Complex Bamboo Space Frame Structures

Forty of the 2nd year students of the University School of Architecture and Planning (USAP) who were a part of the architectural design studio exercise with Abhishek Bij, Malini Kochupillai, Kanishka Prasad and me, completed the full-scale structures for their college festival. A big thank you to everyone who was a part of this!

You can read a detailed description of the project in this previous post.

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Ghosla Roof Update: Paper Accepted to CAADRIA, 2013

A paper outlining the theoretical and technical ideas behind the “Ghosla (nest) Roof” titled “Digitally Designed Architectural Form Built Using Craft-Based Fabrication: Weaving a Complex Surface as a Bamboo Reticulated Shell” has been accepted to the CAADRIA, 2013 conference of the The Association for Computer-Aided Architectural Design Research in Asia, to be held at the National University of Singapore’s Department of Architecture from May 15th to 18th this year. The theme of the conference this year is “Open Systems” which suits the collaborative nature of the Nest Roof project where digital design methodologies are combined with craft-based construction and non-industrial materials.

On site, the bamboo work has been completed, giving final form to the shell. Here are some pictures from the site –

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Welcome to the Craft Machine

Some months ago I found an article about an exhibition titled The Machine organized by the Design Hub Limburg that includes a fascinating tool for designers. This tool is the result of a project called  Computer Augmented Craft, which, the head of the project, Christian Feiberg, says, “is an attempt to utilise advanced technologies without sacrificing the unique qualities of craftsmanship.” The tool combines a set of sensors with Arduino and an interface created in Processing to enable a designer to have a real-time digital model of an artefact that they are physically producing. The software interface also provides “suggestions” at each step of construction to enable the designer to conform to an initial set of parameters or choose not to do so. The following video shows the system in use –

Reading about this tool and the exhibition reminded me of a student project I had done in the Command & Control design studio with Simon KimSkylar Tibbits and Juhong Park in 2009 at MIT. My project in this studio (focusing on using scripting as a design tool) included a script that created mass-customised joints for a post-earthquake shelter constructed as an irregular space frame out of found rubble. In this project the script did not dictate the form of the structure but only created fabrication data for a mass-customised joint component after the human builder had decided what member to use (from the post-earthquake rubble at hand) and where in the structure to place it. The script overcame the unpredictability of the materials at hand by taking inputs (on the length of a found member that the builder wanted to attach at a particular location) incrementally. The resulting digital model grew in tandem with the physical model allowing the builder to take independent design decisions while the script recorded the builder’s design moves and output fabrication data for the joint components needed at each step. If the builder got stuck and was unable to triangulate the space frame at any point then the script would suggest a method to triangulate.

My poster from the Command & Control studio in 2009. The green members in the main figure denote “found” members while the red members denote those added by the script to triangulate the space frame.

Re-visiting this old student project in the light of the “The Machine” exhibition resulted in a project for the Patterns and Performance 2nd year, B.Arch design studio I am teaching with Abhishek Bij at the University School of Architecture and Planning (USAP). For this exercise we collaborated with the studio taught by Malini Kochupillai and Kanishk Prasad to design a learning space for a group of 20 students. I wrote a new version of the script I had coded for my Command & Control project for use by the students. The new script did not focus on the joints and instead was designed for the specific design problem given to the students for this exercise – the design of a learning space housing 15 to 20 people using a space frame structure constructed from available members of irregular lengths. The students were given tutorials on space frames and introduced to the script written for them. They were introduced to different forms of education and their spatial implications – both interior and exterior.

After this, the students began their designs in groups of four, constructing 1:10 or 1:20 scale physical models of their structures and simultaneously using the script to “grow” a 3D computer model. This studio exercise exposed the students to the advantages and disadvantages of physical versus digital design processes, issues of error and tolerance in design and construction, the importance of improvisation and contingency and its incorporation into the design process.

2012-11-26 12.10.07
The physical and digital models growing side-by-side in the studio.

While my initial script written for the Command & Control studio focused on creating digitally fabricated joints, the script written for the USAP students included a panelization tool. This tool allowed the students to choose where to place panels on the space frame and have the script add these panels to the 3D model and also provide fabrication data for the panels so that they could be printed as a 2D triangle, cut and be added to the physical model.

The next step in the design studio will be to use what one has learnt constructing models and build a full-scale bamboo space frame as a learning space on the college campus. Observing the students work on the models I have updated the script for the full-scale structure. The updated script calculates the centre of gravity of the structure at each iteration of the design and construction process and gives a warning if the structure is likely to topple over without support. The reason for the addition of this feature in the script is that while it is easy to support a table-top model by hand if it is toppling over, this is not a trivial task during full-scale construction. This feature will allow the script to inform the steps in the physical construction process, while design decisions in response to space and material are taken in the physical world and fed into the script. Such a design process will aid in bringing the digital and physical worlds closer together to create a digitally augmented, craft-based, design process.

The latest version of the script written for the studio is given below (please note that there are still some bugs in calculating the centre of gravity) –

Option Explicit
‘Script written by <Ayodh Kamath>
‘Script version 18 November 2012 12:02:10

Call Main()
Sub Main()

Dim strStart, arrExist
Dim arrDots, arrLines, strExit
Dim i

Call Rhino.AddLayer(“uncut_members”, RGB(0,255,0))
Call Rhino.CurrentLayer(“uncut_members”)

Do

strStart = Rhino.GetString(“Start from scratch [S], use existing geometry[G], triangulate with a single member [T], panelize [P], or exit[X]?”,,Array(“S”,”G”,”T”,”P”,”X”))

arrExist = Rhino.AllObjects()

If strStart = “S” Then

If IsArray(arrExist) Then

Call Rhino.DeleteObjects(arrExist)

End If

arrDots = Triangle(arrLines)
Call Rhino.UnselectAllObjects
arrDots = Tetrahedron(arrDots, arrLines)
Call Rhino.UnselectAllObjects

ElseIf strStart = “G” Then

Call Rhino.ZoomExtents(,True)
arrDots = Rhino.GetObjects(“Please drag a selection box around the existing text dot points and ‘Click+Cntrl’ to de-select any unwanted geometry.”,8192)
arrLines = Rhino.GetObjects(“Please drag a selection box around the existing lines and ‘Click+Cntrl’ to de-select any unwanted geometry.”,4)
arrDots = Sort(arrDots)

strExit = “A”

Do

arrDots = Tetrahedron(arrDots, arrLines)
Call Rhino.UnselectAllObjects
strExit = Rhino.GetString(“Make another tetrahedron [A], or exit [X]?”,”A”, Array(“A”,”X”))

Loop While strExit <> “X”

ElseIf strStart = “T” Then

Call Triangulate(arrLines,arrDots)

ElseIf strStart = “P” Then

Call Panelize()

End If

Loop While strStart <> “X”

End Sub

Function Triangle(ByRef arrLines)

Dim dblLt1, dblLt2, dblLt3
Dim strLn0, strLn1, strLn2
Dim strDotP0, strDotP1, strDotP2a, strDotP2b, strDotP2
Dim strTempCirc1, strTempCirc2
Dim arrInt, arrIntPt0, arrIntPt1, strPt0, strPt1, strPt2
Dim strChoice, blnLoop

blnLoop = 0

Do While blnLoop = 0

dblLt1 = Rhino.GetReal(“Enter first lenght:”)

strLn0 = Rhino.AddLine(Array(0,0,0), Array(dblLt1,0,0))
strDotP0 = Rhino.AddTextDot(“P0”,Array(0,0,0))
strDotP1 = Rhino.AddTextDot(“P1”,Rhino.CurveEndPoint(strLn0))
Call Rhino.ZoomExtents(,True)

dblLt2 = Rhino.GetReal(“Enter second lenght:”)

strTempCirc1 = Rhino.AddCircle(Rhino.WorldXYPlane(),dblLt2)
strTempCirc1 = Rhino.MoveObject(strTempCirc1,Array(0,0,0),Array(dblLt1,0,0))

dblLt3 = Rhino.GetReal(“Enter third lenght:”)

strTempCirc2 = Rhino.AddCircle(Rhino.WorldXYPlane(),dblLt3)

arrInt = Rhino.CurveCurveIntersection(strTempCirc1,strTempCirc2)
Call Rhino.DeleteObject(strTempCirc1)
Call Rhino.DeleteObject(strTempCirc2)

If IsArray(arrInt) Then

arrIntPt0 = arrInt(0,1)
arrIntPt1 = arrInt(1,1)

strDotP2a = Rhino.AddTextDot(“P2a”,arrIntPt0)
strDotP2b = Rhino.AddTextDot(“P2b”,arrIntPt1)

Call Rhino.ZoomExtents(,True)
strChoice = Rhino.GetString(“Point P2a[A] or point P2b[B]?”,”A”, Array(“A”,”B”))

If strChoice = “A” Then

Call Rhino.DeleteObject(strDotP2b)
Call Rhino.DeleteObject(strDotP2a)
strDotP2 = Rhino.AddTextDot(“P2”,arrIntPt0)
strLn1 = Rhino.AddLine(Rhino.CurveEndPoint(strLn0),arrIntPt0)
strLn2 = Rhino.AddLine(arrIntPt0,Rhino.CurveStartPoint(strLn0))

ElseIf strChoice = “B” Then

Call Rhino.DeleteObject(strDotP2a)
Call Rhino.DeleteObject(strDotP2b)
strDotP2 = Rhino.AddTextDot(“P2”,arrIntPt1)
strLn1 = Rhino.AddLine(Rhino.CurveEndPoint(strLn0),arrIntPt1)
strLn2 = Rhino.AddLine(arrIntPt1,Rhino.CurveStartPoint(strLn0))

End If

Triangle = Array(strDotP0,strDotP1,strDotP2)
ReDim arrLines(2)
arrLines(0) = strLn0
arrLines(1) = strLn1
arrLines(2) = strLn2
blnLoop = 1

Else

Call Rhino.DeleteObject(strLn0)
Call Rhino.DeleteObject(strDotP0)
Call Rhino.DeleteObject(strDotP1)
Call Rhino.MessageBox(“The member lengths can not be triangulated. Please try a different set of members.”)

End If

Loop

End Function

Function Sort(arrTxtDot)

Dim strMin, blnSwap
Dim i, j, k

Do

blnSwap = False
For i = 1 To UBound(arrTxtDot)

If Rhino.TextDotText(arrTxtDot(i-1)) > Rhino.TextDotText(arrTxtDot(i)) Then

strMin = arrTxtDot(i)
arrTxtDot(i) = arrTxtDot(i-1)
arrTxtDot(i-1) = strMin
blnSwap = True

End If

Next

Loop While blnSwap = True

Sort = arrTxtDot

End Function

Function Tetrahedron(arrTxtDots, ByRef arrLines)

ReDim arrInPts(2)
ReDim arrTempDots(2)
ReDim arrInLts(2)
ReDim arrTempSphs(2)
Dim arrIntSrf, strJoinCrv, arrIntCrvSrf
ReDim arrIntDots(1)
Dim strChoice, arrIntPt
Dim i, j
Dim blnLoop
Dim intPtNum
Dim intCGChoice
ReDim arrTempLines(2)
Dim intLineCount
Dim blnGoal, arrGoalPt

blnLoop = 0

Do While blnLoop = 0

blnGoal = Rhino.GetString(“Select a goal point?”,,Array(“Y”,”N”))

If blnGoal = “Y” Then

arrGoalPt = Rhino.GetPoint(“Select goal point”)
Call GoalPoint(arrTxtDots,arrGoalPt)

End If

For i = 0 To 2

arrInPts(i) = Rhino.GetPoint(“Select point #”&CStr(i+1))
Call Rhino.UnselectAllObjects
arrTempDots(i) = Rhino.AddTextDot(CStr(i+1),arrInPts(i))
Call Rhino.SelectObject(arrTempDots(i))

arrInLts(i) = Rhino.GetReal(“Enter member length at this node:”)
arrTempSphs(i) = Rhino.AddSphere(arrInPts(i),arrInLts(i))
Call Rhino.ZoomExtents(,True)

If i = 1 Then

arrIntSrf = Rhino.SurfaceSurfaceIntersection(arrTempSphs(0),arrTempSphs(1),,True)

If IsArray(arrIntSrf) Then

If UBound(arrIntSrf,1)>0 Then

strJoinCrv = JoinCurve(arrIntSrf)

Else

strJoinCrv = arrIntSrf(0,1)

End If

Else

Call Rhino.DeleteObject(arrTempDots(0))
Call Rhino.DeleteObject(arrTempDots(1))
Call Rhino.DeleteObject(arrTempSphs(0))
Call Rhino.DeleteObject(arrTempSphs(1))
blnLoop = 0
Call Rhino.MessageBox(“The member lengths can not be triangulated. Please try a different set of members.”)
Exit For

End If

ElseIf i = 2 Then

arrIntCrvSrf = Rhino.CurveSurfaceIntersection(strJoinCrv,arrTempSphs(2))

If IsArray(arrIntCrvSrf) Then

blnLoop = 1
arrIntDots(0) = Rhino.AddTextDot(“IntA”,arrIntCrvSrf(0,1))
arrIntDots(1) = Rhino.AddTextDot(“IntB”,arrIntCrvSrf(1,1))
Call Rhino.SelectObjects(arrIntDots)

strChoice = Rhino.GetString(“Point IntA[A] or point IntB[B]?”,”A”, Array(“A”,”B”))

If strChoice = “A” Then

arrIntPt = arrIntCrvSrf(0,1)

ElseIf strChoice = “B” Then

arrIntPt = arrIntCrvSrf(1,1)

End If

Else

Call Rhino.DeleteObjects(arrTempDots)
Call Rhino.DeleteObjects(arrTempSphs)
Call Rhino.DeleteObject(strJoinCrv)
blnLoop = 0
Call Rhino.MessageBox(“The member lengths can not be triangulated. Please try a different set of members.”)
Exit For

End If

End If

Next

Loop

Call Rhino.DeleteObjects(arrIntDots)
Call Rhino.DeleteObjects(arrTempSphs)
Call Rhino.DeleteObjects(arrTempDots)
Call Rhino.DeleteObject(strJoinCrv)

For i = 0 To 2

arrTempLines(i) = Rhino.AddLine(arrInPts(i),arrIntPt)

Next

intLineCount = UBound(arrLines)
ReDim Preserve arrLines(intLineCount+3)
arrLines(intLineCount+1) = arrTempLines(0)
arrLines(intLineCount+2) = arrTempLines(1)
arrLines(intLineCount+3) = arrTempLines(2)

intPtNum = UBound(arrTxtDots)
ReDim Preserve arrTxtDots(intPtNum+1)
arrTxtDots(intPtNum+1) = Rhino.AddTextDot(“P”&CStr(intPtNum+1),arrIntPt)

intCGChoice = CG(arrTxtDots,arrLines)

If intCGChoice = 7 Then

Call Rhino.DeleteObjects(arrTempLines)
Call Rhino.DeleteObject(arrTxtDots(intPtNum+1))
ReDim Preserve arrTxtDots(intPtNum)
ReDim Preserve arrLines(intLineCount)

End If

Tetrahedron = arrTxtDots

End Function

Function JoinCurve(arrCrvs)
‘takes the two dimensional array resulting from a SurfaceSurfaceIntersection command and returns the string identifier of the joined intersection segments

Dim intSegments, arrJoin
Dim i

intSegments = UBound(arrCrvs,1)

ReDim arrJoinCrvs(intSegments)

For i = 0 To intSegments

arrJoinCrvs(i) = arrCrvs(i,1)

Next

arrJoin = Rhino.JoinCurves(arrJoinCrvs, True)
JoinCurve = arrJoin(0)

End Function

Function Triangulate(ByRef arrLines, arrTxtDots)

Dim arrInPt1, arrInPt2, strTempDot1, strTempDot2, strTempLine
Dim intMsg, intLineCount, intCGChoice

arrInPt1 = Rhino.GetPoint(“Select first point”)
strTempDot1 = Rhino.AddTextDot(“1”,arrInPt1)
Call Rhino.SelectObject(strTempDot1)

arrInPt2 = Rhino.GetPoint(“Select second point”)
strTempDot2 = Rhino.AddTextDot(“2”,arrInPt2)
Call Rhino.SelectObject(strTempDot2)

intMsg = Rhino.MessageBox(“The member length required between these points is “&CStr(Rhino.Distance(arrInPt1,arrInPt2)),4)

If intMsg = 6 Then

Call Rhino.AddLayer(“cut_members”, RGB(255,0,0))
Call Rhino.CurrentLayer(“cut_members”)
intLineCount = UBound(arrLines)
ReDim Preserve arrLines(intLineCount+1)
arrLines(intLineCount+1) = Rhino.AddLine(arrInPt1,arrInPt2)
Call Rhino.CurrentLayer(“uncut_members”)

End If

intCGChoice = CG(arrTxtDots,arrLines)

If intCGChoice = 7 Then

Call Rhino.DeleteObject(arrLines(intLineCount+1))
ReDim Preserve arrLines(intLineCount)

End If

Call Rhino.DeleteObject(strTempDot1)
Call Rhino.DeleteObject(strTempDot2)

End Function

Function Panelize

Dim strStart
Dim strDot1, strDot2, strDot3
ReDim arrPts(2)
Dim strSrf
ReDim arrEdges(2)
ReDim arrDgs(2)
Dim arrTempDiv
ReDim strDots(2)
Dim intMsg, arrFlat, arrFlatOrPt, arrBox

strDot1 = Rhino.GetObject(“Select first point”,8192)
Call Rhino.SelectObject(strDot1)

strDot2 = Rhino.GetObject(“Select second point”,8192)
Call Rhino.SelectObject(strDot2)

strDot3 = Rhino.GetObject(“Select third point”,8192)
Call Rhino.SelectObject(strDot3)

arrPts(0) = Rhino.TextDotPoint(strDot1)
arrPts(1) = Rhino.TextDotPoint(strDot2)
arrPts(2) = Rhino.TextDotPoint(strDot3)

strSrf = Rhino.AddSrfPt(arrPts)

arrEdges(0) = Rhino.AddLine(arrPts(0),arrPts(1))
arrEdges(1) = Rhino.AddLine(arrPts(1),arrPts(2))
arrEdges(2) = Rhino.AddLine(arrPts(2),arrPts(0))

arrDgs(0) = Rhino.AddLine(arrPts(0),Rhino.CurveMidPoint(arrEdges(1)))
arrDgs(1) = Rhino.AddLine(arrPts(1),Rhino.CurveMidPoint(arrEdges(2)))
arrDgs(2) = Rhino.AddLine(arrPts(2),Rhino.CurveMidPoint(arrEdges(0)))

arrTempDiv = Rhino.DivideCurve(arrDgs(0),4)
strDots(0) = Rhino.CopyObject(strDot1,arrPts(0),arrTempDiv(1))

arrTempDiv = Rhino.DivideCurve(arrDgs(1),4)
strDots(1) = Rhino.CopyObject(strDot2,arrPts(1),arrTempDiv(1))

arrTempDiv = Rhino.DivideCurve(arrDgs(2),4)
strDots(2) = Rhino.CopyObject(strDot3,arrPts(02),arrTempDiv(1))

Call Rhino.DeleteObjects(arrEdges)
Call Rhino.DeleteObjects(arrDgs)
Call Rhino.UnselectAllObjects()

intMsg = Rhino.MessageBox(“Flatten this panel?”,4)

If intMsg = 7 Then

Call Rhino.DeleteObject(strSrf)
Call Rhino.DeleteObjects(strDots)

ElseIf intMsg = 6 Then

If Not IsArray(arrFlatOrPt) Then

arrFlatOrPt = Rhino.GetPoint(“Select origin point for unroll”)

End If

arrFlat = RhinoUnrollSurface(strSrf,strDots,False,False)
arrFlat = Rhino.MoveObjects(arrFlat,Array(0,0,0),arrFlatOrPt)
arrBox = Rhino.BoundingBox(arrFlat)
arrFlatOrPt = arrBox(1)
Call Rhino.DeleteObjects(strDots)

End If

End Function

Function RhinoUnrollSurface(strSurface, arrCurves, blnExplode, blnLabels)

‘ Default return value
RhinoUnrollSurface = Null

‘ For speed, turn of screen redrawing
Call Rhino.EnableRedraw(False)

‘ Save any selected objects
Dim arrSaved : arrSaved = Rhino.SelectedObjects

‘ Unselect all objects
Rhino.UnSelectAllObjects

‘ Select the surface to unroll
Rhino.SelectObject strSurface

‘ Format curve string
Dim i : i = 0
Dim strCurves : strCurves = ” _Enter”
If IsArray(arrCurves) Then
strCurves = “”
For i = 0 To UBound(arrCurves)
strCurves = strCurves & ” _SelId ” & arrCurves(i)
Next
strCurves = strCurves & ” _Enter”
End If

‘ Format explode string
Dim strExplode : strExplode = ” _Explode=_Yes”
If (blnExplode = False) Then strExplode = ” _Explode=_No”

‘ Format labels string
Dim strLabels : strLabels = ” _Labels=_No”
If (blnLabels = True) Then strLabels = ” _Labels=_Yes”

‘ Script the command
Dim strCommand : strCommand = “_-UnrollSrf” & strExplode & strLabels & strCurves
Call Rhino.Command(strCommand, 0)

‘ Return the results
RhinoUnrollSurface = Rhino.LastCreatedObjects

‘ Unselect all objects
Rhino.UnSelectAllObjects

‘ If any objects were selected before calling
‘ this function, re-select them
If IsArray(arrSaved) Then Rhino.SelectObjects(arrSaved)

‘ Don’t forget to turn redrawing back on
Call Rhino.EnableRedraw(True)

End Function

Function CG(arrDots, ByRef arrLines)

ReDim arrDotPts(UBound(arrDots))
Dim dblSumLength, arrMidPt
Dim dblX, dblY, dblZ, dblLength
Dim i
ReDim arrMemCGPt(2)
ReDim arrJtCGPt(2)
ReDim arrCGPt(2)
Dim strTempCGPt, strTempCGLine, intCount
intCount = 0
ReDim arrBasePts(intCount)
Dim arrSortBasePts, strBaseCrv, intInside, arrCGBasePt
Dim intChoice

Dim dblMemDens, dblJtWt
dblMemDens = 1 ‘average bamboo density assumed to be 1kg/running meter = 1g/running mm
dblJtWt = 2000 ‘average weight per joint assumed to be 2kg = 2000g

For i = 0 To UBound(arrLines)

dblSumLength = dblSumLength+Rhino.CurveLength(arrLines(i))

Next

For i = 0 To UBound(arrLines)

arrMidPt = Rhino.CurveMidPoint(arrLines(i))
dblLength = Rhino.CurveLength(arrLines(i))
dblX = dblX+((arrMidPt(0))*(Rhino.CurveLength(arrLines(i))))
dblY = dblY+((arrMidPt(1))*(Rhino.CurveLength(arrLines(i))))
dblZ = dblZ+((arrMidPt(2))*(Rhino.CurveLength(arrLines(i))))

Next

arrMemCGPt(0) = dblX/dblSumLength
arrMemCGPt(1) = dblY/dblSumLength
arrMemCGPt(2) = dblZ/dblSumLength

dblX = 0
dblY = 0
dblZ = 0

For i = 0 To UBound(arrDots)

arrDotPts(i) = Rhino.TextDotPoint(arrDots(i))

dblX = dblX+arrDotPts(i)(0)
dblY = dblY+arrDotPts(i)(1)
dblZ = dblZ+arrDotPts(i)(2)

Next

arrJtCGPt(0) = dblX/i
arrJtCGPt(1) = dblY/i
arrJtCGPt(2) = dblZ/i

arrCGPt(0) = ((dblMemDens*dblSumLength*arrMemCGPt(0))+(dblJtWt*i*arrJtCGPt(0)))/((dblMemDens*dblSumLength)+(dblJtWt*i))
arrCGPt(1) = ((dblMemDens*dblSumLength*arrMemCGPt(1))+(dblJtWt*i*arrJtCGPt(1)))/((dblMemDens*dblSumLength)+(dblJtWt*i))
arrCGPt(2) = ((dblMemDens*dblSumLength*arrMemCGPt(2))+(dblJtWt*i*arrJtCGPt(2)))/((dblMemDens*dblSumLength)+(dblJtWt*i))

strTempCGPt = Rhino.AddPoint(arrCGPt)
strBaseCrv = Base(arrDotPts)

arrCGBasePt = arrCGPt
arrCGBasePt(2) = 0
strTempCGLine = Rhino.AddLine(arrCGPt,arrCGBasePt)
intInside = Rhino.PointInPlanarClosedCurve(arrCGBasePt,strBaseCrv)

Call Rhino.DeleteObject(strBaseCrv)

If intInside <> 1 Then

intChoice = Rhino.MessageBox(“The addition of this point will cause the structure to topple. Carry on anyway?”,4)

Else

intChoice = Rhino.MessageBox(“The addition of this point will not cause the structure to topple”)

End If

Call Rhino.DeleteObject(strTempCGPt)
Call Rhino.DeleteObject(strTempCGLine)
CG = intChoice

End Function

Function Base(arrAllPts)

Dim intPolyCount, intPtCount, intInOut
Dim i, j
Dim arrTempPoly, strTempPoly
Dim dblDist, dblMinDist, intMinPt, bolMin
Dim dblParam, arrClsPt
Dim arrTempPts
Dim arrJoin
intPtCount = 0
intPolyCount = 2
bolMin = 0
ReDim arrPts(intPtCount)
ReDim arrBasePts(intPolyCount)
ReDim arrBaseLns(intPolyCount)

For i = 0 To UBound(arrAllPts)

If arrAllPts(i)(2) = 0 Then

arrPts(intPtCount) = arrAllPts(i)
intPtCount = intPtCount+1
ReDim Preserve arrPts(intPtCount)

End If

Next

intPtCount = intPtCount-1
ReDim Preserve arrPts(intPtCount)

arrBasePts(0) = arrPts(0)
arrBasePts(1) = arrPts(1)
arrBasePts(2) = arrPts(2)

arrBaseLns(0) = Rhino.AddLine(arrBasePts(0),arrBasePts(1))
arrBaseLns(1) = Rhino.AddLine(arrBasePts(1),arrBasePts(2))
arrBaseLns(2) = Rhino.AddLine(arrBasePts(2),arrBasePts(0))

For i = 3 To intPtCount

arrTempPoly = Rhino.JoinCurves(arrBaseLns)
strTempPoly = arrTempPoly(0)

intInOut = Rhino.PointInPlanarClosedCurve(arrPts(i),strTempPoly)

Call Rhino.DeleteObject(strTempPoly)

If intInOut = 0 Then

For j = 0 To intPolyCount

dblDist = Rhino.Distance(arrBasePts(j),arrPts(i))

If j = 0 Then

dblMinDist = dblDist
intMinPt = j
bolMin = 0

Else

If dblDist < dblMinDist Then

dblMinDist = dblDist
intMinPt = j
bolMin = 0

End If

End If

Next

For j = 0 To intPolyCount

dblParam = Rhino.CurveClosestPoint(arrBaseLns(j),arrPts(i))
arrClsPt = Rhino.EvaluateCurve(arrBaseLns(j),dblParam)
dblDist = Rhino.Distance(arrClsPt,arrPts(i))

If dblDist < dblMinDist Then

dblMinDist = dblDist
intMinPt = j
bolMin = 1

End If

Next

If bolMin = 0 Then

arrBasePts(intMinPt) = arrPts(i)

Call Rhino.DeleteObjects(arrBaseLns)

For j = 0 To intPolyCount-1

arrBaseLns(j) = Rhino.AddLine(arrBasePts(j),arrBasePts(j+1))

Next

arrBaseLns(intPolyCount) = Rhino.AddLine(arrBasePts(intPolyCount),arrBasePts(0))

ElseIf bolMin = 1 Then

arrTempPts = arrBasePts
intPolyCount = intPolyCount+1
ReDim Preserve arrBasePts(intPolyCount)

arrBasePts(intMinPt+1) = arrPts(i)

For j = intMinPt+2 To intPolyCount

arrBasePts(j) = arrTempPts(j-1)

Next

Call Rhino.DeleteObjects(arrBaseLns)
ReDim Preserve arrBaseLns(intPolyCount)

For j = 0 To intPolyCount-1

arrBaseLns(j) = Rhino.AddLine(arrBasePts(j),arrBasePts(j+1))

Next

arrBaseLns(intPolyCount) = Rhino.AddLine(arrBasePts(intPolyCount),arrBasePts(0))

End If

End If

Next

arrJoin = Rhino.JoinCurves(arrBaseLns,True)
Base = arrJoin(0)

End Function

Function GoalPoint(arrTextDots,arrGoalPt)

Dim strMin, blnSwap
Dim i, j, k

ReDim arrDist(UBound(arrTextDots))

Do

blnSwap = False
For i = 1 To UBound(arrTextDots)

If Rhino.Distance(Rhino.TextDotPoint(arrTextDots(i-1)),arrGoalPt) > Rhino.Distance(Rhino.TextDotPoint(arrTextDots(i)),arrGoalPt) Then

strMin = arrTextDots(i)
arrTextDots(i) = arrTextDots(i-1)
arrTextDots(i-1) = strMin
blnSwap = True

End If

Next

Loop While blnSwap = True

Call Rhino.SelectObject(arrTextDots(0))
Call Rhino.MessageBox(“The closest node to the goal point has been selected”)

End Function

Ghosla Roof Construction Update

After some delays in the project, construction on the woven bamboocrete “Ghosla” (nest) roof has finally begun. The video below shows how the weaving process enables  a team of traditional bamboo craftsmen to easily construct the digitally form-found, double-curved, funicular shell using only linear measurements read out to them by the contractor. The drawing provided by Kamath Design Studio to the contractor is a plan consisting of linear dimensions along each bamboo member where that member intersects other members. The drawing also communicates the weaving scheme, that is, whether a member goes above or below another member when they intersect. Our studio provided the height above ground at each intersection to verify that the bamboo members are curving as desired, and that the shape of the shell conforms to the digitally form-found funicular shape.

While a 1:50 scale construction model of this roof had been built using the same drawing set to test the concept of weaving a complex curved surface using only linear dimensional information, the idea was so far untested at full scale.

I had outlined the concept of using weaving to build complex digitally modeled surfaces using manual methods of construction in this earlier post.

Article Published in Int|AR – Journal of the RISD Department of Interior Architecture

An article I co-authored with members of Kamath Design Studio on the planning, design and construction of an Interpretation Centre for a black buck sanctuary in Churu District, in Rajasthan was published in Int|AR – the RISD Department of Interior Architecture’s journal on adaptive re-use. My personal involvement in the project had been in the site documentation and context analysis stages way back in 2007 so seeing the final design and constructed buildings and working on the paper was a very satisfying experience. Though this project has nothing to do with digital design and fabrication, it showcases the contemporary use of indigenous craft skills and building systems that I seek to integrate with digital design work-flows. Here is a link to the article.

A Photograph of a Nearby Settlement from the Context Documentation

Curve Fitting Script

This is a very simple curve fitting script to find where a short curve fits best along longer curve. I’ve developed this script in the context of my on-going work with bamboo weaving.

The curve fitting script finds where a short curve fits best along longer curve.

The Nest Roof is a result of woven bamboo beams following paths of minimum curvature along a funicular surface.

A 1:50 scale model of the Nest Roof

While the bamboo beams may follow paths of minimum curvature, one is still left with the possibility to further optimize the selection of where along a beam profile to use each individual piece of bamboo. Bamboo being a natural material does not have uniform properties and every piece of bamboo is different. Every piece has a different shape and bends by a different amount. Therefore different pieces of bamboo will be suited to different parts of the roof with different beam curvature. Selecting the right piece of bamboo for a given segment of a beam is fundamentally finding where along the beam a given piece of bamboo fits best so that it will have to be bent a minimum amount, which is what this script does. However, it is far from clear how exactly, and if at all, the script can be used during construction. The principal problem is finding a work flow whereby the curvature of each individual piece of bamboo can be recorded and digitized so as to form an input for this script (or some version of it) during construction, and a way to convey the result of the script in real time to the craftspersons building the roof. These issues were tackled in my SMArchS thesis, but only at a theoretical level and at a table top model scale. I hope to be able to carry this forward to a building scale and a live project through the Nest Roof.

The script uses a very crude brute force algorithm that incrementally slides a short curve (representing an individual piece of bamboo) along a longer curve (the beam profile) while checking the deviation between the two curves at each increment. The length of the increment can be specified and the smaller the increment the more accurate the result will be. An interesting by-product of the brute force algorithm is the plant like shapes that it produces. “Leaves” appear to sprout as the script slides one curve along the other, and then the “leaves” are then shed as the script deletes all but the best-fit result.

"Leaves" formed during the running of the script

Below is a version of the script that works on planar curves, but the same idea can be expanded to apply to 3D curves as well –

Option Explicit
‘Script written by <Ayodh Kamath>
‘Script copyrighted by <Kamath Design Studio/PostScriptDesign>
‘Script version 08 April 2012 14:18:42

Call Main()
Sub Main()

Dim strCrv1, strCrv2, dblDivLength, arrDivPts1, arrDivPts2
Dim intCheckPt, strAlignCrv
Dim intCount, intMin
Dim j, i

strCrv1 = Rhino.GetObject(“Select guide curve to check against”,4)
strCrv2 = Rhino.GetObject(“Select curve to check”,4)

dblDivLength = (Rhino.CurveLength(strCrv2))/10
dblDivLength = Rhino.GetReal(“Enter division length:”, dblDivLength)

arrDivPts1 = Rhino.DivideCurveLength(strCrv1, dblDivLength)
arrDivPts2 = Rhino.DivideCurveLength(strCrv2, dblDivLength)

ReDim arrDot(UBound(arrDivPts1))

For i = 0 To UBound(arrDivPts1)

arrDot(i) = Rhino.AddTextDot(CStr(i), arrDivPts1(i))

Next

intCheckPt = Rhino.GetInteger(“Enter point number to check from”, 0, 0, (UBound(arrDivPts1) – UBound(arrDivPts2)))
Call Rhino.DeleteObjects(arrDot)

ReDim arrDev(((UBound(arrDivPts1) – UBound(arrDivPts2) – intCheckPt + 1)*(UBound(arrDivPts2))) – 1)
ReDim arrAlignCrvs(((UBound(arrDivPts1) – UBound(arrDivPts2) – intCheckPt + 1)*(UBound(arrDivPts2))) – 1)

intCount = 0

For i = intCheckPt To (UBound(arrDivPts1) – UBound(arrDivPts2))

For j = 1 To UBound(arrDivPts2)

arrAlignCrvs(intCount) = Rhino.OrientObject(strCrv2, Array( arrDivPts2(0), arrDivPts2(j)), Array(arrDivPts1(i), arrDivPts1(i + j)),1)

arrDev(intCount) = Deviation(strCrv1, arrAlignCrvs(intCount), i, dblDivLength, arrDivPts1)

intCount = intCount + 1

Next

Next

intCount = intCount – 1

intMin = Minimum(arrDev)

For i = 0 To UBound(arrDev)

If i <> intMin Then

Call Rhino.DeleteObject(arrAlignCrvs(i))

End If

Next

Call Rhino.SelectObject(arrAlignCrvs(intMin))

End Sub

Function Deviation(ByRef strCrv1, strAlignCrv, intFnCheckPt, ByRef dblDivLength, ByRef arrDivPts1)

End Function

Function Minimum(arrCheck)
End Function

Digitally Guided Weaving & Other Installations from the Spanz Workshop at SSAA.

“Floating Triads”Canopy Design from the Spanz Workshop at Atharva 2012. Photograph: Yogesh Verma
Lighting Module from the Spanz Workshop. Image: Pragya Vij, Saalanki Saraf

A part of this semester’s 3rd year design studio at Sushant School of Art & Architecture consisted of an introductory workshop on the use of digital design tools that we called Spanz. The workshop was taught by Abhishek Bij and me (both visiting design faculty at the 3rd year design studio) and supported by the rest of the 3rd year design faculty consisting of Shikha Doogar, Gaurav Shorey, Swati Singh, Thomas Oomen and Neeraj Khosla. The workshop started with a crash course on a variety of digital design tools including 3D modelling software, form finding tools, parametric modelling software and form rationalization tools – tools that are applicable to different stages of the digital design workflow, from conceptualization to fabrication. The tools developed tackled a range of structural systems (tensile membranes, funicular shells and folded plates) and fabrication methods (weaving, pipe bending, sheet metal forming, concrete casting etc.).

The students were encouraged to mix and matched these tools to suit their design goals and design styles and no specific methodology was imposed on them. The tools were applied to various real life campus development projects as a part of their annual college festival (Atharva 2012, 30th-31st March) and ranged from canopies to installations to lighting design. The nuances of the digital tools were mastered by them while using them for their developing their designs.

The Interlace Installation. Photo: Gauri Varshney

A student installation of specific interest here is “The Interlace” designed by Akshita, Anushree, Gauri, Parush, Sumit and Suvrita because it is the first time the weaving script I had developed and posted earlier has been applied to a large scale project. The weaving script simply takes a given fibre spacing and fibre thickness and uses the U- and V- curves of a surface to derive fabrication data for the weaving process. My interest in weaving comes from the way it allows complex 3D curved surfaces to be fabricated using only linear measurements (which I have discussed in detail in this earlier post). In “The Interlace” the students started out by using a form finding algorithm based on David Rutten’s classic mesh relaxation algorithm. The basic mesh relaxation algorithm was modified specifically for the workshop to allow the students to model the effects of gravity and thereby generate funicular forms in addition to tensile membranes (I will be explaining the modifications made to the algorithm in another blog post shortly). The relaxed mesh was converted to a NURBS surface and the weaving script was applied to it. The script outputted the lengths of individual fibres and the points of intersection with other fibres along their length. The fabrication data was used to first build a 1:10 scale construction model where the students could test the fabrication process and the steps involved.

The 1:10 Construction Model

Once the construction process was developed and understood in the studio, the students proceeded to build the final installation. Since the college festival is student-run and student-managed, the direct role of the design faculty ended at the construction model stage. Comparing the construction model to the final installation, it is interesting to note that the percentage error in the linear measurements was more in the construction model and less in the final installation, meaning that the final installation was a closer match to the computer model than the construction model. The properties of the pipe used to make the final installation were different from the construction model in terms of their ability to resist compression, resulting in a small amount of creasing of the surface of the final installation. Overall, however, this installation appears to verify the feasibility of using weaving to manually fabricate computer generated 3D curved surfaces at a 1:1 scale.

The Hypar Solar Cooker

The Hypar Solar Cooker is a solar cooker with a hypar reflector developed by Kamath Design Studio about five years ago. The hypar surface is easily constructed using an old basket, bamboo and mud with embedded pieces of broken mirror (or any other reflective material). The curvature of the hypar surface helps to concentrate more sunlight on to the cooking food compared to a conventional flat reflector on a box solar cooker. The old basket gives shape to the base which holds a cooking pot with a glass lid. The mud acts as a cheap and readily available insulating material as well as an easily mouldable material to create the curved surface of the hypar on the bamboo framework. However, the exact shape of the hypar was, up to this point being found by trial and error.

I am now working on a digital tool that can customize the shape of the hypar based on the geographical location of the solar cooker, its orientation, and the time of the day it will be most used. The digital tool will give the lengths of the bamboo edge members and central members required to build the customized, optimal hypar shape. I hope to test the efficacy of this through physical prototypes as soon as the fog lifts off North India and we have more sun in Delhi. The main issue I want to test through the prototypes is how much the manual construction methods using bamboo, mud and mirrors deviate from the digitally derived hypar surface and the effect the deviation has on the performance of the reflector.

Ghosla: A Curvature Optimized Woven Bamboocrete Roof

“Ghosla” (meaning “nest” in Hindi) is a bamboocrete roof designed by Kamath Design Studio for a 150 square meter guest house unit at the Gnostic Centre in New Delhi, India.

Curvature optimized weaving: Surface paths with minimum cumulative curvature compared to a UV transformed hexagonal grid

The shape of the roof comes from a structural form-finding process dictated by the floor plan of the building and the resulting positions of the supporting columns. A RhinoScript was used to find optimized paths for woven members on this surface. The paths found using the script are those with minimum cumulative curvature passing through a given set of points on the surface. This enables the bamboo members used in the weaving to have as large a cross-sectional diameter as possible (and thus as high a load bearing capacity as possible) since they do not need to bend much and need not be extremely flexible. The advantage of using these optimized paths can be seen when comparing them (extreme right, above) to the simple UV transformed hexagonal grid (second from the right, above). The simple UV transformed grid has member paths with significantly higher curvature which will require more flexible (and thus thinner and weaker) bamboo members for its construction.

Stepping back in the design process, the design-computational reason for constructing this roof by weaving bamboo came from the need to devise a work-flow and construction methodology that would enable the construction of a digitally designed complex curved surface (the form-found roof shape) by simple manual construction techniques in a non-industrial setting. Weaving is an ancient process that is in the technological repertoire of most cultures. What makes weaving especially suited to the construction of curved surfaces is the fact that it can use linear, one-dimensional elements to produce a surface curving in three-dimensions and requires only linear measurements during construction. I have discussed the details of this in my earlier post on Weaving and Linear Measurement in Digitally Guided Construction.

The success of this digital-to-physical work-flow can be seen in the 1:25 scale model of the roof that was constructed by carpenter Ram Lakhan with the guidance of Inderjeet Singh Seera of Kamath Design Studio using linear dimensional information obtained from a 3D computer model of the woven roof. Here are some photographs of the model just before completion –

1:25 Scale Model of the Woven Bamboo Roof Under Construction
1:25 Scale Model of the Woven Bamboo Roof Under Construction

 

1:25 Scale Model of the Woven Bamboo Roof Under Construction

While there is no doubt that there will be numerous challenges that will have to be overcome during full-scale construction, the progress on this project so far shows the ability of weaving to be used for the construction of complex curved surfaces by manual means using linear dimensional information.

The bamboocrete roof that this woven structure will support will be similar to earlier bamboocrete roofs designed by Kamath Design Studio. The woven bamboo structure of the “Ghosla” roof will replace the steel and eucalyptus log trusses used to support these earlier roofs.

Exterior View of the Bamboocrete Roof at the Kamath Residence
Interior View of the Bamboocrete Roof at the Kamath Residence

Weaving and Linear Measurement in Digitally Guided Construction

Measuring the length of a straight line in the physical world is to test the geometric congruency of two one-dimensional objects – an object of standardized length against an object of unknown length. All one-dimensional objects share the property of similarity and can therefore be “placed against each other” as physical objects (strictly speaking there are no “real” one-dimensional objects but this statement will still apply to the one-dimensional edges of higher-dimensional objects). To make two one-dimensional objects congruent requires breaking/cutting the longer of the two at a single point or stretching the shorter of the two along a single direction.

While all this may seem painfully obvious, the uniqueness of the situation is highlighted when you think about how hard it is to make two non-similar objects of higher dimensions congruent or similar. For example, here is a device for replicating three-dimensional sculptures with the ability to change the size of the reproduction. (For more information about this device you can read this article). Now compare this device to using a ruler and pair of scissors to make two pieces of string the same length.

Source: http://www.thecarvingpath.net/forum/index.php?showtopic=1278

George Stiny shows how a boundary function is able to map algebras of different dimensions to each other (Shape: Talking About Seeing and Doing, p. 98).  In terms of construction, a boundary function can provide ‘templates’ or ‘jigs’ or ‘frameworks’ or ‘guides’ (depending on your method of construction) for objects of a higher dimension using objects of lower dimensions. To cite an example of a project I was personally involved in, the form-work of the Santa Monica Cradle project is an example of two-dimensional plywood ribs being used as a framework for creating a complex, curved, three-dimensional surface from strips of flexible ‘luaun’ ply. In fact, most approaches to constructing an architectural surface involves some kind of underlying linear framework.

The skinning of the plywood framework with strips of flexible luaun.
A Surface
A Divided Surface
The Boundaries Of The Divisions Form A Framework

If a complex three-dimensional shape can be built using a ‘framework’ of linear shapes, then it can be constructed through simple measurements of length. The most basic way to go from a one-dimensional boundary to a two-dimensional shape through linear measurement alone is through triangles. This method has been used since the time of ancient Egypt where it was used to measure the (two-dimensional) area of land holdings using (one-dimensional) rope as a measuring device.

The ‘Suspension’ series of installations by Ball-Nogues Studio (some of which I was fortunate to be a part of) consist of a series of threads cut to specific lengths, coloured at specific intervals and hung from specific points to form a series of catenaries. When seen together, the strings form complex, multi-coloured, three-dimensional “clouds” suspended in mid air.

“Suspensions: Feathered Edge by Ball-Nogues Studio”. MoCA PDC, Los Angeles, 2007.

A sturdier and more ancient way of combining linear elements into objects of higher dimensions is weaving. The weaving of cloth goes from one-dimensional thread to a two-dimensional cloth, and the weaving of baskets goes from one-dimension strips (of cane, bamboo, rattan or other materials) to a three-dimensional surface. Kenneth Snelson shows how a tensegrity structure can be thought of as a three-dimensional polyhedron woven out of linear elements.

A surface woven from digitally derived linear fabrication data.
The first bamboo Parametric Pavilion. Kamath Design Studio, New Delhi, 2010.

The process of weaving is therefore an ideal candidate for a manual construction process involving only linear measurement that can be used to construct a digitally designed, complex curved surface. I had woven a quick model based on this premise some months ago using linear fabrication data obtained by running this script on a test surface. After the successful construction of the first bamboo Parametric Pavilion I am now attempting the design and construction of a more complex woven bamboo roof structure for a 150 square meter guest house building. This project will be a test case for implementing the idea of using digitally derived linear construction data for the manual weaving of a complex curved surface.