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When using the Laser Cutter to produce a model, prototype or engraving, the geometries used in the generation of the object will not only derive from the digital model, they will affect the final appearance and finish of the real object.  

Certain models lend themselves to specific geometries – a contour is normally associated with a layering process (slicing through the solid form) while a polyhedral or net form will usually be made by folding (¿engraving¿ the fold lines and cutting the boundaries) and a semi-solid or surface could be formed using modular components (a jigsaw like solution of identical or iconographic parts) or unique parts (each part is unlike the other), for example. 
Geometries focused on in this study:

  • Point to Point
  • Edge to Edge
  • Intersections
  • Layering
  • Modular
    Creating a model using CAD/CAM systems that is to be prototyped by the laser cutter raises two questions initially: [1] What function(s) does the laser cutter perform which will be used to realise this model? [2] How will the 3D object be visualised in two dimensions to ¿print¿ on a planar material? Further questions include those of resolution, method of joining, optimisation, materiality and minimisation of waste.  Analysis of geometry is primarily concerned with the answer to the second of these questions, but the first question should determine to some degree the formation of the digital model¿s geometry.  

    Translation is the selected method by which the 3D model becomes a 2D print and is as much a decision of aesthetics as it is of construction. The University of Auckland Laser Cutter is a three-axis Flying Optics system – it can cut at a certain Power (Z-axis, especially Boolean ON and OFF) along the XY-axes. 

    Resolution factors into some geometries more than others. For Edge to Edge and Folded, only the linear function resolution is of concern. For Contour, the thickness of the material determines the vertical resolution of the model. For Point to Point and Modular, the scale of the components relative to the object determines the facet resolution. 

    Construction of the model in the real world can be simplified by considering the method of joining (glue, tolerance, slotting, etc.), the optimisation of parts (repetition, points of reference, etc.), the materiality (advantages and disadvantages), and the minimisation of waste (positioning the geometric components so as to reduce or eliminate wasted negative space).

Point to Point:

Firstly, a definition of ¿point to point¿ in relation to a geometrical form is needed. Point to point geometries can be described as containing a system of ¿connections¿ and ¿web¿ members, where the object contains no outer or inner ¿membrane¿. To differentiate point to point relationships from other geometries, it could be said that the ¿form¿ created by using the web/connection system is given by how this system forms itself as a whole or as a collection of these webs and connections, rather than the shape that the individual members take. Often the shapes formed in the voids between web membranes and path followed by the web/connection system may approximate an overall solid in a ¿wireframe¿, such as in the example below where, to the viewer, a cube is approximated by what is really just a series of parallel and perpendicular web members, connected at their ends.

Figure 1: Basic point to point geometry

Point to point geometries are particularly efficient for the creation of the structural/gestural frame of larger forms due to their minimal use of material. The overall ¿geometry¿ created by this frame is essentially a reflection of how different types of web members are arranged, and in which way they are connected to one another. Web members involved in point to point relationships may be one of compression or tension members, with the connections between them being either fixed/rigid, or flexible, where a flexible connection may be for example hinged, expandable or rotatable.

¿Tensegrity¿ (or tensional integrity) structures are a special case of geometries with point to point relationships, consisting of a such a combination of compression and tension members so that tensile and compressive forces are balanced equally in the structure as a whole, resulting in an optimum strength to material use ratio.

To illustrate tensegrity and point to point relationships, the example in this study will be an approximation of an dodecahedron, a 12 sided prism, utilising a collection of 30 identical web members (acting in compression), fabricated using the laser cutter,  and rubber bands (acting in tension). Most interesting in this geometry, and in tensegrity structures in general, is the fact that at no point are the compression members touching each other (as shown in Figure 2), connected only by the string/tension members used in combination. This unique relationship has an interesting structural implication in that forces applied to the dodecahedron geometry are distributed throughout the whole web/connection system, and taken up equally by each compression/tension member involved.

Figure 2: Single pentagonal face

The advantage of using the laser cutter to fabricate the compression members involved comes to light here, in that it is important that these members are equal in size and proportion, avoiding isolated areas of more or less compressive/tensile force within the structure, as the variance of the members in turn varies their individual ability to take up the compressive/tensile stress imposed by an applied force.

Figure 4: Laser cutting pattern and 3D Form

The dodecahedron form is obtained by the connection of 12 pentagonal faces, with each face sharing one compression member each with the adjacent faces, as shown in Figure 3. Each compression member, as shown in Figure 2, is hooked into the tensile rubber band looped through the adjacent compression member, with both the hooking mechanism and rubber band groove exhibiting the advantage of the laser cutter¿s precision at forming the intricately small-scale details.

Figure 3: Overall structure

Through variation in connection types and arrangement of compressive/tensile web members in point to point relationships it is possible to construct a wide range of geometries. When used as a structural frame a balance must be struck between these two types of members, the types of connections becoming of great importance, providing flexible connections where movement must be allowed, and conversely rigid jointing where it is to be minimised. The use of the laser cutter allows for the accurate production of both connecting and web members, ensuring accurate assembly and resultantly, correct handling of internal forces by these members.

Edge to edge:

The use of nets to form 3d objects becomes more viable to design when 3d computer modelling is applied. Using tools to unfold complex 3d geometries into 2d ¿nets¿ can then be processed by the laser cutter. Once cut out, folded and joined computer models become tactile prototypes. The laser cutter aids in this process by increasing accuracy and speed when many cuts and scores are made in complex shapes.
When unfolding 3d models it is best to treat each surface individually and minimise the facets needed to a manageable number. Unfolding only works for so long until, on more complex surfaces many facets will need to be connected rather than folded.
There are several ways to unwrap, using UVW unwrap in 3ds max, or similar modifiers in other 3d software packages. Another method I found useful was.

Pepakura, a Japanese designed program, which was designed to create paper nets for cutting and folding with paper by hand. Pepakura can be used with 3ds files and exports to bmp images, .dxf and other cad files.

Using a cad package or Adobe Illustrator, it is important to edit the 2d nets into a compatible format for the laser cutter. Check line weights and colours of the lines correspond to the cutting methods of the laser cutter.


The exploration of possibilities and opportunities of interlocking geometry is the aim or the primary objective. Branching from this primary objective is the secondary objective of interesting possibilities.
Accurate reproduction of forms from what is created in software to the physical object is what the computer---laser interface allows for. Hence, it is now possible to apply mass repetition and not have the inherent human error of cutting compounding with every consecutive part cut. 

Concurrent with this opportunity of eliminating human error in the cutting phase, the brief is therefore most fittingly the exploitation of such an advantage. The brief henceforth, is to apply repetition to a distinct part.


Model the object which is in question in a vector format, i.e. AutoCAD or illustrator, remember that the laser cutter recognizes anything raster-based as an engraving job rather than a cutting job.
Things to note:

For parts to fit properly one must insure some sort of tolerance (in this case an allowance or room for the pats to slide into position) of about ±0.5mm or so.

When sliding certain materials into place, some materials may shear easily under the stress in small joints etc. Careful choice of a more flexible material will insure better results


Modular Design optimises a system by subdividing into smaller parts (modules), either a singular component or set of components, or a specific iconography of modules. As well as a reduction in production cost, modularity aims to combine the advantages of standardisation with those of customisation. The Laser Cutter is easily more precise and capable of intricacy than a human, especially over hundreds or thousands of iterations, and thus is the perfect tool for standardised (as well as non-standard) design.
The Ring System

The example we will use to illustrate modularity is derived using the simplest of geometries, a circle, and a tolerance based linkage.

Using the Laser Cutter, a single sheet of 800mm x 450mm MDF of 3mm thickness produced 312 standard rings, each with a circle subunit (from the internal cut).

Shown in the diagram Fig 1:
The delta (A) is 90-degrees allowing a simple and linear linkage between rings.

Fig 1:  A Single Ring

This difference between internal and external radii (B) is twice the thickness of the material, thus 6mm.
The depth of the notch (C) and more importantly the width (D) is equal to the thickness of the material and thus half of B, 3mm.

Fig 2: Connections Explored

The component was designed to connect to itself as well as the subunits by tolerance-fit notches. Because of the above design considerations, there are at least 4 different means to attach one component to another: notch-notch parallel, notch-notch tangent, notch-edge, and notch-sub. The connections are shown in Fig 2. The standard notch-notch in parallel allows a linear chain to be formed, while the sub-unit circles can be non-linear as any angle of connection can occur, and the remaining connections are more obscure.

The simplicity of the circle in contrast to the complexity of objects that can be formed through a systematic approach proves the relevance of modular design as a printing method, a rapid prototyping process, and as full scale tectonic elements

While versatile and virtually limitless in application, the nature of standardised design relinquishes some control of the final object – form is always a summation of the parts.

But the obvious advantage to modular design is that one component with another becomes a link, which becomes a part, which becomes a module, which becomes a system. Examples on the right in Fig 3 and Fig 4 can be considered modules – a series of parts made up of links between components. Each example is clearly different fundamentally, yet made of exactly the same components.

Due to the repetition of standardised printing (even though there is an inherent complexity in each component) it is usually simple to minimise the wasted material in the negative space (the area not included in a component)


The key to Modular Design is optimisation. From design to translation and resolution, the optimal solution must be found to maximise the quality of the final object. As the entire system is based on small parts, those components must be optimised and must be applicable in all iterations of the design. Finding the perfect component for the task will ensure a solid and workable solution, an object with inherent complexity from the simplest concept.

Modular Examples

Modularity in Design can be found in many examples, from nature and invention, traditional and modern. Simple yet inherently complex, modularity allows the designer to create efficient systems and continue to develop or change them over many iterations and applications.

The most common illustrations for modular physical systems and their varying applications are Human Cells, Bricks, and Cars. While not often thought of as belonging to a common group, these three things are all based on the efficiency of the equilibrium between optimization and repetition that is integral to modular design.
The Human Cell is itself made up of smaller standard parts, but functions too as a modular component in our bodies. Similarly constructed cells perform varied tasks and can together form standard ¿materials¿ for use as different components of a larger scale – muscles, brain-tissue, arms, legs, etc. The autonomation of the cell results in the sum (the Human Body) being greater than the parts.

The standard Brick finds itself beside the Human Cell in comparison due to its similarities as a ¿building block¿. Each part is near useless on its own, save for a paperweight, but aligned and piled atop one another the Brick is part of a Wall – a solid surface of near limitless application and dimension. Various block sizes do not necessarily mean proportionally scaled walls, but the optimum brick for the task is selected.

Furthermore, a ¿brick¿ can be any repeated component of a surface. The Aegis Hypo-surface by Mark Goulthorpe is by definition a modular system – a series of standard ¿bricks¿ forming a surface in the traditional way, but affected by an array of pneumatic pistons this surface can deform in unusual and non-standard, non-linear ways responding environmental factors.

A car is an assembly of many parts, with many of these parts able to be changed (or upgraded) to improve the performance of the car as a whole. This modular design is in response to consumer demand, for each consumer can decide the price based on the features they specify. Furthermore, the ubiquitous nature of the car means its parts are likely to be standardised between models and manufacturers (aside from proprietary components) to allow their parts to be used in as many cars as possible so as to maximize the economies of scale.

Modular Design has obvious benefits as shown in real-world examples, but obviously cannot cater to all demands. Therefore, the most important consideration for modular design should be in these terms – What scalability, reproduction, complexity, control, do you require? And how will a modular system of single or iconographic components benefit the whole object or design?





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First published Mon. 1 Feb. 2010.


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