Week 5 « parametric realizations fall 2008

Week 5

——————-Week 5 Homework——————–

1. Focus on studio

2. Final gathering will be at 6:00 on Friday, December 12th in Ware Lounge

——————-Week 5 Class Session——————–

This session will introduce you to the concept of L-Systems. We will use the L-System to generate a dome structure.

———————Step 1—————————-

Option Explicit
‘Script written by mark.bearak
‘Script copyrighted by dtls.Architecture
‘Script version Tuesday, November 11, 2008 7:06:57 PM

Call Main()
Sub Main()
Dim arrPoint : arrPoint = Rhino.getPoint (“Select your start point”)
End Sub

———————Step 2—————————-

Call Main()
Sub Main()
Dim i
Dim arrPoint : arrPoint = Rhino.getPoint
Dim dblLength : dblLength = 8
For i = -180 To 179 Step 90
Dim arrNewPoint : arrNewPoint = Rhino.Polar (arrPoint, i, 10)
Call Rhino.AddLine (arrPoint, arrNewPoint)
Next
End Sub

———————Step 3—————————-

Call Main()
Sub Main()
Dim i, strCrv
Dim arrPoint : arrPoint = Rhino.getPoint
Dim dblLength : dblLength = 8
For i = -180 To 179 Step 90
    Dim arrNewPoint : arrNewPoint = Rhino.Polar (arrPoint, i, 10)
    strCrv = Rhino.AddLine (arrPoint, arrNewPoint)
    Call LSystem(strCrv)
Next
End Sub

Function LSystem(strCrv)
Dim arrNewestPt, strNewCrv, tempAnglea, tempAngleb
Dim arrNewPt : arrNewPt = Rhino.CurveEndPoint (strCrv)
Dim dblDist : dblDist = Rhino.CurveLength (strCrv)
Dim dblAngle : dblAngle = Rhino.Angle (Rhino.CurveStartPoint (strCrv), Rhino.CurveEndPoint (strCrv))
Call Rhino.Print (“Angle: ” & CStr(dblAngle(0)))
dblDist = dblDist – 1
tempAnglea = dblAngle(0) – 10
If dblDist > 0 Then
    arrNewestPt = Rhino.Polar (arrNewPt, tempAnglea, dblDist)
    strNewCrv = Rhino.addLine (arrNewPt,arrNewestPt)
    Call LSystem(strNewCrv)
End If
End Function

———————Step 4—————————-

Function LSystem(strCrv)
Dim i, arrNewestPt, strNewCrv, tempAnglea, tempAngleb
Dim arrNewPt : arrNewPt = Rhino.CurveEndPoint (strCrv)
Dim dblDist : dblDist = Rhino.CurveLength (strCrv)
Dim dblAngle : dblAngle = Rhino.Angle (Rhino.CurveStartPoint (strCrv), Rhino.CurveEndPoint (strCrv))
dblDist = dblDist – 1
If dblDist > 1 Then
    For i = 0 To 1
      If i Mod 2 = 0 Then
        tempAnglea = dblAngle(0) – 20
      Else
        tempAnglea = dblAngle(0) + 20
      End If
      arrNewestPt = Rhino.Polar (arrNewPt, tempAnglea, dblDist)
      strNewCrv = Rhino.addLine (arrNewPt,arrNewestPt)
      Call LSystem(strNewCrv)
    Next
End If
End Function

———————Step 5—————————-

Call Main()
Sub Main()
Dim i, strCrv, strCrvCount(), counter
Dim arrPoint : arrPoint = Rhino.getPoint
Dim dblLength : dblLength = 8
counter = -1
For i = -180 To 179 Step 90
    Dim arrNewPoint : arrNewPoint = Rhino.Polar (arrPoint, i, 10)
    strCrv = Rhino.AddLine (arrPoint, arrNewPoint)
    counter = counter + 1
    ReDim Preserve strCrvCount(counter)
    strCrvCount(counter) = strCrv
    Call LSystem(strCrv,counter,strCrvCount)
Next
Call Rhino.SelectObjects (strCrvCount)
End Sub

Function LSystem(strCrv,counter,strCrvCount)
Dim i, arrNewestPt, strNewCrv, tempAnglea, tempAngleb
Dim arrNewPt : arrNewPt = Rhino.CurveEndPoint (strCrv)
Dim dblDist : dblDist = Rhino.CurveLength (strCrv)
Dim dblAngle : dblAngle = Rhino.Angle (Rhino.CurveStartPoint (strCrv), Rhino.CurveEndPoint (strCrv))
dblDist = dblDist – 1
If dblDist > 1 Then
    For i = 0 To 1
      If i Mod 2 = 0 Then
        tempAnglea = dblAngle(0) – 20
      Else
        tempAnglea = dblAngle(0) + 20
      End If
      arrNewestPt = Rhino.Polar (arrNewPt, tempAnglea, dblDist)
      strNewCrv = Rhino.addLine (arrNewPt,arrNewestPt)
      counter = counter + 1
      ReDim Preserve strCrvCount(counter)
      strCrvCount(counter) = strNewCrv
      Call LSystem(strNewCrv,counter,strCrvCount)
    Next
End If
End Function

———————Step 6—————————-

Function LSystem(strCrv,counter,strCrvCount)
Dim i,n, arrNewestPt, strNewCrv, tempAnglea, tempAngleb, strCrvCt, arrCCX, intCounter
Dim arrNewPt : arrNewPt = Rhino.CurveEndPoint (strCrv)
Dim dblDist : dblDist = Rhino.CurveLength (strCrv)
Dim dblAngle : dblAngle = Rhino.Angle (Rhino.CurveStartPoint (strCrv), Rhino.CurveEndPoint (strCrv))
n=0
dblDist = dblDist – 1
If dblDist > 1 Then
    For i = 0 To 1
      If i Mod 2 = 0 Then
        tempAnglea = dblAngle(0) – 20
      Else
        tempAnglea = dblAngle(0) + 20
      End If
      arrNewestPt = Rhino.Polar (arrNewPt, tempAnglea, dblDist)
      strNewCrv = Rhino.addLine (arrNewPt,arrNewestPt)
      intCounter = 0
      For Each strCrvCt In strCrvCount
        arrCCX = Rhino.CurveCurveIntersection (strCrvCt, strNewCrv)
        If IsArray (arrCCX) Then
          If (Rhino.Pt2Str(Rhino.CurveStartPoint (strNewCrv)) <> Rhino.Pt2Str(Rhino.CurveEndPoint (strCrvCt))) Then
            If (Rhino.Pt2Str(Rhino.CurveEndPoint (strNewCrv)) <> Rhino.Pt2Str(Rhino.CurveStartPoint (strCrvCt))) Then
              If (Rhino.Pt2Str(Rhino.CurveStartPoint (strNewCrv)) <> Rhino.Pt2Str(Rhino.CurveStartPoint (strCrvCt))) Then
                Call Rhino.AddPoint (arrCCX(n,1))
              End If
            End If
          End If
        End If
      Next
      counter = counter + 1
      ReDim Preserve strCrvCount(counter)
      strCrvCount(counter) = strNewCrv
      Call LSystem(strNewCrv,counter,strCrvCount)
    Next
End If
End Function

———————Step 7—————————-

Function LSystem(strCrv,counter,strCrvCount)
Dim i,n, arrNewestPt, strNewCrv, tempAnglea, tempAngleb, strCrvCt, arrCCX, intCounter, strTempCrv, arrIntPt()
Dim arrNewPt : arrNewPt = Rhino.CurveEndPoint (strCrv)
Dim dblDist : dblDist = Rhino.CurveLength (strCrv)
Dim dblAngle : dblAngle = Rhino.Angle (Rhino.CurveStartPoint (strCrv), Rhino.CurveEndPoint (strCrv))
n=0
dblDist = dblDist – 1
If dblDist > 1 Then
    For i = 0 To 1
      If i Mod 2 = 0 Then
        tempAnglea = dblAngle(0) – 20
      Else
        tempAnglea = dblAngle(0) + 20
      End If
      arrNewestPt = Rhino.Polar (arrNewPt, tempAnglea, dblDist)
      strTempCrv = Rhino.addLine (arrNewPt,arrNewestPt)
      intCounter = 0
      For Each strCrvCt In strCrvCount
        arrCCX = Rhino.CurveCurveIntersection (strCrvCt, strTempCrv)
        If IsArray (arrCCX) Then
          If (Rhino.Pt2Str(Rhino.CurveStartPoint (strTempCrv)) <> Rhino.Pt2Str(Rhino.CurveEndPoint (strCrvCt))) Then
            If (Rhino.Pt2Str(Rhino.CurveEndPoint (strTempCrv)) <> Rhino.Pt2Str(Rhino.CurveStartPoint (strCrvCt))) Then
              If (Rhino.Pt2Str(Rhino.CurveStartPoint (strTempCrv)) <> Rhino.Pt2Str(Rhino.CurveStartPoint (strCrvCt))) Then
                ReDim Preserve arrIntPt(intCounter)
                arrIntPt(intCounter) = arrCCX(n,1)
                intCounter = intCounter + 1
              End If
            End If
          End If
        End If
      Next

      If intCounter > 0 Then
        Call Rhino.Deleteobject (strTempCrv)
      Else
        strNewCrv = strTempCrv
        counter = counter + 1
        ReDim Preserve strCrvCount(counter)
        strCrvCount(counter) = strNewCrv
        Call LSystem(strNewCrv,counter,strCrvCount)
      End If
    Next
End If
End Function

———————Step 8—————————-

Function LSystem(strCrv,counter,strCrvCount)
Dim i,n, arrNewestPt, strNewCrv, tempAnglea, tempAngleb, strCrvCt, arrCCX, intCounter, strTempCrv, arrIntPt, arrIntPts(), tempDistance, dblDistance, NewEndPoint
Dim arrNewPt : arrNewPt = Rhino.CurveEndPoint (strCrv)
Dim dblDist : dblDist = Rhino.CurveLength (strCrv)
Dim dblAngle : dblAngle = Rhino.Angle (Rhino.CurveStartPoint (strCrv), Rhino.CurveEndPoint (strCrv))
n=0
dblDist = dblDist – 1
dblDistance = 1000000
If dblDist > 1 Then
    For i = 0 To 1
      If i Mod 2 = 0 Then
        tempAnglea = dblAngle(0) – 20
      Else
        tempAnglea = dblAngle(0) + 20
      End If
      arrNewestPt = Rhino.Polar (arrNewPt, tempAnglea, dblDist)
      strTempCrv = Rhino.addLine (arrNewPt,arrNewestPt)
      intCounter = 0
      For Each strCrvCt In strCrvCount
        arrCCX = Rhino.CurveCurveIntersection (strCrvCt, strTempCrv)
        If IsArray (arrCCX) Then
          If (Rhino.Pt2Str(Rhino.CurveStartPoint (strTempCrv)) <> Rhino.Pt2Str(Rhino.CurveEndPoint (strCrvCt))) Then
            If (Rhino.Pt2Str(Rhino.CurveEndPoint (strTempCrv)) <> Rhino.Pt2Str(Rhino.CurveStartPoint (strCrvCt))) Then
              If (Rhino.Pt2Str(Rhino.CurveStartPoint (strTempCrv)) <> Rhino.Pt2Str(Rhino.CurveStartPoint (strCrvCt))) Then
                ReDim Preserve arrIntPts(intCounter)
                arrIntPts(intCounter) = arrCCX(n,1)
                intCounter = intCounter + 1
              End If
            End If
          End If
        End If
      Next

      If intCounter > 0 Then
        For Each arrIntPt In arrIntPts
          tempDistance = Rhino.Distance (Rhino.CurveStartPoint (strTempCrv),arrIntPt)
          If tempDistance < dblDistance Then
            dblDistance = tempDistance
            NewEndPoint = arrIntPt
          End If
        Next
        strNewCrv = Rhino.AddLine (Rhino.CurveStartPoint (strTempCrv),NewEndPoint)
        Call Rhino.Deleteobject (strTempCrv)
        counter = counter + 1
        ReDim Preserve strCrvCount(counter)
        strCrvCount(counter) = strNewCrv
      Else
        strNewCrv = strTempCrv
        counter = counter + 1
        ReDim Preserve strCrvCount(counter)
        strCrvCount(counter) = strNewCrv
        Call LSystem(strNewCrv,counter,strCrvCount)
      End If
    Next
End If
End Function

———————Step 9—————————-

Call Main()
Sub Main()
Dim i, strCrv, strCrvCount(), counter, arrTopPt, dblheight
Dim arrPoint : arrPoint = Rhino.getPoint
Dim dblLength : dblLength = 8
counter = -1
For i = -180 To 179 Step 90
    dblHeight = 12
    arrtopPt = Array(arrPoint(0),arrPoint(1),arrPoint(2)+dblHeight)
    Dim arrNewPoint : arrNewPoint = Rhino.Polar (arrtopPt, i, 10)
    strCrv = Rhino.AddLine (arrtopPt, arrNewPoint)
    counter = counter + 1
    ReDim Preserve strCrvCount(counter)
    strCrvCount(counter) = strCrv
    Call LSystem(strCrv,counter,strCrvCount,arrTopPt(2))
Next
End Sub

Function LSystem(strCrv,counter,strCrvCount,dblHeight)
Dim i,n, arrNewestPt, strNewCrv, tempAnglea, tempAngleb, strCrvCt, arrCCX, intCounter, strTempCrv, arrIntPt, arrIntPts(), tempDistance, dblDistance, NewEndPoint
Dim arrNewPt : arrNewPt = Rhino.CurveEndPoint (strCrv)
Dim dblDist : dblDist = Rhino.CurveLength (strCrv)
Dim dblAngle : dblAngle = Rhino.Angle (Rhino.CurveStartPoint (strCrv), Rhino.CurveEndPoint (strCrv))
n=0
dblDist = dblDist – 1.5
dblDistance = 1000000
If dblHeight > 0 Then
    For i = 0 To 1
      If i Mod 2 = 0 Then
        tempAnglea = dblAngle(0) – 20
      Else
        tempAnglea = dblAngle(0) + 20
      End If
      arrNewestPt = Rhino.Polar (arrNewPt, tempAnglea, dblDist)
      strTempCrv = Rhino.addLine (arrNewPt,Array(arrNewestPt(0),arrNewestPt(1),arrNewestPt(2)-2))
      dblHeight = arrNewestPt(2)-2
      intCounter = 0
      For Each strCrvCt In strCrvCount
        arrCCX = Rhino.CurveCurveIntersection (strCrvCt, strTempCrv)
        If IsArray (arrCCX) Then
          If (Rhino.Pt2Str(Rhino.CurveStartPoint (strTempCrv)) <> Rhino.Pt2Str(Rhino.CurveEndPoint (strCrvCt))) Then
            If (Rhino.Pt2Str(Rhino.CurveEndPoint (strTempCrv)) <> Rhino.Pt2Str(Rhino.CurveStartPoint (strCrvCt))) Then
              If (Rhino.Pt2Str(Rhino.CurveStartPoint (strTempCrv)) <> Rhino.Pt2Str(Rhino.CurveStartPoint (strCrvCt))) Then
                ReDim Preserve arrIntPts(intCounter)
                arrIntPts(intCounter) = arrCCX(n,1)
                intCounter = intCounter + 1
              End If
            End If
          End If
        End If
      Next

      If intCounter > 0 Then
        For Each arrIntPt In arrIntPts
          tempDistance = Rhino.Distance (Rhino.CurveStartPoint (strTempCrv),arrIntPt)
          If tempDistance < dblDistance Then
            dblDistance = tempDistance
            NewEndPoint = arrIntPt
          End If
        Next
        strNewCrv = Rhino.AddLine (Rhino.CurveStartPoint (strTempCrv),NewEndPoint)
        Call Rhino.Deleteobject (strTempCrv)
        counter = counter + 1
        ReDim Preserve strCrvCount(counter)
        strCrvCount(counter) = strNewCrv
      Else
        strNewCrv = strTempCrv
        counter = counter + 1
        ReDim Preserve strCrvCount(counter)
        strCrvCount(counter) = strNewCrv
        Call LSystem(strNewCrv,counter,strCrvCount,dblHeight)
      End If
    Next
End If
End Function

———————Step 10—————————-

Call Main()
Sub Main()
Dim i,j, strCrv, strCrvCount(), counter, arrTopPt, dblheight, strCrvCt, strPath, strExtSrf, strOffSrfa, strOffSrfb, arrDupEdgea, arrDupEdgeb
Dim arrPoint : arrPoint = Rhino.getPoint
Dim dblLength : dblLength = 8
counter = -1
For i = -180 To 179 Step 90
    dblHeight = 12
    arrtopPt = Array(arrPoint(0),arrPoint(1),arrPoint(2)+dblHeight)
    Dim arrNewPoint : arrNewPoint = Rhino.Polar (arrtopPt, i, 10)
    strCrv = Rhino.AddLine (arrtopPt, arrNewPoint)
    counter = counter + 1
    ReDim Preserve strCrvCount(counter)
    strCrvCount(counter) = strCrv
    Call LSystem(strCrv,counter,strCrvCount,arrTopPt(2))
Next
strPath = Rhino.addLine (Array(0,0,0),Array(0,0,-0.3))
For Each strCrvCt In strCrvCount
    strExtSrf = Rhino.ExtrudeCurve (strCrvCt, strPath)
    strOffSrfa = Rhino.OffsetSurface (strExtSrf, 0.065)
    Call Rhino.FlipSurface (strExtSrf, True)
    strOffSrfb = Rhino.OffsetSurface (strExtSrf, 0.065)
    Call Rhino.DeleteObject (strExtSrf)
    arrDupEdgea = Rhino.DuplicateEdgeCurves (strOffSrfa)
    arrDupEdgeb = Rhino.DuplicateEdgeCurves (strOffSrfb)
    For j = 0 To UBound(arrDupEdgea)
      Call Rhino.AddLoftSrf (Array(arrDupEdgea(j),arrDupEdgeb(j)))
    Next
Next
Call Rhino.command (“selcrv “)
Call Rhino.command (“delete “)
End Sub

——————-Week 5 Pre-Tutorial Session——————–

This session will introduce you to the concept of L-Systems. We will use the L-System to generate a dome structure.

———————Step 1—————————-

Option Explicit
‘Script written by mark.bearak
‘Script copyrighted by dtls.Architecture
‘Script version Tuesday, November 11, 2008 7:06:57 PM

Call Main()
Sub Main()
Dim arrPoint : arrPoint = Rhino.getPoint (“Select your start point”)
End Sub

———————Step 2—————————-

_Polar

Call Main()
Sub Main()
Dim arrPoint : arrPoint = Rhino.getPoint

Dim dblLength : dblLength = 8
Dim dblAngle : dblAngle = 90
Dim arrNewPoint : arrNewPoint = Rhino.Polar (arrPoint, dblAngle, 10)
Call Rhino.AddLine (arrPoint, arrNewPoint)
End Sub

———————Step 3—————————-

_Function

_Curve End Point

_Curve Length

_Angle

_Recursive Functions

Call Main()
Sub Main()
Dim arrPoint : arrPoint = Rhino.getPoint
Dim arrNewPoint : arrNewPoint = Rhino.Polar (arrPoint, 90, 10)
Dim strCrv : strCrv = Rhino.AddLine (arrPoint, arrNewPoint)
Call LSystem(strCrv)
End Sub

———————Step 4—————————-

_Adding If/Then

_Bifrication of lines

———————Step 5—————————-

_Randomization of strands

Function LSystem(strCrv)
Dim i, arrNewestPt, strNewCrv, tempAnglea, tempAngleb, intRandom
Dim arrNewPt : arrNewPt = Rhino.CurveEndPoint (strCrv)
Dim dblDist : dblDist = Rhino.CurveLength (strCrv)
Dim dblAngle : dblAngle = Rhino.Angle (Rhino.CurveStartPoint (strCrv), Rhino.CurveEndPoint (strCrv))
dblDist = dblDist – 1
If dblDist > .1 Then
    intRandom = Random(0, 2)
    Call Rhino.Print (intRandom)
    For i = 0 To intRandom
      If i Mod 2 = 0 Then
        tempAnglea = dblAngle(0) – 20
      Else
        tempAnglea = dblAngle(0) + 20
      End If
      arrNewestPt = Rhino.Polar (arrNewPt, tempAnglea, dblDist)
      strNewCrv = Rhino.addLine (arrNewPt,arrNewestPt)
      Call LSystem(strNewCrv)
    Next
End If
End Function

Function Random(nMin, nMax)
Randomize
Random = Int((nMax – nMin + 1) * Rnd + nMin)
End Function

———————Step 6—————————-

_Loop in Sub

Call Main()
Sub Main()
Dim i
Dim arrPoint : arrPoint = Rhino.getPoint
For i = -180 To 179 Step 90
    Dim arrNewPoint : arrNewPoint = Rhino.Polar (arrPoint, i, 10)
    Dim strCrv : strCrv = Rhino.AddLine (arrPoint, arrNewPoint)
    Call LSystem(strCrv)
Next
End Sub

Function LSystem(strCrv)
Dim i, arrNewestPt, strNewCrv, tempAnglea, tempAngleb, intRandom
Dim arrNewPt : arrNewPt = Rhino.CurveEndPoint (strCrv)
Dim dblDist : dblDist = Rhino.CurveLength (strCrv)
Dim dblAngle : dblAngle = Rhino.Angle (Rhino.CurveStartPoint (strCrv), Rhino.CurveEndPoint (strCrv))
dblDist = dblDist – 1
If dblDist > .1 Then
    intRandom = Random(0, 2)
    For i = 0 To intRandom
      If i Mod 2 = 0 Then
        tempAnglea = dblAngle(0) – 20
      Else
        tempAnglea = dblAngle(0) + 20
      End If
      arrNewestPt = Rhino.Polar (arrNewPt, tempAnglea, dblDist)
      strNewCrv = Rhino.addLine (arrNewPt,arrNewestPt)
      Call LSystem(strNewCrv)
    Next
End If
End Function

Function Random(nMin, nMax)
Randomize
Random = Int((nMax – nMin + 1) * Rnd + nMin)
End Function

———————Step 7—————————-

_Changes in Vertical Height

Function LSystem(strCrv)
Dim i, arrNewestPt, strNewCrv, tempAnglea, tempAngleb, intRandom
Dim arrNewPt : arrNewPt = Rhino.CurveEndPoint (strCrv)
Dim dblDist : dblDist = Rhino.CurveLength (strCrv)
Dim dblAngle : dblAngle = Rhino.Angle (Rhino.CurveStartPoint (strCrv), Rhino.CurveEndPoint (strCrv))
dblDist = dblDist – 1.25
If dblDist > 2 Then
    intRandom = Random(0, 2)
    For i = 0 To intRandom
      If i Mod 2 = 0 Then
        tempAnglea = dblAngle(0) – 20
      Else
        tempAnglea = dblAngle(0) + 20
      End If
      arrNewestPt = Rhino.Polar (arrNewPt, tempAnglea, dblDist)
      strNewCrv = Rhino.addLine (arrNewPt,Array(arrNewestPt(0),arrNewestPt(1),arrNewestPt(2)-2))
      Call LSystem(strNewCrv)
    Next
End If
End Function

Function Random(nMin, nMax)
Randomize
Random = Int((nMax – nMin + 1) * Rnd + nMin)
End Function

———————Step 8—————————-

_Structural Viability Tweaking

Call Main()
Sub Main()
Dim i
Dim arrPoint : arrPoint = Rhino.getPoint
Dim dblheight : dblHeight = 12
Dim arrTopPt : arrtopPt = Array(arrPoint(0),arrPoint(1),arrPoint(2)+dblHeight)
For i = -180 To 179 Step 90
    Dim arrNewPoint : arrNewPoint = Rhino.Polar (arrtopPt, i, 10)
    Dim strCrv : strCrv = Rhino.AddLine (arrtopPt, arrNewPoint)
    Call LSystem(strCrv,arrTopPt(2))
Next
End Sub

Function LSystem(strCrv,arrheight)
Dim i, arrNewestPt, strNewCrv, tempAnglea, tempAngleb, intRandom
Dim arrNewPt : arrNewPt = Rhino.CurveEndPoint (strCrv)
Dim dblDist : dblDist = Rhino.CurveLength (strCrv)
Dim dblAngle : dblAngle = Rhino.Angle (Rhino.CurveStartPoint (strCrv), Rhino.CurveEndPoint (strCrv))
dblDist = dblDist – 1.25
If arrheight > 0 Then
    intRandom = Random(0, 2)
    For i = 0 To intRandom
      If i Mod 2 = 0 Then
        tempAnglea = dblAngle(0) – 20
      Else
        tempAnglea = dblAngle(0) + 20
      End If
      arrNewestPt = Rhino.Polar (arrNewPt, tempAnglea, dblDist)
      strNewCrv = Rhino.addLine (arrNewPt,Array(arrNewestPt(0),arrNewestPt(1),arrNewestPt(2)-1.5))
      Call LSystem(strNewCrv,arrNewestPt(2)-2)
    Next
End If
End Function

Function Random(nMin, nMax)
Randomize
Random = Int((nMax – nMin + 1) * Rnd + nMin)
End Function

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parametric realizations fall 2008

Week 5

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