Knot Making by zhiwei liao

Knot Making Exploring the boundary between digital modeling and physical fabrication

by Zhiwei Liao September 2005

A thesis submitted to the Faculty of the Graduate School of the State University of New York at Buffalo in partial fulfillment of the requirements for the degree of

Master of Architecture

Department of Architecture

Acknowledgments

I would like to thank: My chair and committee, Prof. Annette LeCuyer and Prof. Omar Khan, for giving me enormous knowledge, guidance and endless encouragement. Prof. Frank Fantauzzi and Michael Zebrowski for their comments and support. Justin T Allen, for his patience and extreme dedication to my thesis. David L Rooth, James Carr, Yin Hong, Felix J Lomonaco for their warm hearted help. Tom Allen and his P. Tool & Die Co., Inc. Haoyan Chi, a Mathematics Ph. D candidate, for her expertise on the knot. Dick Yencer for his shop advice.

III

……………………………………………….

Author: Zhiwei Liao Department of Architecture June 27, 2005

………………………………………. Annette LeCuyer Professor of Architecture Thesis Chair

………………………………………. Omar Khan Assistant Professor of Architecture Thesis Committee

TABLE OF CONTENTS

Acknowledgments

III

List of Figures

Small: Seamless fabric

Abstract

Medium: Hand-size knot

1 INTRODUCTION

Large: Room- size concrete knot

2 BACKGROUND

The first study: 3/4” Birch plywood

Erwin Hauer`s screen wall

The second study: 1/8” Luan plywood

Digital fabrication tools

The third study: 3/8” bendable plywood

The final study: 3/4” Birch plywood

3 EARLY STUDIES

5 KNOT FABRICATION

Dune units

6 CONCLUSION

Three dimensional loop

References

The woven model

4 KNOT STUDY

List of Figures molds, Franken Architekten

1.1

Small: Fabric knot

1.2

Medium: hand-size knot

1.3

Large: room-size knot

(2000) in Dusseldort, Germany, pre-cast in

2.1

Single component, Erwin Hauer

CNC-milled Styrofoam molds, Tomas

2.2

Screen wall, Erwin Hauer

Mayer

2.3

Mold, Erwin Hauer

3.1

NURBS curved-surface as a repetitive unit

2.4

Antoni Gaudi`s Sagrada Familia Church in

3.2

Array of dune units

Barcelona, Mark Burry

3.3

Cutting layout for a loop

Unfolding curved surfaces into strips of

3.4

Digital model of folded paper

polygons, William J. Mitchell and

3.5

Digital model of infinity loop

Malcolm McCullough, image by Girish

3.6

Woven in computer

Ramachandran

3.7

Unwoven in computer

Double-curved acrylic glass panels for

3.8

Woven in paper

Bernhard Franken`s â&#x20AC;&#x153;bubbleâ&#x20AC;? BMW

4.1

Knot zoo, Sean Collom

pavilion (1999) produced using CNC- milled

4.2

Manipulating the control points

2.5

2.6- 2.8

2.9- 2.11

Concrete panels for Gehry`s Zollhof Towers

4.3

Turn the curve into mesh for 3D printer

5.10

Connection recess

4.4

Plastic knot created by 3D printer

5.11

Connecting two pieces

4.5

Making the bottom support material

5.12

Casting plaster

(Dimension STT 3D printer)

5.13

Casting and mold

Layering the ABS plastic to make a physical

5.14 a-b

Design table of the connection

object

5.15

Stainless steel connection parts, done using a

4.6

5.1

Stone lion, Jiangsheng Yu

5.2

Arrangement of 60 modules in computer

5.16

Stainless steel connection assembly

5.3

3D physical print of 60 knots

5.17

1/6 standard parts

5.4

60 knots seamless fabric

5.18

Snake-like mold

5.5

Flexibility

5.19

Connecting two pieces

5.6

Interlocking digitally

5.20

Hand-size knot

5.7

Interlocking physically

5.21

Room-size concrete knot

5.8

Rendering of hand-size knot

5.22

Diagram of unfolded formwork, 1/3 of a

5.9

Mold, 3D drawing in Rhino, ready for 3D printer

wire EDM machine

knot 5.23

Formwork study 1: Âžâ&#x20AC;? birch plywood

VII

5.24

Formwork study 1, plotted templates

5.25

Formwork study 2: 1/3 section of a knot, 1/8â&#x20AC;? luan plywood panel and 2 x 4 parts for

5.39

3D modeling of final formwork, with guidelines for kerfs and drilling

5.40

3D modeling of the bottom panel, to which the bolts are perpendicular

connection 5.26

Details of formwork study 1

5.41

Laying out the guidelines for cuts and kerfs

5.27

Details of formwork study 2

5.42

Drilling the connection holes with the

5.28

Formwork study 3: 3/8â&#x20AC;? bendable plywood

guidelines

panels and 2 x 4 parts for connection

5.43

Making kerfs to make the plywood bendable

5.29

Knot curve of formwork study 3

5.44

Side pieces with drilled holes and kerfs

5.30

Knot curve of final formwork

5.45

The bottom panel with bendable kerfs is

5.31- 5.34 Working process of formwork study 3

ready for connecting with side pieces

5.35

Paper model and construction work

5.36

Final formwork for casting

5.37

Plotted templates of final formwork, with

5.50

Unfinished formwork

guide-lines for kerfs and drilling

5.51

Finished formwork

Assembling side pieces

5.52

Prefabricate wire mesh for reinforcement

5.38

5.46-5.49

Assembling the side pieces with the bottom panel

VIII

5.53

Sifting the concrete mixture

5.54

Placing first layer of concrete

5.55

Placing wire mesh

5.56

Trowelling the concrete

5.57

Keeping damp while concrete cures

5.58

Casting

5.59- 5.62 Counter-bored bolt heads do not interfere 5.63

with finishing of top surface of concrete

5.64

View of formwork from below

5.65

Stripping formwork

5.66

Concrete knot with temporary supporter Lift the concrete knot to remove temporary supporter

5.67- 5.71 Concrete knot 5.72

Formwork after casting

Abstract

This thesis is about touching the boundary between digital modeling and physical making, between the limitation of hand craft and the precision of the computer, between material resistance and the boundary of the two- dimensional interface of the computer. It is about using different materials to make objects of different sizes as well as â&#x20AC;&#x153;untanglingâ&#x20AC;? the infinity idea of a knot within the physical world.

Digital technology, through the use of NURBS (Non-Uniform Rational B-Spline) geometry gives its user the ability to digitally fabricate complex geometries without the difficulty or resistance of physical reality. This thesis, through making a rigid knot in 3 different scales- small (fabric), medium (hand held size) and large (room size) - investigates the combination of digital modeling, digital fabrication and existing techniques of physical making as a means to understand the limitation of digital drawing, the constraints of physical reality, as well as the problem of translation between the digital and physical realms.

1. INTRODUCTION The earlier research explored complex plaster casting:

NURBS curved-surface to generate a three dimensional

Erwin Hauer`s screen wall, made in the mid-1950s, is

repetitive unit. The three dimensional loop introduces the

composed of the artistic effect and topology geometry. It is

focus of topology.

a study of pure physical making compared with contemporary digital technologies in the architectural realm.

The woven model starts to relate digital modeling of

By the early 1990s CAD/CAM was beginning to penetrate

NURBS geometries to paper modeling.

into architectural practice, providing the opportunity to

These explorations provide a foundation f investigation of

fabricate complex forms. Automatic fabrication devices

the mix of physical making and digital modeling.

and digital modeling are now widely used. Is the building process simply stated as â&#x20AC;&#x153;from files to fabricationâ&#x20AC;?? What

The knot study focus on the topology of the knot with

is the new role of materiality study, traditional assembly

particular alteration to relative relationships of points and

processes and design evaluation?

curves. It then becomes the vehicle to explore the translation from digital to physical.

The initial studies of this thesis include dune units, a three The fabrication of a knot deals with complex physical dimensional loop and a woven model which contain an fabrication processes with the aid of CAD/CAM. Through infinity idea. Dune units are a virtual form using the

making three different scales of a knot with different methods and materials, the insight of physical making, in terms of material analysis, computer modeling and assembly processes, is evident in the products.

To construct the large size knot in concrete, four iterations of wooden formwork were studied. These studies help to understand the bendable nature of plywood and its corresponding digital representation using NURBS geometries.

1.1 Small: Fabric knot

1.2 Medium: hand-size knot

1.3 Large: room-size knot

2. BACKGROUND Erwin Hauer`s screen wall In the mid-1950s, a complex screen wall, designed by

material for most of the walls was Hydrostone, a gypsum

Austrian-born sculptor Erwin Hauer, focused on three

cement of very high strength. A few were made in cast

dimensional patterns and organic forms. These patterns

stone, a mixture of white Portland cement and crushed

provided an innovative light diffusing effect. They were

limestone or marble.

made of plaster, whose assembling seam can be hidden to

Erwin Hauer`s screen wall is an interesting example

create a continuous 3D woven rigid surface. Most of

because of its complex geometry which makes the

Hauerâ&#x20AC;&#x2122;s work was originally produced as single, hand-size

formwork and casting process difficult. Its standard unit is

components that were joined into a square tile. In the mid-

seamless, repetitive and generated with three dimensional

1950s, with the increasing availability of sophisticated

curvature. Because the design was carried out without the

molding and casting materials, square modular units were

aid of CAM/CAD at that time, the scale had to be limited to

cast monolithically. Later still, molds were attached to each

the hand-size units, which can be tiled up to form an

other, creating continuous cavities and allowing the casting

architectural screen wall.

of two, and later four, modules at a time. The casting

2.1 Single component

2.2 Screen wall

2.3 Wooden Mold

Digital fabrication With the aid of CAD/CAM, complex forms need not only

Plotted templates and computer-controlled cutters are used

exist in the computer, but can also be realized in the

to cut sheet material, Therefore, a three-dimensional

physical world. In his Digital design media, William J.

physical model can be assembled by converting a surface

Mitchell describes some prototyping techniques and

or solid into separate polygonal shapes. A model of curved

methodologies: Plotted templates, computer-controlled

surfaces can be produced from flat sheet material by

cutters (2D fabrication), multi-axis milling (i.e. CNC

following this procedure.

milling machines), incremental forms (3D system or 3D printer), reshaping (mechanical forces, restricting forms, or

Multi-axis milling can remove specified volumes of

use of heat or steam applied to material) or reproduction

material from solids. Stone cutting is most the obvious

using

application of automated milling technology to produce

molds

and

dies

(combo).

Computer-control

production reduces the amount of traditional drawing, and

full-scale architectural components. Some of the stones for

also reduces dependence on standardized, mass produced

New Yorkâ&#x20AC;&#x2122;s Cathedral of Saint John the Divine and the

construction components. 1

columns needed to complete Antoni Gaudi` s (1852-1926) Sagrada Familia Church in Barcelona, were cut in this

William J. Mitchell and Malcolm McCullough, Digital design media, New York : Van Nostrand Reinhold, c1995.

manner. Disney Concert Hall, Los Angeles, by Frank

Gehry was the first comprehensive and systematic use of

Dusseldort, Germany, concrete panels were pre-cast in

CAD/CAM technology to produce the architectural

CNC-milled styrofoam molds.

stonework for a major project. Incremental forming processes are the converse of milling processes; instead of gradually revealing three-dimensional shapes by removing material from a solid, they add material layer-by-layer in order to build up forms.

Reshaping the material is through the application of force, heat, steam, etc. In Bernhard Franken`s â&#x20AC;&#x153; bubbleâ&#x20AC;? BMW pavilion (1999), double-curved acrylic glass panels were produced using the die created by CNC- milled molds.

Rapid- prototyping machinery can reproduce molds and dies needed to reproduce objects in other materials or in multiple copies. In Gehry`s Zollhof Towers (2000) in

2.4 Antoni Gaudi` s Sagrada Familia Church in Barcelona

2.5 Unfolding curved surfaces into strips of polygons

2.6

2.7

2.8

2.6- 2.8 Double-curved acrylic glass panels for Bernhard Franken`s â&#x20AC;&#x153; bubbleâ&#x20AC;? BMW pavilion (1999) produced using CNC- milled molds.

2.9

2.10

2.11

2.9- 2.11 Concrete panels for Gehry`s Zollhof Towers (2000) in Dusseldort, Germany, pre-cast in CNC-milled styrofoam molds.

3. EARLY STUDIES Initial investigations focused on complex geometries which

surface with dune-like texture. The three dimensional

contain an infinity idea. Early studies used digital modeling

repetitive unit of NURBS curved-surfaces were integrated

tools to generate multi-curved surfaces; the first motive was

in this virtual form.

to create the infinity form by both 2D and 3D digital drawings. Infinity is defined in two ways: one is endless repetition and the other is the loop. Simultaneously, it is helpful to understand the digital drawing by using sheet material to construct a physical model, i.e. bending material such as paper to create a curved surface following the

3.1 NURBS curved-surface as a repetitive unit

digital drawing (which can be cut in sheet material) and similar procedures.

Dune units The curved-surfaces, constructed by using three identical curves in different locations, can be arrayed to form a 3.2 Array of dune units

Three Dimensional Loop The loop study introduces three dimensional concerns. It then leads to a topology study, which is about relative but not exact geometry, i.e. â&#x20AC;&#x153;a topologist cannot distinguish between a doughnut and a coffee cupâ&#x20AC;?. This study begins turning the ambiguity of topology into architectural 3.3 Cutting layout for a loop

materiality and exact geometries. The study product is one of the representations of the topology geometry which is generated by a parameter so as to be constructed physically.

In order to construct the three-dimensional loop, a flattened layout was developed. There is no thickness in the digital model which allows for easier translation into the physical, especially with the intention of using paper as a material. 3.4 Digital model of folded paper

3.5 Digital model of infinity loop

The woven model In this study, the transformation from 2D to 3D in the computer is easy due to the immaterial nature of the digital model. The shift, from drawing in plane to a physical woven model in three dimensions helps to understand the translation gap between digital drawing and physical making. 3.7 Woven in computer.

3.6 Woven in paper

3.8 Unwoven in computer

4. KNOT STUDY This study focused on the topology of the knot with

material world, and still maintain its perfection-without

particular attention to relative relationships of points and

joints-became the problem.

curves. A knot is a non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to

The Dimension STT 3-D printer was used to translate the

produce a simple loop (i.e., the unknot). While in common

digital information into a hand-size object. It created the

usage, knots can be tied in string and rope such that one or

knot by layering ABS plastic horizontally, instead of

more strands are left open on either side of the knot, the

traditional making by bending and connecting planes. The

mathematical theory of knots terms an object of this type a

printer reconstructs the knot in a way that the layers are so

"braid" rather than a knot. 2

subtle that it seems like a monolithic construction of a perfect knot. One curve was created by connecting

While it is simple to make a knot using rope, it is difficult

precisely located points. The symmetrical knot, which can

to make a knot with inflexible materials.

be divided into three standard units, was selected so that the

Digital modeling of the knot offered no resistance; it was a

making became easier.

â&#x20AC;&#x2DC;perfectâ&#x20AC;&#x2122; virtual knot. To bring the virtual knot into the 2

Eric W. Weisstein. "Knot." From MathWorld--A Wolfram Web Resource.

http://mathworld.wolfram.com/Knot.html

4.1 Knot zoo

4.2 Manipulating the control points

4.3 Turn the curve into mesh for 3D printer

4.4 Plastic knot created by 3D printer

The five step process of the Dimension SST 3-D printer: 1. Create a digital model of the knot 2. Convert the digital model to STL format 3. Slice the STL file into thin cross-sectional layers using Catalystâ&#x201E;˘ software 4. Construct the model one layer on top of another 5. Clean and finish the model 4.5 Making the bottom support material (Dimension STT 3-D printer)

Note: The 3-D printer is similar to a CNC milling machine, but different in a very important way. The 3-D printer uses its own material to produce the computer generated object, while the CNC uses an outside material, requiring knowledge on how to set and program the machine properly, as it is acting on a real physical material.

The rapid prototyping printer produced a rigid knot, approximately 1 inch across. 4.6 Layering the ABS plastic to make a physical object

5. KNOT FABRICATION Based on earlier investigations of the knot form, this study

The shock occurs as the physical object emerges, from the

explores physical making, through three scales. Different

3-D printer, transforming with a huge leap from a static

tools and technologies and a range of digital drawing and

three dimensional drawing to a piece of flexible fabric. This

physical material are used.

is similar to the surprise when we read the movable ball in the stone lion` s mouth, which was not put in but carved out

Small: Seamless Fabric of the same piece of stone as the lion. With each module approximately a half inch in diameter and the whole fabric 8 X 8 inches, this fabric is composed of 60 standard modules. It was constructed digitally; that is, 60 knots were put in a certain position in the computer so as to interlock with each other. The measurement of the spacing of the 60 knots takes the place of physical assembly.

5.1 Stone lion

5.2 Arrangement of 60 modules in computer

5.3 3D physical print of 60 knots

5.4 60 knots seamless fabric

5.6 Interlocking digitally

5.5 Flexibility

5.7 Interlocking Physically

Medium: Hand-size knot Plaster was selected to construct the hand-size knot. The

The small stainless steel connection parts were made using

scale determined the section contour and the thickness of

a wire EDM (Electrical discharge machine), providing the

the knot which should be light weight but stiff enough to

required precision.

support itself and hold its shape. The symmetrical form helps to divide the knot into 6 standard parts which can be reproduced by a 3-D printer mold. The consequence was that it required six connection joints.

The snake-like mold was composed of two parts with

5.8 Rendering of hand-size knot

flanges with 19 holes for bolts. Considering the liquidity of the plaster, openings had to be horizontal. The mold from the 3D printer was sanded and finished using polyurethane. A recess accommodates the metal connector which clamps two parts together.

5.9 Mold, 3-D drawing in rhino, ready for 3D printer

5.10 Connection recess

5.12 Casting plaster

5.11 Connecting two pieces

5.13 Casting and mold

5.14a Design table of the connection

5.14b Design table of the connection

5.15 Stainless steel connection parts, made using a wire EDM machine

5.16 Stainless steel connection assembly

5.17 1/6 standard part

5.18 Snake-like mold

5.19 Connecting two pieces

5.20 Hand-size knot

Large: Room size concrete knot The plastic knot fabricated from the 3D printer was

Points connect to make lines, which become 3-dimensional.

successful in form, but it had steps and ridges along its

Once the 3-dimensional object was created, it was

surface. Further knowledge and practice using the 3D

necessary to go back to two dimensions, but using a

printer might illuminate other methods and techniques,

different 2-dimensional process. Attempting to make the

which could produce more perfect effects, but this was not

knot from concrete, it was necessary to make formwork.

the central problem this thesis was looking to address.

Wood was used for the formwork because of its

Even if the 3D printer produced a perfect knot, it was not at

construction properties: it is common, cheap, rigid, flexible

large scale and did not use necessary methods of

and mass-produced in standard dimensions. Transforming

fabrication that might be used at an architectural scale. To

the 3-dimensional object in virtual space to 2-dimensions

produce the virtual knot using common building materials

required CAD shop drawings of side panels (formwork

and strategies, concrete, a material which is flexible and

walls) and bases (formwork floors).

rigid, was chosen.

The fabrication of 3-dimensional objects in virtual space must begin in 2-dimensions, always starting with a point.

To construct this knot, approximately 7 feet in diameter, four iterations of formwork were studied in terms of material and construction details. The fourth one was used to cast concrete.

5.21 Room-size concrete knot

The first study: 3/4” Birch plywood The first study model was done by cutting a side panel and

Is there a better way to construct the formwork for the knot,

base of 1/6 section of the knot. UV curves (created by

a way which is more economical, quicker and efficient?

‘rebuild surface’ 3 in Rhinoceros) generate the necessary lines to make kerfs into the sides and base in order to make the plywood panels bendable. Holes were drilled in the sides and base to provide a means to connect the two giving the panels their form and structure. The side panel is 5.22 Diagram of unfolded formwork, 1/3 of a knot

placed on the base, and a bolt connects and clamps the two together at one end; this is repeated until the whole side piece is connected to the base.

Although the first study model worked, it raised many questions: Should there be more UV curves and cuts? Is ¾” birch plywood the best material? 5.23 Formwork study 1: ¾” birch plywood 3

A tool in Rhinoceros

5.24 Formwork study 1, plotted templates of study 1

The second study: 1/8” Luan plywood Study 2 was similar to the first, but without UV curves. The second study also attempted to complete the knot in three parts instead of six. Holes were not drilled in the side piece, but instead a jig was made to quickly drill holes in 2 x 4 blocks, which would be glued to the side piece.

This study worked, but the luan had to be handled delicately because it was only a 1/8” thick and weak

5.25 Details of formwork study 1

compared to the ¾” birch plywood.

5.26 Details of formwork study 2

5.27 Formwork study 2: 1/3 section of a knot, material: 1/8â&#x20AC;? luan plywood panel and 2 x 4 blocks for connection

The third study: 3/8” bendable plywood Because the luan and bendable plywood were less expensive and easier to work with than the ¾” plywood, it was critical to see if it could be made to work. The problem, however, was that in attempting to connect the three sections of formwork for the whole knot, it completely lost its flexibility in one direction. Bendable plywood only

5.28 Knot curve of formwork study 3

bends the long way or the short way of the panel. Because the knot demanded complex curves, the bendable plywood resisted certain flexibilities, making it impossible to complete the formwork. Another theory was that the peripheral curves were too tight for the bendable plywood formwork. For the next study, the computer drawing was 5.29 Knot curve of final formwork revised to make the curve gentler.

5.30 Formwork study 3: 3/8â&#x20AC;? bendable plywood panels and 2 x 4 blocks for connection

5.31

5.33

5.32

5.34 5.31- 5.34 Working process of formwork study 3

5.35 Paper model and construction work

The final study: 3/4” Birch plywood Go back to what works. The ¾” birch plywood was very strong and could be made to be more flexible with more UV kerfs. The formwork was completed with minor difficulty.

5.36 Final formwork for casting, material: ¾” birch plywood

5.37 Plotted templates of final formwork with guidelines for kerfs and drilling

5.38 Assembling side pieces

5.39 3D modeling of final formwork, with guidelines for kerfs and drilling

5.40 3D modeling of the bottom panel, to which the bolts are perpendicular

5.41 Laying out the guidelines for cuts and kerfs

5.42 Drilling the connection holes with the guidelines

5.43 Making kerfs to make the plywood bendable.

5.44 Side pieces with drilled holes and kerfs

5.45 The bottom panel with bendable kerfs is ready for connecting with side pieces

5.46

5.47

5.48

5.49 5.46-5.49 Assembling the side pieces with the bottom panel

In order to move the formwork from the wood shop to the casting site, 2 X 4s were used as structural components to reinforce the formwork for transportation. Wood putty, polyurethane and seam caulker and temporary support structure for weight of concrete. 5.50 Unfinished formwork

5.51 Finished formwork

5.52 Prefabricate wire mesh for reinforcement

5.53 Sifting the concrete mixture

Â˝â&#x20AC;? wire mesh was used for reinforcement. The concrete mixture was sifted.

The first layer of concrete was put in to support the wire mesh, which was then covered with more concrete.

5.54 Placing first layer of concrete

5.55 Placing wire mesh

5.56 Trowelling the Concrete

5.57 Keeping damp while concrete cures

5.58 Casting

5.59

5.60

5.61 5.62 5.59 -5.62 Countersunk bolt heads do not interfere with finishing of top surface of concrete

5.63 View the formwork from below

5.64 Stripping formwork

5.65 Concrete knot with temporary support structure

5.66 Lift the concrete knot to remove temporary support structure

5.67 Concrete knot

5.68 Concrete knot

5.69 Concrete knot

5.70 Concrete knot

5.71 Concrete knot

5.72 Formwork after casting

6. CONCLUSION The transition from digital modelling to a physical object is

printer could not be shifted to a bigger scale to create

always related to existing techniques of fabrication and

architectural components. As a study moving toward the

material capabilities. Digital modeling, through the use of

architectural realm, the hand-size knot introduces the idea

NURBS (Non-Uniform Rational B-Spline) geometry, gives

of reproducing standard components and their assembly. It

us a new way to analyze, define, and construct complex

moves between physical prototyping and digital modeling.

geometries, which has potential to be applied to architectural practice. New physical construction thinking

The room size concrete knot has a similar scale to an

comes with the aid of the new digital fabrication devices.

architectural entity. The one simple cast concrete knot reveals nothing of the complex assembly process of the

The three scale studies provided an opportunity to

wooden formwork, as the plywood is not the ultimate

investigate different techniques from purely digital to a mix

material which will be perceived. The attempt to bend the

of digital and physical. The fabric size knot represents the

plywood precisely with complex curvature requires

topology idea in a physical form with the aid of the 3D

understanding of the NURBS curve and the nature of

printer. It can help to evaluate the design in a physical form.

plywood and building methods. This formwork making

However, unlike the CNC machine, the scale of the 3D

process without the aid of digital fabrication devices is an

interim step between traditional machine work and full CAD/CAM. The formwork could be made precisely and efficiently in the digital realms by using an automated CNC machine. The digital model would be easier to adjust if parametric modeling were used to define constraints in the digital entities- i.e, the lines of the bolt must be perpendicular to the curve base so that the change of the curve ratio would be easier to generate. Parametric modeling would be more efficient, eliminating the need to remake everything through trial and error from the beginning.

References Kolarevic, Branko. Architecture in the digital age : design and manufacturing, ed, Branko Kolarevic, New York, NY : Spon Press, 2003. Mitchell, William J. and McCullough, Malcolm, Digital design media, New York : Van Nostrand Reinhold, 1995. Weisstein, Eric W. "Knot" From MathWorld -A Wolfram Web Resource. http://mathworld.wolfram.com/Knot.html Hauer, Erwin, Erwin Hauer : continua-architectural screen and walls, New York : Princeton Architectural, 2004.