Archive for the ‘geometry’ Category

SmartGeometry 2011, use the force cluster

Sunday, April 17th, 2011

Project Palmtrees

http://smartgeometry.org/index.php?option=com_community&view=groups&groupid=2&task=viewgroup

http://archinect.com/features/article/2112195/smartgeometry-2011-copenhagen-denmark

Using given parameters, project “palmtree” tries to create a flexible model that adapts to user input using physical bending parameters of flexible plastic rods of 6 mm diameter.

The “dancefloor”, a 2×3 m timber construction reads in user movement through a series of pressure sensors. They are connected to an Ardurino board and linked to a grasshopper model using firefly. So is a camera, tracking position and rotation of reacTVision markers.
The “dancefloor” represents the buildings plan. Positioning a marker “grows” a tree at the relative position in the room. Moving around and activating the pressure sensors, applies forces to the top of the tree making it bend towards the user’s position.
The trees themselves are woven from elastic plastic rods. Their bending stiffness is approximated using Kangaroo physics plugin. The structure tries to become as straight as possible while the external forces of the user input deform it. The ends of the rods move freely and are attracted to the room’s ceiling using spring forces. When a tree bends, these loose ends “crawl” along the ceiling to find a new connection position.
The project balances real physical input (firefly), physical simulation (Kangaroo) and a physical model: One instance in time was “frozen” and built as a 1:1 structure in the workshop space. While this final structure can’t move or react to user interaction, physical modeling allows a flexible and intuitive formfinding process.

Smartgeometry 1
Smartgeometry
Smartgeometry 3
Smartgeometry 4

together with:
Asbjorn Sondergard
Pablo Resende
Mario Guidoux

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Posted in conference, elasticity, exhibition, geometry, Grasshopper, Parametric Design, research | Comments Closed

Morphogenetic Studio at Aarhus School of Architecture 2010-2011

Saturday, January 29th, 2011

Morphogenetic Studio is an experimental investigation of form generating processes through digital as well as analogue tools. The studio takes its starting point in an exploration of how relations between the general and the specific might be challenged by digital design techniques. Architects have of course always been interested in how general principles could be unfolded in specific design solutions informed by specific contextual conditions, but digital tools offer new ways of investigating these questions through the use of scripting and parametrically controlled models.  Digital models also offer new ways of linking design and realisation processes, which is another core interest of the studio. Morphogenetic Studio investigates these questions with an emphasis on spatial and tectonic potentials and possibilities.

 The studio is based on an integration of architectural teaching and research in the field of digital tectonics and algorithmic design.  The goal is to create an environment that is rooted in specific research subjects and which can generate products that reflect the research and at the same time can become a part of it.

Final installations

101015-London-3

101015-London-3

101015-London-3

101015-London-3

101015-London-3

Exhibition and Presentation

101015-London-3

101015-London-3

101015-London-3

 

 Final books and videos 

 
.interference by Bjarke Schødt, Mathias Meldgaard, Thomas Bang & Troels Holm | Make Your Own Book

 

 
MORPHOGENESIS OF ANT SWARM INTELLIGENCE by Christine Hauge Ringsmose, Agnija Rubene, Mikkel Horsbøl Lauridsen & Tobias Theil Konishi | Make Your Own Book

 

Morphogenesis Of Ant Swarm Intelligence from Tobias Theil Konishi on Vimeo.

Morphogenetic Studio // Cell Structures by Kristoffer Rauff, Lars Borgen, Annica Carina Tomasdotter Ekdahl, Anne Winther Worm | Make Your Own Book
 

Students:

  • Lars Borgen,
  • Annica Carina Tomasdotter Ekdahl,
  • Kristoffer Rauff,
  • Anne Winther Worm,
  • Troels Holm,
  • Thomas Bang Madsen,
  • Mathias Meldgaard,
  • Bjarke Lehmann Schødt
  • Nikolaj Bogensee Johansen,
  • Ragnar Zachariasen,
  • Tatiana Mukhina
  • Tobias Theil Konishi,
  • Mikkel Horsbøl Lauridsen,
  • Christine Hauge Ringsmose,
  • Agnija Rubene
  • Anita Vårbo Berglund,
  • Pelle Hviid Andersen,
  • Mateusz Bartczak

 

Teachers: 

  • Claus Peder Pedersen,
  • Niels Martin Larsen,
  • Sebastian Gmelin
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Posted in exhibition, geometry, Grasshopper, Parametric Design, Processing, research, Rhino Script, teaching, Uncategorized | Comments Closed

Uniform Nonrational B-Splines in B-Processor

Tuesday, May 4th, 2010

Implementation in B-Processor / Java:
public static class UniformNonrationalBSpline extends Command {
  private Space net;
  /**
   * Constructs a frame command
   * @param net Space
   */
  public UniformNonrationalBSpline(Space net) {
    this.net = net;   
    parameters.put(“subdivisions”, 5.0);
    parameters.put(“UNRBSname”, “Unifrom Nonrational BSpline”);
  }
  /**
   * {@inheritDoc}
   */
  public String title() {
    return “Unifrom Nonrational BSpline”;
  }
  //bring edges in order
  public static List<Edge> order(List<Edge> edges) {
      LinkedList<Edge> ordered = new LinkedList();
      if (edges.size() > 0) {
       Edge first = edges.get(0);
          ordered.add(first);
          edges.remove(0);
          while (edges.size()>0) {
           for (int i = 0; i < edges.size(); i++) {
            search:
            if (edges.get(i).contains(ordered.get(ordered.size()-1).to)) {
             //check direction
             if (!edges.get(i).from.equals(ordered.get(ordered.size()-1).to)) {
              Vertex temp = edges.get(i).to;
              edges.get(i).to = edges.get(i).from;
              edges.get(i).from = temp;
             }
             //add at end of Linked list
             ordered.add(edges.get(i));
             edges.remove(i);
             break search;
            } else if (edges.get(i).contains(ordered.get(0).from)) {
           //check direction
             if (!edges.get(i).to.equals(ordered.get(ordered.size()-1).from)) {
              Vertex temp = edges.get(i).to;
              edges.get(i).to = edges.get(i).from;
              edges.get(i).from = temp;
             }
             // add at beginning of Linked List
             ordered.add(0, edges.get(i));
             edges.remove(i);
             break search;
            }
           }
          }
      }
      return ordered;
    }
 
  public Vertex unrbsCalc(List<Vertex> gConst, double t) {
   Vertex blend = new Vertex(0,0,0);
   if (gConst.size()==4) {
    double[] tempCalc = new double[4];
    tempCalc[0] = ((1-t)*(1-t)*(1-t))/6;
    tempCalc[1] = (3*t*t*t-6*t*t+4)/6;
    tempCalc[2] = (-3*t*t*t+3*t*t+3*t+1)/6;
    tempCalc[3] = (t*t*t)/6;
    for (int i=0; i<=3; i++) {
     blend.x = blend.x + tempCalc[i]*gConst.get(i).x;
     blend.y = blend.y + tempCalc[i]*gConst.get(i).y;
     blend.z = blend.z + tempCalc[i]*gConst.get(i).z;
    }
    System.out.println(blend.x);
   }
 return blend;
  }
  /** {@inheritDoc} */
  @Override
  public void evaluate() {
    String UNRBSname = (String) parameters.get(“UNRBSname”);
    double subdiv = parameters.getDouble(“subdivisions”);
   
    List<Vertex> vertices = new ArrayList(net.getVertices());
    List<Edge> edges = new ArrayList(net.getEdges());
    List<Vertex> orderPoints = new ArrayList();
    List<Vertex> curvePoints = new LinkedList();
    if (vertices.size()>=3) {
     LinkedList<Edge> nEdges = new LinkedList();
     nEdges = (LinkedList) order(edges);
     // write into List
     for (int i=0; i<nEdges.size(); i++) {
      orderPoints.add(nEdges.get(i).from);
     }
     orderPoints.add(nEdges.get(nEdges.size()-1).to);
     // make Spline go through endpoints
     for (int i=0; i<=2; i++) {
      orderPoints.add(orderPoints.get(orderPoints.size()-1));
      orderPoints.add(0,orderPoints.get(0));
     }
     
     // create space object to draw new elements
  Space result = Space.createUnion(UNRBSname);
 // calculate Uniform Nonrational Spline Curve
  for (int i=3; i<= orderPoints.size()-2; i++) {
   for (int t=0; t<subdiv; t++) {
    curvePoints.add(unrbsCalc(orderPoints.subList(i-3, i+1),t/subdiv));
   }
  }
  // draw Spline Curve
  for (int i=1;i<curvePoints.size()-1;i++) {
   result.add(new Edge(curvePoints.get(i-1),curvePoints.get(i)));
  }
  
  
  net.getOwner().add(result);
    }
  }
}
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Posted in B-processor, geometry, Java, research, scripting, Uncategorized | Comments Closed

Chain model – simple simulation

Sunday, November 15th, 2009

Wrote a simple script that simulates chain models in Microstation. A series of chain segments of a specific length is defined. Some knots are fix others can move.

 

‘Simulation of a chain model
‘Sebastian Gmelin
’15.11.2009

Option Explicit

Const gravity As Double = 1 / 5
Const springforce As Double = 1 / 8
Const attrForce As Double = 3

Public Type sphere
    number As Long
    radius As Double
    center As Point3d
    newCenter As Point3d
    sElements(3) As Element
    numNeighbours As Long
    Neighbours(10) As Long
    connections(10) As Element
    moveable As Boolean
End Type

Dim spheres() As sphere

Function createSphere(pos As Point3d, rad As Double, number As Long, moveable As Boolean) As sphere
   
    Dim elem As Element
    Dim mat As Matrix3d
   
    createSphere.center = pos
    createSphere.newCenter = pos
    createSphere.radius = rad
    createSphere.moveable = moveable
    createSphere.number = number
    createSphere.numNeighbours = 0
   
    Set elem = CreateLineElement2(Nothing, pos, pos)
    elem.Color = 3
    If moveable Then elem.Color = 1
    elem.LineWeight = 8
    elem.LineStyle = ActiveDesignFile.LineStyles(1)
    ActiveModelReference.AddElement elem
    elem.Redraw
    Set createSphere.sElements(0) = elem
   
    mat = Matrix3dFromAxisAndRotationAngle(2, 0)
    Set elem = CreateEllipseElement2(Nothing, pos, rad, rad, mat, msdFillModeNotFilled)
    elem.Color = 6
    elem.LineWeight = 0
    elem.LineStyle = ActiveDesignFile.LineStyles(2)
    ActiveModelReference.AddElement elem
    elem.Redraw
    Set createSphere.sElements(1) = elem
   
    mat = Matrix3dFromAxisAndRotationAngle(1, Pi / 2)
    Set elem = CreateEllipseElement2(Nothing, pos, rad, rad, mat, msdFillModeNotFilled)
    elem.Color = 6
    elem.LineWeight = 0
    elem.LineStyle = ActiveDesignFile.LineStyles(2)
    ActiveModelReference.AddElement elem
    elem.Redraw
    Set createSphere.sElements(2) = elem
   
    mat = Matrix3dFromAxisAndRotationAngle(0, Pi / 2)
    Set elem = CreateEllipseElement2(Nothing, pos, rad, rad, mat, msdFillModeNotFilled)
    elem.Color = 6
    elem.LineWeight = 0
    elem.LineStyle = ActiveDesignFile.LineStyles(2)
    ActiveModelReference.AddElement elem
    elem.Redraw
    Set createSphere.sElements(3) = elem
   
End Function

Sub moveSphere(s As sphere, vec As Point3d)

    Dim i As Long
   
    s.center = Point3dAdd(s.center, vec)
   
    For i = 0 To UBound(s.sElements)
        Call s.sElements(i).Move(vec)
        s.sElements(i).Rewrite
        s.sElements(i).Redraw
        ‘ActiveDesignFile.Views(1).Redraw
    Next i
   
End Sub

Sub moveConnections()

    Dim s As Long
    Dim c As Long
   
    For s = 0 To UBound(spheres)
        For c = 0 To spheres(s).numNeighbours – 1
            Call spheres(s).connections(c).AsLineElement.ModifyVertex(0, spheres(s).center)
            Call spheres(s).connections(c).AsLineElement.ModifyVertex(1, spheres(spheres(s).Neighbours(c)).center)
            spheres(s).connections(c).Rewrite
            spheres(s).connections(c).Redraw
        Next c
    Next s

End Sub

Sub makeSphereFix(s As Long)

    spheres(s).moveable = False
    spheres(s).sElements(0).Color = 3
    spheres(s).sElements(0).Rewrite
    spheres(s).sElements(0).Redraw

End Sub

Sub makeSphereMoveAble(s As Long)

    spheres(s).moveable = True
    spheres(s).sElements(0).Color = 1
    spheres(s).sElements(0).Rewrite
    spheres(s).sElements(0).Redraw

End Sub

Sub drawConnections(s As Long)

    Dim elem As Element
    Dim points(1) As Point3d
    Dim i As Long
   
    For i = 0 To spheres(s).numNeighbours – 1
        points(0) = spheres(s).center
        points(1) = spheres(spheres(s).Neighbours(i)).center
        Set elem = CreateLineElement1(Nothing, points)
        elem.Color = 2
        elem.LineWeight = 2
        elem.LineStyle = ActiveDesignFile.LineStyles(1)
        ActiveModelReference.AddElement elem
        elem.Redraw
        Set spheres(s).connections(i) = elem
    Next i

End Sub

Sub calculateSphereMove(s As Long)

    Dim i As Long
    Dim k As Long
    Dim direction As Point3d
    Dim dist As Double
    Dim length As Double
    Dim grav As Boolean
    Dim vec As Point3d
    Dim tension As Double
   
    If spheres(s).moveable Then
    tension = 0
        For i = 0 To spheres(s).numNeighbours – 1
            direction = Point3dSubtract(spheres(spheres(s).Neighbours(i)).center, spheres(s).newCenter)
            dist = Abs(Point3dMagnitude(direction))
            ‘Debug.Print (“distance ” + CStr(dist))
            length = spheres(s).radius + spheres(spheres(s).Neighbours(i)).radius
            ‘Debug.Print (“length ” + CStr(length))
            tension = tension + dist – length
        Next i
        tension = tension / (spheres(s).numNeighbours)
        grav = True
        If tension > 0 Then
            spheres(s).newCenter = Point3dAdd(spheres(s).newCenter, Point3dFromXYZ(0, 0, -0.1 * gravity))
        Else
            spheres(s).newCenter = Point3dAdd(spheres(s).newCenter, Point3dFromXYZ(0, 0, -1 * gravity))
        End If
        vec = Point3dFromXYZ(0, 0, 0)
        For i = 0 To spheres(s).numNeighbours – 1
            direction = Point3dSubtract(spheres(spheres(s).Neighbours(i)).center, spheres(s).newCenter)
            dist = Abs(Point3dMagnitude(direction))
            ‘Debug.Print (“distance ” + CStr(dist))
            length = spheres(s).radius + spheres(spheres(s).Neighbours(i)).radius
            ‘Debug.Print (“length ” + CStr(length))
            If (dist – length) > 0 Then
                grav = False
                direction = Point3dScale(direction, attrForce * springforce * (dist – length) / (dist))
            Else
                direction = Point3dScale(direction, springforce * (dist – length) / (dist))
            End If
            vec = Point3dAdd(vec, direction)
        Next i
        spheres(s).newCenter = Point3dAdd(spheres(s).newCenter, vec)
    End If

End Sub

Sub moveSpheres()

    Dim i As Long
    Dim s As Long
    Dim vec As Point3d
   
    For s = 0 To UBound(spheres)
        vec = Point3dSubtract(spheres(s).newCenter, spheres(s).center)
        spheres(s).center = spheres(s).newCenter
   
        For i = 0 To UBound(spheres(s).sElements)
            Call spheres(s).sElements(i).Move(vec)
            spheres(s).sElements(i).Rewrite
            spheres(s).sElements(i).Redraw
            ‘ActiveDesignFile.Views(1).Redraw
        Next i
    Next s
End Sub

 

Sub Main()

    Dim i As Long
    Dim k As Long
    Dim s As Long
   
    Randomize

    ReDim spheres(99)
    For i = 0 To 9
        For k = 0 To 9
            spheres(i * 10 + k) = createSphere(Point3dFromXYZ(i, k, 0), 0.65, i * 10 + k, True)
        Next k
    Next i
   
    For i = 0 To 9
        For k = 0 To 9
            ‘spheres(i * 10 + k) = createSphere(Point3dFromXYZ(i, k, 0), rnd * 0.2 + 0.5, i * 10 + k, True)
            If i < 9 Then
                spheres(i * 10 + k).Neighbours(spheres(i * 10 + k).numNeighbours) = i * 10 + k + 10
                spheres(i * 10 + k).numNeighbours = spheres(i * 10 + k).numNeighbours + 1
            End If
            If k < 9 Then
                spheres(i * 10 + k).Neighbours(spheres(i * 10 + k).numNeighbours) = i * 10 + k + 1
                spheres(i * 10 + k).numNeighbours = spheres(i * 10 + k).numNeighbours + 1
            End If
            If i > 0 Then
                spheres(i * 10 + k).Neighbours(spheres(i * 10 + k).numNeighbours) = i * 10 + k – 10
                spheres(i * 10 + k).numNeighbours = spheres(i * 10 + k).numNeighbours + 1
            End If
            If k > 0 Then
                spheres(i * 10 + k).Neighbours(spheres(i * 10 + k).numNeighbours) = i * 10 + k – 1
                spheres(i * 10 + k).numNeighbours = spheres(i * 10 + k).numNeighbours + 1
            End If
            Call drawConnections(i * 10 + k)
        Next k
    Next i
   
    ‘Call makeSphereFix(0)
    Call makeSphereFix(9)
    ‘Call makeSphereFix(55)
    Call makeSphereFix(90)
    Call makeSphereFix(99)
   
    For i = 0 To 75
‘        Call moveSphere(spheres(Round(Rnd * 99)), Point3dFromXYZ(0, 0, Rnd * 0.5 – 0.25))
‘        Call moveConnections
        For s = 0 To UBound(spheres)
            Call calculateSphereMove(s)
        Next s
        Call moveSpheres
        Call moveConnections
        ActiveDesignFile.Views(1).Redraw
    Next i
   
End Sub

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Posted in chain models, geometry, Microstration VBA, Parametric Design, scripting | Comments Closed

Bezier Curves, algorithm of de Casteljau

Sunday, November 1st, 2009

I started reading on Curve models and geometries, different types of Spline algorithms. This is a first attempt to generate Bezier curvers using the algorithm of de Casteljau. The script uses a selected polyline as the control polygon of the curve. The Bezier is created in several steps to illustrate the process. It runs under Microstation MVBA.

Bezier curve of degree 3

Bezier curve of degree 3

Bezier curve of degree 4

Bezier curve of degree 4

Bezier curve of degree 5

Bezier curve of degree 5

Bezier curve of degree 8

Bezier curve of degree 8

‘Linestring Bezier Approximation after Casteljau’s algorithm
‘Sebastian Gmelin
’24.10.2009

‘draw and select linestring and run script

Const cDiv As Long = 5 ‘subdivision at which guidlines are drawn and a copy of the drawing set is created
Const div As Long = 50 ‘subdivision between cDiv for bezier spline points (total subdivision = cDiv * div)

Dim cPoints() As Point3d
Dim bPoints() As Point3d
Dim cSize As Point3d
Dim cLine As Element
Private Sub ScanDesignFile()
‘scan active designfile for selected linestrings
    Dim oElEnum As ElementEnumerator
    Dim oElem As Element

    ‘get collection of selected elements
    Set oElEnum = ActiveModelReference.GetSelectedElements
    ActiveModelReference.UnselectAllElements
   
    ‘go through selection set
    While oElEnum.MoveNext
        Set oElem = oElEnum.Current
        ‘check if active element is linestring
        If (oElem.IsVertexList) Then
            Debug.Print (“Linestring”)
            cPoints = oElem.AsVertexList.GetVertices ‘save collection of vertices
            Set cLine = oElem
        End If
    Wend
End Sub

Private Sub getSize()
‘get linestring size for element copies offset

Dim i As Long
Dim min As Point3d
Dim max As Point3d
Dim lineString As Element

    min = Point3dFromXYZ(1E+17, 1E+17, 1E+17)
    max = Point3dFromXYZ(-1E+17, -1E+17, -1E+17)
   
    For i = 0 To UBound(cPoints)
        If cPoints(i).X > max.X Then max.X = cPoints(i).X
        If cPoints(i).Y > max.Y Then max.Y = cPoints(i).Y
        If cPoints(i).Z > max.Z Then max.Z = cPoints(i).Z
        If cPoints(i).X < min.X Then min.X = cPoints(i).X
        If cPoints(i).Y < min.Y Then min.Y = cPoints(i).Y
        If cPoints(i).Z < min.Z Then min.Z = cPoints(i).Z
    Next
   
    cSize = Point3dFromXYZ(0, max.Y – min.Y, 0)
    cSize.Y = cSize.Y * -1.2
   
End Sub

Sub Casteljau()

Dim i As Long
Dim k As Double
Dim p As Long
Dim points() As Point3d ‘last parent point collection
Dim dPoints() As Point3d ‘division points
Dim mPoints() As Point3d ‘points to draw
Dim lineString As Element
Dim color As Long
Dim count As Long
Dim moveCount As Long

ReDim bPoints(0)
bPoints(0) = cPoints(0)
count = 0
moveCount = 0

For k = 1 / (div * cDiv) To 1 Step 1 / (div * cDiv) ‘k is scale factor of divisions
    points = cPoints
    dPoints = cPoints
    color = 48
    ‘calculate divisions
    While UBound(dPoints) > 1
    ‘points is the collection of vertices of the parent linestring
    ‘dPoints is the child linestring at scalefactor k
        For i = 0 To UBound(points) – 1
            dPoints(i) = Point3dAdd(Point3dScale(Point3dSubtract(points(i + 1), points(i)), k), points(i))
        Next i
        ReDim Preserve dPoints(UBound(points) – 1)
        ‘draw guidlines
        If count = div Then
            mPoints = dPoints
            ‘calculate offset
            For p = 0 To UBound(mPoints)
                mPoints(p) = Point3dAdd(mPoints(p), Point3dScale(cSize, moveCount))
            Next
            ‘draw line
            Set lineString = CreateLineElement1(Nothing, mPoints)
            lineString.color = color
            lineString.LineStyle = ActiveDesignFile.LineStyles(3)
            ActiveModelReference.AddElement lineString
            lineString.Redraw
            color = color + 48
        End If
        points = dPoints
    Wend
    count = count + 1
    ‘draw progress of bezier curve
    If count > div Then
        count = 0
        ‘copy control polygon
        Set lineString = ActiveModelReference.CopyElement(cLine)
        Call lineString.Move(Point3dScale(cSize, moveCount))
        ActiveModelReference.AddElement lineString
        lineString.Redraw
        moveCount = moveCount + 1
        ‘calculate offset of beziers pline
        mPoints = bPoints
        For p = 0 To UBound(mPoints)
            mPoints(p) = Point3dAdd(mPoints(p), Point3dScale(cSize, moveCount – 1))
        Next
        ‘draw bezier progress
        Set lineString = CreateLineElement1(Nothing, mPoints)
        lineString.color = 3
        lineString.LineWeight = 2
        ActiveModelReference.AddElement lineString
        lineString.Redraw
    End If
    ‘add calculated division point to collection of bezier points
    ReDim Preserve bPoints(UBound(bPoints) + 1)
    bPoints(UBound(bPoints)) = Point3dAdd(Point3dScale(Point3dSubtract(points(1), points(0)), k), points(0))
Next k

‘draw final bezier curve
mPoints = bPoints
For p = 0 To UBound(mPoints)
    mPoints(p) = Point3dAdd(mPoints(p), Point3dScale(cSize, moveCount – 1))
Next
Set lineString = CreateLineElement1(Nothing, mPoints)
lineString.color = 3
lineString.LineWeight = 2
ActiveModelReference.AddElement lineString
lineString.Redraw

End Sub
Sub Main()

    If ActiveModelReference.AnyElementsSelected Then
        ScanDesignFile
        getSize
        Casteljau
    End If

End Sub

more Bezier curves

more Bezier curves

more Bezier curves

more Bezier curves

more Bezier curves

more Bezier curves

more Bezier curves

more Bezier curves

more Bezier curves

more Bezier curves

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Posted in geometry, Microstration VBA, Parametric Design, scripting | Comments Closed

Johannes Itten – “Tower of Fire”,parametric model

Wednesday, October 21st, 2009

Having seen a rebuilt of Itten’s “Tower of Fire” at the Bauhaus exhibition, I started swcripting a parametric model of the tower in the spirit of the workshop we’re planning to do next year. The VBA script runs in Microstation and is modified by the following parameters:

  • cSize As Double = edgeLength of the bottom cube
  • cAngle As Double = rotation in plan between each cube
  • cNumber As Long = number of cubes / levels
  • cScale As Double = the bottom radii of the cones equals the diagnal conrner distance by default. This is scaled by cScale parameter
  • uSeg As Long = Number of linear panels on cone
  • vSeg As Long = Number of circular panels on cone
  • cRad As Double = Radius of panel frames

Images of rebuilts of the tower:

Examples of towers using different parameters:
tower of fire 01

tower of fire 01

tower of fire 01 top view

tower of fire 01 top view

tower of fire 02

tower of fire 02

tower of fire 02 top view

tower of fire 02 top view

tower of fire 03

tower of fire 03

tower of fire 03 top view

tower of fire 03 top view

Source code for Microstation MVBA:

‘Draw a “tower of fire”
‘Parametric approach to Johannes Itten’s design
‘Sebastian Gmelin
’19.10.2009

Option Explicit

Const cSize As Double = 60
Const cAngle As Double = 3
Const cNumber As Long = 40
Const cScale As Double = 2
Const uSeg As Long = 10
Const vSeg As Long = 1
Const cRad As Double = 0.05

Public Type cube
    height As Double
    startPoint As Point3d
    endPoint As Point3d
    direction As Point3d
    botVertex(5) As Point3d
    topVertex(5) As Point3d
End Type

Dim cubes() As cube
Sub Main()
    Dim i As Long
    Dim k As Long
    Dim p As Long
    Dim q As Long
    Dim size As Double
    Dim direction As Point3d
    Dim startPoint As Point3d
    Dim endPoint As Point3d
    Dim height As Double
    Dim cOffset As Double
    Dim conePoints(4) As Point3d
    Dim cSpans() As Point2d
   
    Dim cSurface As New BsplineSurface
    Dim cCurves(2) As New BsplineCurve
    Dim isoCurves() As New BsplineCurve
    Dim cPath As New BsplineCurve
       
    Dim line As Element
    Dim coneEdge(2) As Element
    Dim cLine(3) As Element
    Dim cArc As Element
    Dim cSurfElement As BsplineSurfaceElement
    Dim cSpline As BsplineCurveElement
   
    ReDim cubes(cNumber)
    
    size = cSize
    direction = Point3dFromXYZ(1, 0, 0)
    startPoint = Point3dFromXYZ(size / -2, size / 2, 0)
    endPoint = Point3dFromXYZ(size / 2, size / 2, 0)
    height = Point3dDistance(endPoint, startPoint)
   
    For i = 1 To cNumber
        Call createBox(startPoint, endPoint)
       
        cOffset = Atn(cAngle * 3.141 / 180) * height
        height = Point3dDistance(endPoint, startPoint)
       
        ‘store data
        cubes(i).height = height
        cubes(i).startPoint = startPoint
        cubes(i).endPoint = endPoint
        cubes(i).direction = direction
        cubes(i).botVertex(1) = startPoint
        cubes(i).botVertex(2) = endPoint
        cubes(i).botVertex(3) = Point3dSubtract(endPoint, Point3dCrossProduct(Point3dSubtract(endPoint, startPoint), Point3dFromXYZ(0, 0, 1)))
        cubes(i).botVertex(4) = Point3dSubtract(startPoint, Point3dCrossProduct(Point3dSubtract(endPoint, startPoint), Point3dFromXYZ(0, 0, 1)))
        cubes(i).botVertex(0) = cubes(i).botVertex(4)
        cubes(i).botVertex(5) = cubes(i).botVertex(1)
        For k = 0 To 5
            cubes(i).topVertex(k) = cubes(i).botVertex(k)
            cubes(i).topVertex(k).z = cubes(i).botVertex(k).z + height
        Next
       
        ‘draw testpoints
        CadInputQueue.SendCommand “ACTIVE STYLE 1″
       
        Set line = CreateLineElement2(Nothing, cubes(i).botVertex(1), cubes(i).topVertex(3))
        ActiveModelReference.AddElement line
        line.Redraw
       
        Set line = CreateLineElement2(Nothing, cubes(i).botVertex(2), cubes(i).topVertex(4))
        ActiveModelReference.AddElement line
        line.Redraw
       
        Set line = CreateLineElement2(Nothing, cubes(i).botVertex(3), cubes(i).topVertex(1))
        ActiveModelReference.AddElement line
        line.Redraw
       
        Set line = CreateLineElement2(Nothing, cubes(i).botVertex(4), cubes(i).topVertex(2))
        ActiveModelReference.AddElement line
        line.Redraw
       
        ‘change data for next cube
        startPoint = Point3dSubtract(startPoint, Point3dScale(Point3dNormalize(Point3dCrossProduct(direction, Point3dFromXYZ(0, 0, 1))), cOffset))
        endPoint = Point3dSubtract(endPoint, Point3dScale(Point3dNormalize(direction), cOffset))
        direction = Point3dSubtract(endPoint, startPoint)
        startPoint.z = startPoint.z + height
        endPoint.z = endPoint.z + height
    Next
       
    For i = 2 To cNumber
        For k = 1 To 4
            SetCExpressionValue “tcb->symbology.color”, 0, “MGDSHOOK”
            CadInputQueue.SendCommand “ACTIVE STYLE 2″
            conePoints(0) = cubes(i).topVertex(k)
            conePoints(1) = cubes(i – 1).topVertex(k)
            conePoints(2) = cubes(i).topVertex(k + 1)
            conePoints(3) = Point3dScale(Point3dAdd(conePoints(1), conePoints(2)), 0.5)
            conePoints(4) = Point3dAdd(conePoints(3), Point3dScale(Point3dNormalize(Point3dCrossProduct(Point3dSubtract(conePoints(3), conePoints(0)), Point3dSubtract(conePoints(2), conePoints(1)))), cubes(i).height * cScale))
            
            Set coneEdge(1) = CreateLineElement2(Nothing, cubes(i – 1).topVertex(k), cubes(i).topVertex(k))
            ActiveModelReference.AddElement coneEdge(1)
            coneEdge(1).Redraw
            Set coneEdge(2) = CreateLineElement2(Nothing, cubes(i).topVertex(k), cubes(i).topVertex(k + 1))
            ActiveModelReference.AddElement coneEdge(2)
            coneEdge(2).Redraw
           
            Set cLine(1) = CreateLineElement2(Nothing, conePoints(1), conePoints(2))
            ActiveModelReference.AddElement cLine(1)
            cLine(1).Redraw
            Set cLine(1) = CreateLineElement2(Nothing, conePoints(0), conePoints(3))
            ActiveModelReference.AddElement cLine(1)
            cLine(1).Redraw
            Set cLine(1) = CreateLineElement2(Nothing, conePoints(3), conePoints(4))
            ActiveModelReference.AddElement cLine(1)
            cLine(1).Redraw
           
            Set cArc = CreateArcElement3(Nothing, conePoints(1), conePoints(4), conePoints(2))
            ActiveModelReference.AddElement cArc
            cArc.Redraw
           
            Call cCurves(0).FromElement(coneEdge(1))
            Call cCurves(1).FromElement(coneEdge(2))
            Call cCurves(2).FromElement(cArc)
           
            SetCExpressionValue “tcb->symbology.color”, k, “MGDSHOOK”
            CadInputQueue.SendCommand “ACTIVE STYLE 0″
            Call cSurface.FromRailsAndSweptSections(cCurves(0), cCurves(1), cCurves(2), Nothing)
            Set cSurfElement = CreateBsplineSurfaceElement1(Nothing, cSurface)
            ActiveModelReference.AddElement cSurfElement
            cSurfElement.Redraw
           
            ‘create Network U
            For q = 0 To uSeg
                isoCurves = cSurface.ExtractIsoparametricCurve(cSpans, q / uSeg, msdBsplineSurfaceU)
                For p = LBound(isoCurves) To UBound(isoCurves)
                    Set cSpline = CreateBsplineCurveElement1(Nothing, isoCurves(p))
                    ActiveModelReference.AddElement cSpline
                    cSpline.Redraw
                    Call createTube(cRad, isoCurves(p))
                Next p
            Next q
           
            ‘create Network V
            For q = 0 To vSeg
                isoCurves = cSurface.ExtractIsoparametricCurve(cSpans, q / vSeg, msdBsplineSurfaceV)
                For p = LBound(isoCurves) To UBound(isoCurves)
                    Set cSpline = CreateBsplineCurveElement1(Nothing, isoCurves(p))
                    ActiveModelReference.AddElement cSpline
                    cSpline.Redraw
                    Call createTube(cRad, isoCurves(p))
                Next p
            Next q
        Next k
    Next i

End Sub
Sub createBox(startPoint As Point3d, endPoint As Point3d)

    CadInputQueue.SendCommand “ACTIVE STYLE 0″
    SetCExpressionValue “tcb->symbology.color”, 0, “MGDSHOOK”
   
‘   Start a command
    CadInputQueue.SendCommand “MODELER BLOCK”

‘   Set a variable associated with a dialog box
    SetCExpressionValue “tcb->ms3DToolSettings.block.axisMode”, 0, “FEATURESOLID”
    SetCExpressionValue “tcb->ms3DToolSettings.block.length.value”, (ActiveModelReference.UORsPerMasterUnit * Abs(Point3dDistance(startPoint, endPoint))), “FEATURESOLID”
    SetCExpressionValue “tcb->ms3DToolSettings.block.width.value”, (ActiveModelReference.UORsPerMasterUnit * Abs(Point3dDistance(startPoint, endPoint))), “FEATURESOLID”
    SetCExpressionValue “tcb->ms3DToolSettings.block.height.value”, (ActiveModelReference.UORsPerMasterUnit * Abs(Point3dDistance(startPoint, endPoint))), “FEATURESOLID”
    SetCExpressionValue “tcb->ms3DToolSettings.block.height.locked”, 0, “FEATURESOLID”
    SetCExpressionValue “tcb->ms3DToolSettings.block.width.locked”, 0, “FEATURESOLID”
    SetCExpressionValue “tcb->ms3DToolSettings.block.length.locked”, 0, “FEATURESOLID”

    CadInputQueue.SendDataPoint startPoint, 1

‘   Send a keyin that can be a command string
    CadInputQueue.SendKeyin “AccuDraw Rotate Top”

    CadInputQueue.SendDataPoint endPoint, 1

    CadInputQueue.SendDataPoint Point3dSubtract(startPoint, Point3dCrossProduct(Point3dSubtract(endPoint, startPoint), Point3dFromXYZ(0, 0, 1))), 1
   
    CadInputQueue.SendDataPoint Point3dAdd(startPoint, Point3dFromXYZ(0, 0, Abs(Point3dDistance(startPoint, endPoint)))), 1

    CadInputQueue.SendCommand “CHOOSE ELEMENT”

    CommandState.StartDefaultCommand
End Sub
Sub createTube(rad As Double, path As BsplineCurve)
    Dim Frame As Matrix3d
    Dim Curvature As Double
    Dim Torsion As Double
    Dim Parameter As Double
    Dim LinearNormal As Point3d
    Dim Normal As Point3d
    Dim cPoint As Point3d
    Dim circ As Element
    Dim Rot As Matrix3d
    Dim line As Element
    Dim x As Point3d
    Dim y As Point3d
    Dim z As Point3d
    Dim startPoint As Point3d
    Dim endPoint As Point3d
   
    Dim cSurface As New BsplineSurface
    Dim cSurfElement As BsplineSurfaceElement
    Dim cSection As New BsplineCurve
       
    endPoint = path.EvaluatePointFrame(Frame, Curvature, Torsion, 1, LinearNormal)
    startPoint = path.EvaluatePointFrame(Frame, Curvature, Torsion, 0, LinearNormal)
    cPoint = startPoint
   
    y = Point3dNormalize(Point3dCrossProduct(Frame.RowY, Frame.RowX))
    z = Point3dNormalize(Frame.RowX)
    x = Point3dNormalize(Point3dCrossProduct(y, z))
   
    Rot = Matrix3dFromPoint3dColumns(x, y, z)
   
    Set line = CreateLineElement2(Nothing, cPoint, Point3dAdd(cPoint, x))
    line.Color = 1
    ActiveModelReference.AddElement line
    line.Redraw
   
    Set line = CreateLineElement2(Nothing, cPoint, Point3dAdd(cPoint, y))
    line.Color = 2
    ActiveModelReference.AddElement line
    line.Redraw
   
    Set line = CreateLineElement2(Nothing, cPoint, Point3dAdd(cPoint, z))
    line.Color = 3
    ActiveModelReference.AddElement line
    line.Redraw
   
    Set circ = CreateEllipseElement2(Nothing, cPoint, rad, rad, Rot)
    ActiveModelReference.AddElement circ
    circ.Redraw
   
    Call cSection.FromElement(circ)
    SetCExpressionValue “tcb->symbology.color”, 6, “MGDSHOOK”
    CadInputQueue.SendCommand “ACTIVE STYLE 0″
    Call cSurface.FromRailAndSweptSection(path, cSection)
    Set cSurfElement = CreateBsplineSurfaceElement1(Nothing, cSurface)
    ActiveModelReference.AddElement cSurfElement
    cSurfElement.Redraw
       
End Sub

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Posted in education, geometry, Microstration VBA, Parametric Design | Comments Closed

sketchup sandbox tool

Sunday, September 27th, 2009

Google sketchup sandbox is a free-form modeler based on a meshed surface. It can be pushed and pulled with a ‘smoove‘ tool. The diameter of the tool can be adjusted numerically. Complex surfaces can be created very intuitively. This is what I had in mind for B-processor. The deformation should then follow material properties.

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Posted in B-processor, geometry, methodology, software | Comments Closed

Idea / Sketch

Friday, September 18th, 2009
material properties driving modelling tools

material properties driving modelling tools

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Posted in diagram, geometry | Comments Closed