command line, blinks it with a red background colour and  then offers a set of options.
'Might be handy to use for feedback...
Private Function FlashMessage(strMessage, arrOptions)
 Dim rgbCurrent, rgbFlash
 Dim lngFlashPause
 lngFlashPause = 175
 rgbCurrent = Rhino.AppearanceColor(12)
 rgbFlash = RGB(255,0,0)

 Rhino.Prompt strMessage
 Rhino.AppearanceColor 12, rgbFlash
 Rhino.Sleep lngFlashPause
 Rhino.AppearanceColor 12, rgbCurrent
 Rhino.Sleep lngFlashPause
 Rhino.AppearanceColor 12, rgbFlash
 Rhino.Sleep lngFlashPause
 Rhino.AppearanceColor 12, rgbCurrent

FlashMessage = Rhino.GetString(strMessage, "", arrOptions)

End Function

'This function creates 4 textdots at the surface corners and prompts the user to pick some.
'You have to remove the objects again by calling the function CLEARPREVIEW afterwards.
'The return value is an array that contains the indices of the edges or NULL on error/nopick
'0=umin,vmin 1=umax,vmin 2=umin,vmax 3=umax,vmax
Private Function GetTips(ByVal idSurface, ByVal strPrompt)
 GetTips = Null
 Dim arrDots(3), selDots
 Dim srfDomain, i, j
 Dim arrAll(), S

 If Rhino.IsSurfacePeriodic(idSurface, 0) Or Rhino.IsSurfacePeriodic(idSurface, 1) Or _
 Rhino.IsSurfaceClosed(idSurface, 0) Or Rhino.IsSurfaceClosed(idSurface, 1) Then
  FlashMessage "The surface has no corners... You'll need to fix or link the edges  instead.", Array("OK")

Else

  srfDomain = Array(Rhino.SurfaceDomain(idSurface,0), Rhino.SurfaceDomain(idSurface,1))
  arrDots(0) = Rhino.AddTextDot("A", Rhino.EvaluateSurface(idSurface,  Array(srfDomain(0)(0), srfDomain(1)(0))))
  arrDots(1) = Rhino.AddTextDot("B", Rhino.EvaluateSurface(idSurface,  Array(srfDomain(0)(1), srfDomain(1)(0))))
  arrDots(2) = Rhino.AddTextDot("C", Rhino.EvaluateSurface(idSurface,  Array(srfDomain(0)(0), srfDomain(1)(1))))
  arrDots(3) = Rhino.AddTextDot("D", Rhino.EvaluateSurface(idSurface,  Array(srfDomain(0)(1), srfDomain(1)(1))))
  Rhino.ObjectName arrDots, "GelflingRelaxationPreviewObjects"
 
  selDots = Rhino.GetObjects(strPrompt, 0, False, False, True, arrDots)
  If IsNull(selDots) Then Exit Function
  S = 0
  For i = 0 To UBound(selDots)
   For j = 0 To 3
    If selDots(i) = arrDots(j) Then
     ReDim Preserve arrAll(S)
     arrAll(S) = j
     S = S+1
    End If
   Next
  Next
  GetTips = arrAll
 End If
End Function

'This function is a wrapper for the Rhino.ExtractIsoCurve method. Differences:
'- it returns only a single ID instead of an array.
'-if the extracted edge is very short a point will be drawn instead.
Private Function ExtractIsoCurveWrapper(ByVal idSurface, ByVal arrParam, ByVal Direction)
 Dim varResult
 varResult = Rhino.ExtractIsoCurve(idSurface, arrParam, Direction)
 If IsNull(varResult) Then
  ExtractIsoCurveWrapper = Rhino.AddPoint(Rhino.EvaluateSurface(idSurface, arrParam))
  If IsNull(ExtractIsoCurveWrapper) Then ExtractIsoCurveWrapper = "null-object"
 ElseIf Rhino.CurveLength(varResult(0)) <= Rhino.UnitAbsoluteTolerance Then   Rhino.DeleteObject varResult(0)   ExtractIsoCurveWrapper = Rhino.AddPoint(Rhino.EvaluateSurface(idSurface, arrParam))   If IsNull(ExtractIsoCurveWrapper) Then ExtractIsoCurveWrapper = "null-object"  Else   ExtractIsoCurveWrapper = varResult(0)  End If End Function  'This function copies the edges of a surface and prompts the user to pick some. 'The return value is an array with edge indices or NULL on error/nopick '0=umin 1=umax 2=vmin 3=vmax Private Function GetEdges(ByVal idSurface, ByVal strPrompt)  GetEdges = Null  Dim arrEdges(3), selEdges  Dim srfDomain(1), midDomain(1)  Dim i, j  Dim arrAll(), S      srfDomain(0) = Rhino.SurfaceDomain(idSurface,0)  midDomain(0) = (srfDomain(0)(0) + srfDomain(0)(1))/2  srfDomain(1) = Rhino.SurfaceDomain(idSurface,1)  midDomain(1) = (srfDomain(1)(0) + srfDomain(1)(1))/2  If Rhino.IsSurfacePeriodic(idSurface, 1) Or Rhino.IsSurfaceClosed(idSurface, 1) Then    arrEdges(2) = ExtractIsoCurveWrapper(idSurface, Array(srfDomain(0)(0), midDomain(1)),  1)   arrEdges(3) = ExtractIsoCurveWrapper(idSurface, Array(srfDomain(0)(1), midDomain(1)),  1)  ElseIf Rhino.IsSurfacePeriodic(idSurface, 0) Or Rhino.IsSurfaceClosed(idSurface, 0) Then   arrEdges(0) = ExtractIsoCurveWrapper(idSurface, Array(midDomain(0), srfDomain(1)(0)),  0)   arrEdges(1) = ExtractIsoCurveWrapper(idSurface, Array(midDomain(0), srfDomain(1)(1)),  0)  Else   arrEdges(0) = ExtractIsoCurveWrapper(idSurface, Array(midDomain(0), srfDomain(1)(0)),  0)   arrEdges(1) = ExtractIsoCurveWrapper(idSurface, Array(midDomain(0), srfDomain(1)(1)),  0)   arrEdges(2) = ExtractIsoCurveWrapper(idSurface, Array(srfDomain(0)(0), midDomain(1)),  1)   arrEdges(3) = ExtractIsoCurveWrapper(idSurface, Array(srfDomain(0)(1), midDomain(1)),  1)  End If    For i = 0 To 3   If IsNull(arrEdges(i)) Or IsEmpty(arrEdges(i)) Then arrEdges(i) = "null-object"  Next  Rhino.ObjectName arrEdges, "GelflingRelaxationPreviewObjects"     selEdges = Rhino.GetObjects(strPrompt, 0, False, False, True, arrEdges)  If IsNull(selEdges) Then Exit Function  S = 0  For i = 0 To UBound(selEdges)   For j = 0 To 3    If selEdges(i) = arrEdges(j) Then     ReDim Preserve arrAll(S)     arrAll(S) = j     S = S+1    End If   Next  Next  GetEdges = arrAll End Function   'This function draws a set of curves on a surface, either in U/warp or V/weft 'You have to call the CLEARPREVIEW function to remove the curves again afterwards. Private Sub DrawWarpWeftPreview(ByVal strSurface, ByVal intDirection, ByVal dblDensity)  Dim uDomain, vDomain  Dim i, u, v  Dim crvAdd     uDomain = Rhino.SurfaceDomain(strSurface, 0)  vDomain = Rhino.SurfaceDomain(strSurface, 1)   Rhino.EnableRedraw False  For i = 0 To 1 Step 1/dblDensity   u = uDomain(0) + (uDomain(1)-uDomain(0))*i   v = vDomain(0) + (vDomain(1)-vDomain(0))*i   crvAdd = Rhino.ExtractIsoCurve(strSurface, Array(u,v), intDirection)   Rhino.ObjectName crvAdd, "GelflingRelaxationPreviewObjects"  Next  Rhino.EnableRedraw True End Sub  'This function removes all objects from the document that have been created by functions in this  script. 'Basically it removes all objects that are named "GelflingRelaxationPreviewObjects" Private Sub ClearPreview()  Dim allPreviewObjects  allPreviewObjects = Rhino.ObjectsByName("GelflingRelaxationPreviewObjects", False)  If IsNull(allPreviewObjects) Then Exit Sub  Rhino.DeleteObjects allPreviewObjects End Sub   'This function checks a surface to see whether it is suitablefor FDM relaxation. 'If it turns out not to be, then it will prompt the user for action. 'If the surface could not be or was not fixed NULL will be returned. 'If the surface is acceptable or was fixed the new ID will be returned Private Function CheckNURBSSurface(ByVal idSurface)  CheckNURBSSurface = Null  Dim strResult  Dim idNewSurface    idNewSurface = idSurface     If Not Rhino.IsSurface(idNewSurface) Then Exit Function  If (Rhino.IsSurfaceClosed(idSurface,0) Or Rhino.IsSurfacePeriodic(idSurface,0)) And _  (Rhino.IsSurfaceClosed(idSurface,1) Or Rhino.IsSurfacePeriodic(idSurface,1)) Then   strResult = FlashMessage("The surface you selected has no free edges. Relaxation is  not possible.", Array("OK"))    Exit Function  End If     If Rhino.SurfacePointCount(idNewSurface)(0) <= 3 Or Rhino.SurfacePointCount(idSurface)(1) <=3  Then   strResult = FlashMessage("The surface you selected does not have sufficient grips.",  Array("OK"))   Exit Function  End If   '  If Rhino.IsSurfaceRational(idSurface) Then '   strResult = FlashMessage("The surface you selected is rational. Weighted grips will  not translate correctly, what would you like to do?", _ '          Array("Unweight", "Ignore",  "Abort")) '   If IsNull(strResult) Then Exit Function '   Select Case UCase(strResult) '   Case "UNWEIGHT" '    idNewSurface = Rhino.AddNurbsSurface(Rhino.SurfacePointCount(idNewSurface), _ '              Rhino.SurfacePoints(idNewSurface), _  '              Rhino.SurfaceKnots(idNewSurface)(0), _  '               Rhino.SurfaceKnots(idNewSurface)(1), _ '              Rhino.SurfaceDegree(idNewSurface)) '    Rhino.DeleteObject idSurface '   Case "IGNORE" '    'Do not take any action '   Case Else '    Exit Function '   End Select '  End If    If Rhino.IsSurfaceTrimmed(idNewSurface) Then   strResult = FlashMessage("The surface you selected is trimmed. Trims are not  supported, what would you like to do?", Array("Untrim", "Ignore", "Abort"))    If IsNull(strResult) Then Exit Function   Select Case UCase(strResult)   Case "UNTRIM"    idNewSurface = Rhino.AddNurbsSurface(Rhino.SurfacePointCount(idNewSurface), _               Rhino.SurfacePoints(idNewSurface), _                Rhino.SurfaceKnots(idNewSurface)(0), _               Rhino.SurfaceKnots(idNewSurface)(1), _               Rhino.SurfaceDegree(idNewSurface), _               Rhino.SurfaceWeights(idNewSurface))    Rhino.DeleteObject idSurface    Case "IGNORE"    'Do not take any action   Case Else    Exit Function   End Select  End If    If Rhino.IsSurfacePeriodic(idNewSurface, 1) Then   strResult = FlashMessage("Only u-periodic surfaces are supported, what would you like  to do?", Array("Swap_UV_Directions", "Abort"))   If IsNull(strResult) Then Exit Function   If UCase(strResult) = "ABORT" Then Exit Function   Rhino.EnableRedraw vbFalse    Rhino.UnselectAllObjects    Rhino.SelectObject idNewSurface    Rhino.Command "-_Dir _SwapUV _Enter", vbFalse   Rhino.EnableRedraw vbTrue  End If   If Rhino.IsSurfaceClosed(idNewSurface, 1) Then   strResult = FlashMessage("Only u-continues surfaces are supported, what would you  like to do?", Array("Swap_UV_Directions", "Abort"))    If IsNull(strResult) Then Exit Function   If UCase(strResult) = "ABORT" Then Exit Function   Rhino.EnableRedraw vbFalse    Rhino.UnselectAllObjects    Rhino.SelectObject idNewSurface    Rhino.Command "-_Dir _SwapUV _Enter", vbFalse   Rhino.EnableRedraw vbTrue  End If    CheckNURBSSurface = idNewSurface End Function   'This is it. The main sub... Private Sub RelaxNURBS_Surface()  Dim arrNodes, arrFaces, arrConnections, arrConstraints  Dim EdgeTension(3), WarpTension, WeftTension  Dim EdgeLink(3), TipLink(3)  Dim strSurfaceID, newSurfaceID  Dim MeshID  Dim DampingFactor, Limitation, PreflightLoops, AccuracyMark, LimitationDecay  Dim Summary  Dim srfBBox, Diagonal  Dim RunAsDeveloper, DestinationFolder, FramePrefix, FrameFormat, FrameDim(1)   'Set to TRUE to save an animation sequence of the relaxation process.  RunAsDeveloper = False    strSurfaceID = Rhino.GetObject("Select a surface for relaxation", 8, True, True)  If IsNull(strSurfaceID) Then Exit Sub  strSurfaceID = CheckNURBSSurface(strSurfaceID)  If IsNull(strSurfaceID) Then   Rhino.Print "Relaxation process aborted due to improper geometry..."   Exit Sub  End If   Rhino.SurfaceIsoCurveDensity strSurfaceID, -1  If Not IsNull(Rhino.GetObjectData(strSurfaceID, "Gelfling_Relaxation", "LastOperation")) Then   EdgeTension(0) = CDbl(Rhino.GetObjectData(strSurfaceID, "Gelfling_Relaxation",  "EdgeTension0"))   EdgeTension(1) = CDbl(Rhino.GetObjectData(strSurfaceID, "Gelfling_Relaxation",  "EdgeTension1"))   EdgeTension(2) = CDbl(Rhino.GetObjectData(strSurfaceID, "Gelfling_Relaxation",  "EdgeTension2"))   EdgeTension(3) = CDbl(Rhino.GetObjectData(strSurfaceID, "Gelfling_Relaxation",  "EdgeTension3"))    WarpTension = CDbl(Rhino.GetObjectData(strSurfaceID, "Gelfling_Relaxation",  "WarpTension"))   WeftTension = CDbl(Rhino.GetObjectData(strSurfaceID, "Gelfling_Relaxation",  "WeftTension"))   EdgeLink(0) = Rhino.GetObjectData(strSurfaceID, "Gelfling_Relaxation", "EdgeLink0")   EdgeLink(1) = Rhino.GetObjectData(strSurfaceID, "Gelfling_Relaxation", "EdgeLink1")   EdgeLink(2) = Rhino.GetObjectData(strSurfaceID, "Gelfling_Relaxation", "EdgeLink2")   EdgeLink(3) = Rhino.GetObjectData(strSurfaceID, "Gelfling_Relaxation", "EdgeLink3")   TipLink(0) = Rhino.GetObjectData(strSurfaceID, "Gelfling_Relaxation", "TipLink0")   TipLink(1) = Rhino.GetObjectData(strSurfaceID, "Gelfling_Relaxation", "TipLink1")   TipLink(2) = Rhino.GetObjectData(strSurfaceID, "Gelfling_Relaxation", "TipLink2")   TipLink(3) = Rhino.GetObjectData(strSurfaceID, "Gelfling_Relaxation", "TipLink3")  Else   WarpTension = 1.0   WeftTension = 1.0   For i = 0 To 3    EdgeTension(i) = 10.0    EdgeLink(i) = "FREE"    TipLink(i) = "FIXED"   Next  If Rhino.IsSurfacePeriodic(strSurfaceID, 0) Or Rhino.IsSurfaceClosed(strSurfaceID, 0) Then     For i = 0 To 3     EdgeLink(i) = "FIXED"    Next   End If  End If    Rhino.Prompt "Loading geometry... please wait"  Summary = NURBS2FDM(strSurfaceID, arrNodes, arrFaces, arrConnections, arrConstraints, _       WarpTension, WeftTension, EdgeTension, EdgeLink,  TipLink)  If IsNull(Summary) Then   MsgBox "Error in building FDM mesh.", vbOKOnly Or vbCritical, "Relaxation error"   Exit Sub  End If     Dim arrOptions, strResult  Dim intObject, i, N  Dim idParent  Do   If RunAsDeveloper Then  arrOptions = Array("Tension_Factors", "Geometry_Links", "Summary", "Relax", "Relax_advanced", "Quit")    Else    arrOptions = Array("Tension_Factors", "Geometry_Links", "Relax", "Quit")   End If   strResult = Rhino.GetString("Relaxation settings", "Relax", arrOptions)   If IsNull(strResult) Then Exit Sub   Select Case Left(UCase(strResult),1)  Case "M"     If UCase(strResult) = "MELLON" Then RunAsDeveloper = True   Case "T"    Do     arrOptions = Array("Warp", "Weft", "Edges", "Return")     strResult = Rhino.GetString("Fabric tension factor properties",  "Return", arrOptions)      If IsNull(strResult) Then strResult = "Return"     Select Case Left(UCase(strResult), 2)     Case "WA"      DrawWarpWeftPreview strSurfaceID, 0, 30      strResult = Rhino.GetReal("Specify a new fabric warp  tension", WarpTension, 0.01, 1000)      If Not IsNull(strResult) Then       WarpTension = CDbl(strResult)      End If      ClearPreview     Case "WE"      DrawWarpWeftPreview strSurfaceID, 1, 30      strResult = Rhino.GetReal("Specify a new fabric weft  tension", WeftTension, 0.01, 1000)  If Not IsNull(strResult) Then        WeftTension = CDbl(strResult)      End If      ClearPreview     Case "ED"      intObject = GetEdges(strSurfaceID, "Select edges to set  tension")      If IsArray(intObject) Then       strResult = Rhino.GetReal("Specify a new edge cable  tension", EdgeTension(intObject(0)), 0.01, 1000)       If Not IsNull(strResult) Then        For i = 0 To UBound(intObject)          EdgeTension(intObject(i)) =  CDbl(strResult)        Next       End If      End If      ClearPreview     Case Else      Exit Do     End Select    Loop   Case "G"    Do     arrOptions = Array("Corners", "Edges", "Return")     strResult = Rhino.GetString("Surface geometry linking options",  "Return", arrOptions)     If IsNull(strResult) Then strResult = "Return"     Select Case Left(UCase(strResult), 1)     Case "C"      intObject = GetTips(strSurfaceID, "Select corners to  restrain")      If IsArray(intObject) Then       arrOptions = Array("Fixed", "Linked")       strResult = Rhino.GetString("Pick a node restraint  type", "Fixed", arrOptions)       If Not IsNull(strResult) Then        Select Case Left(UCase(strResult),2)        Case "LI"         idParent = Rhino.GetObject("Select a  guide object", 4+8+16, False, True)          If Not IsNull(idParent) Then          For i = 0 To  UBound(intObject)           TipLink(intObject(i))  = idParent          Next         End If        Case Else         For i = 0 To UBound(intObject)          TipLink(intObject(i)) =  "FIXED"         Next        End Select       End If      End If      ClearPreview      Rhino.UnSelectAllObjects     Case "E"      intObject = GetEdges(strSurfaceID, "Select edges to  restrain")      If IsArray(intObject) Then       arrOptions = Array("Fixed", "Free", "Linked")       strResult = Rhino.GetString("Edge restraint type?",  "Fixed", arrOptions)        If Not IsNull(strResult) Then        Select Case Left(UCase(strResult),2)        Case "FR"         For i = 0 To UBound(intObject)          EdgeLink(intObject(i)) = ""         Next        Case "LI"         idParent = Rhino.GetObject("Select a  guide object", 4+8+16, False, False)           If Not IsNull(idParent) Then          For i = 0 To  UBound(intObject)            EdgeLink(intObject(i)) = idParent           Next         End If        Case Else         For i = 0 To UBound(intObject)          EdgeLink(intObject(i)) =  "FIXED"         Next        End Select       End If      End If      ClearPreview      Rhino.UnSelectAllObjects     Case Else      Exit Do     End Select    Loop   Case "S"    N = 0    For i = 0 To UBound(arrConnections)     N = N + UBound(arrConnections(i))+1    Next    MsgBox "NURBS surface relaxation data for object; " & vbNewLine & _        "[" & strSurfaceID & "]" & vbNewLine & vbNewLine & _        "Mesh node count; " & UBound(arrNodes)+1 & vbNewLine & _        "Mesh face count; " & UBound(arrFaces)+1 & vbNewLine & _        "Mesh link count; " & N & vbNewLine & _        "Fabric warp-tension; " & WarpTension & "%" & vbNewLine & _        "Fabric weft-tension; " & WeftTension & "%" & vbNewLine & _        "Fabric edge-tension(0); " & EdgeTension(0) & "% (" & EdgeLink(0)  & ")" & vbNewLine & _        "Fabric edge-tension(1); " & EdgeTension(1) & "% (" & EdgeLink(1)  & ")" & vbNewLine & _        "Fabric edge-tension(2); " & EdgeTension(2) & "% (" & EdgeLink(2)  & ")" & vbNewLine & _        "Fabric edge-tension(3); " & EdgeTension(3) & "% (" & EdgeLink(3)  & ")" & vbNewLine & _        "Fabric corner-link(A); " & TipLink(0) & vbNewLine & _        "Fabric corner-link(B); " & TipLink(1) & vbNewLine & _        "Fabric corner-link(C); " & TipLink(2) & vbNewLine & _        "Fabric corner-link(D); " & TipLink(3) & vbNewLine & vbNewLine & _        "end of summary...", vbOKOnly, "FDM-mesh summary"   Case "R"    srfBBox = Rhino.BoundingBox(strSurfaceID)    Diagonal = PointPointDistance(srfBBox(0), srfBBox(6))        If Len(strResult) = 14 Then     AccuracyMark = Rhino.GetReal("Specify relaxation tolerance",  Rhino.UnitAbsoluteTolerance, Rhino.UnitAbsoluteTolerance/100)     DampingFactor = Rhino.GetReal("Specify a global damping factor", 1.0,  0.001, 1000.0)     Limitation = Rhino.GetReal("Specify an initial translation  limitation", Round(Diagonal * 0.05,2), AccuracyMark, Diagonal*10)     LimitationDecay = Rhino.GetReal("Specify a translation limitation  decay factor per iteration", 0.95, 0.1, 0.99)     PreflightLoops = Rhino.GetInteger("Specify the number of  preflight-iterations", 20, 1, 1000)     If IsNull(AccuracyMark) Then AccuracyMark =  Rhino.UnitAbsoluteTolerance     If IsNull(DampingFactor) Then DampingFactor = 1.0     If IsNull(Limitation) Then Limitation = Diagonal * 0.05      If IsNull(LimitationDecay) Then LimitationDecay = 0.95     If IsNull(PreflightLoops) Then PreflightLoops = 20    Else     DampingFactor = 1.0     Limitation = Diagonal * 0.05     PreflightLoops = 20     AccuracyMark = Rhino.UnitAbsoluteTolerance     LimitationDecay = 0.95    End If    Exit Do   Case "Q"    Exit Sub   Case Else    Rhino.Print "Unknown command entered... nothing done."   End Select     Rhino.SetObjectData strSurfaceID, "Gelfling_Relaxation", "LastOperation", CStr(Now)   Rhino.SetObjectData strSurfaceID, "Gelfling_Relaxation", "EdgeTension0",  CStr(EdgeTension(0))   Rhino.SetObjectData strSurfaceID, "Gelfling_Relaxation", "EdgeTension1",  CStr(EdgeTension(1))   Rhino.SetObjectData strSurfaceID, "Gelfling_Relaxation", "EdgeTension2",  CStr(EdgeTension(2))   Rhino.SetObjectData strSurfaceID, "Gelfling_Relaxation", "EdgeTension3",  CStr(EdgeTension(3))   Rhino.SetObjectData strSurfaceID, "Gelfling_Relaxation", "WarpTension",  CStr(WarpTension)    Rhino.SetObjectData strSurfaceID, "Gelfling_Relaxation", "WeftTension",  CStr(WeftTension)   Rhino.SetObjectData strSurfaceID, "Gelfling_Relaxation", "EdgeLink0", EdgeLink(0)   Rhino.SetObjectData strSurfaceID, "Gelfling_Relaxation", "EdgeLink1", EdgeLink(1)   Rhino.SetObjectData strSurfaceID, "Gelfling_Relaxation", "EdgeLink2", EdgeLink(2)   Rhino.SetObjectData strSurfaceID, "Gelfling_Relaxation", "EdgeLink3", EdgeLink(3)   Rhino.SetObjectData strSurfaceID, "Gelfling_Relaxation", "TipLink0", TipLink(0)   Rhino.SetObjectData strSurfaceID, "Gelfling_Relaxation", "TipLink1", TipLink(1)   Rhino.SetObjectData strSurfaceID, "Gelfling_Relaxation", "TipLink2", TipLink(2)   Rhino.SetObjectData strSurfaceID, "Gelfling_Relaxation", "TipLink3", TipLink(3)  Loop    Rhino.UnSelectAllObjects  Rhino.HideObject strSurfaceID    Summary = NURBS2FDM(strSurfaceID, arrNodes, arrFaces, arrConnections, arrConstraints, _       WarpTension, WeftTension, EdgeTension, EdgeLink,  TipLink)  If IsNull(Summary) Then   MsgBox "The surface could not be translated into an FDM-mesh."& vbNewLine & _    "The fact that you're seeing this warning means there" & vbNewLine & _    "is a bug in the script. Please mail your surface file" & vbNewLine & _    "(*.3dm fileformat) to david@rutten.as", vbOKOnly Or vbCritical, "Relaxation  routine bug"   Exit Sub  End If    Rhino.Command "-_AdvancedDisplay _Wires _ShowMeshWires=Yes _Enter _Enter", vbFalse  MeshID = Rhino.AddMesh(arrNodes, arrFaces)      DestinationFolder = Null  If RunAsDeveloper Then   DestinationFolder = Rhino.BrowseForFolder(,"Select a folder to save the animation  sequence. Press 'Cancel' to not save animation.", "Animation settings")   If Not IsNull(DestinationFolder) Then    FramePrefix = Rhino.StringBox("Enter a name for the sequence...",  "RelaxationFrame", "Animation settings")    If IsNull(FramePrefix) Then  DestinationFolder = Null     Else     FrameFormat = Rhino.ListBox(Array("bmp", "tga", "pcx", "jpg", "png",  "tif"), "Select a file format", "Animation settings")     If IsNull(FrameFormat) Then      DestinationFolder = Null     Else      Summary = Rhino.PropertyListBox(Array("Animation width",  "Animation height"), _               Array("1500", "1000"), "Enter frame dimensions", "Animation settings")      If IsNull(Summary) Then       DestinationFolder = Null      Else       FrameDim(0) = Summary(0)       FrameDim(1) = Summary(1)      End If     End If    End If     If Not IsNull(DestinationFolder) Then     Rhino.Command "-_TestViewCaptureToFile " & Chr(34) &  DestinationFolder & FramePrefix & "00000." & FrameFormat & Chr(34) & _            " _Width=" & FrameDim(0) & " _Height=" &  FrameDim(1) &" _DrawCplane=No _DrawWorldAxes=No _Enter", vbFalse    End If   End If  End If    'Analyse current FDM mesh properties  Rhino.Prompt "Performing test relaxation run... please wait"  RelaxMeshNodes arrNodes, arrConnections, arrConstraints, DampingFactor, Limitation, Summary  Rhino.Print "Initial cumulative node translation: " & Round(Summary(0)) &  Rhino.UnitSystemName(False, True, True) & _     "   Initial largest node vector: " & Round(Summary(1), 2) & " N"    'Perform preflight relaxation  For i = 1 To PreflightLoops   Rhino.Prompt "Performing preflight relaxation. Step " & i & " of " & PreflightLoops &  "..."   arrNodes = RelaxMeshNodes(arrNodes, arrConnections, arrConstraints, DampingFactor,  Limitation, Summary)   Rhino.EnableRedraw vbFalse    Rhino.DeleteObject MeshID    MeshID = Rhino.AddMesh(arrNodes, arrFaces)   Rhino.EnableRedraw vbTrue           If Not IsNull(DestinationFolder) Then    Rhino.Command "-_TestViewCaptureToFile " & Chr(34) & DestinationFolder &  FramePrefix & Right("00000" & i, 5) & "." & FrameFormat & Chr(34) & _            " _Width=" & FrameDim(0) & " _Height=" &  FrameDim(1) & " _DrawCplane=No _DrawWorldAxes=No _Enter", vbFalse   End If  Next    'Perform damped relaxation  Do   arrNodes = RelaxMeshNodes(arrNodes, arrConnections, arrConstraints, DampingFactor,  Limitation, Summary)   Rhino.Prompt "Iteration " & i & _       "   Damping: " & Round(DampingFactor*100, 2) & "%" & _       "   Limitation: " & Round(Limitation, 2) &  Rhino.UnitSystemName(False, True, True)    Limitation = Limitation * LimitationDecay   'DampingFactor = DampingFactor * 0.98     Rhino.EnableRedraw vbFalse    Rhino.DeleteObject MeshID    MeshID = Rhino.AddMesh(arrNodes, arrFaces)   Rhino.EnableRedraw vbTrue          If Not IsNull(DestinationFolder) Then    Rhino.Command "-_TestViewCaptureToFile " & Chr(34) & DestinationFolder &  FramePrefix & Right("00000" & i, 5) & "." & FrameFormat & Chr(34) & _            " _Width=" & FrameDim(0) & " _Height=" &  FrameDim(1) &" _DrawCplane=No _DrawWorldAxes=No _Enter", vbFalse   End If     If Limitation < i =" i+1" newsurfaceid =" RecreateFDMSurface(strSurfaceID,">