Studio Matrx Monthly · Volume 1 · Issue 3 · August 2026
Amogh N P
 In loving memory of Amogh N P — Architect · Designer · Visionary 
Subtractive, Additive & FormativeLesson 0.3
DFR for Architecture, Planning & Urban Design/Module 0 · Foundations of Digital Fabrication

Lesson 0.3 · Foundations of Digital Fabrication

Subtractive, Additive & Formative

The taxonomy in depth - milling, laser and waterjet; FDM, SLA, SLS and concrete; bending, thermoforming and moulding

14 min Interactive lessonFree · open lessonByAmogh N P· Architect & interior designer
The hook

There are only three things you can do to a piece of material - take some away, add some on, or bend what is already there. Every machine is one of these.

It is easy to be dazzled by the sheer variety of fabrication machines - lasers, mills, printers, forming presses, robots. Underneath, the field is astonishingly simple: you can only remove, add, or reshape material. Three families, and a fourth activity - joining - that stitches their outputs together.

Get this taxonomy into your bones and every new machine you meet becomes a variation on something you already understand. More importantly, knowing which family a job belongs in tells you most of what you need before you touch a single setting: its speed, its waste, its geometry limits, and whether the thing you have drawn can even be made this way.

Remove / add / reshape / join. Choose the family before you draw the part.

Subtractive - remove what is not the part

Subtractive processes start with solid stock and cut material away until the part remains. The family includes CNC milling and routing (a spinning tool carves a block or sheet), laser cutting (a focused beam vaporises a line through sheet material), and waterjet (a high-pressure jet of water and abrasive slices almost any material cold). Their great strengths are precision, surface quality and speed on the right material - a laser can cut clean 6 mm plywood in seconds; a mill holds tolerances of a few hundredths of a millimetre.

Their limits all come from the same fact: a physical tool has to reach the material. A milling cutter cannot machine an undercut or a fully enclosed cavity, because the tool cannot get behind the surface - this is the defining geometry constraint of the family. Cutting also produces waste: the material removed becomes chips or offcuts, and the cut itself has width. That width is the kerf - typically around 0.1-0.5 mm on a laser, wider on a router or waterjet - and it must be accounted for or slotted joints come out loose. Sheet processes fight waste with nesting, packing parts tightly on the stock. Subtractive is usually the right first thought for flat sheet work, precise metal or wood parts, and moulds - which is exactly why most real fabrication is subtractive, not printed.

SUBTRACTIVE - THE TOOL MUST REACHsolid stocktoolreachable pocketundercutcannot reachchips = waste + kerf
Zoom
The defining limit of subtractive making: a physical tool has to reach the material. A milling cutter carves what it can touch from above, but it cannot reach an undercut or an enclosed cavity - and every cut removes a kerf-width of material as waste. This is why undercuts are the wall you design around for milling.

The tool has to reach it. No reach = no cut. Undercuts are the subtractive wall.

Additive - build the part up in layers

Additive processes build a part by adding material, almost always in layers, straight from a 3D model. FDM / FFF melts a plastic filament and lays it down bead by bead - cheap, robust, the desktop default. SLA / DLP cures liquid resin with light, giving fine detail and smooth surfaces for jewellery-grade parts and moulds. SLS fuses nylon powder with a laser, and because the surrounding powder supports the part, it makes complex geometry with no separate supports. At the other end of scale, concrete and clay printing extrude construction-grade paste to build walls and formwork.

The superpower of additive is geometry: it makes internal channels, lattices and organic shapes that no tool could reach, and it wastes little material. The costs are equally characteristic. Layer building is slow, and it imposes two constraints every designer must respect. First, overhangs beyond a certain angle need throwaway support structures, which cost material and leave marks. Second, parts are anisotropic - a typical FDM print is markedly weaker in the Z direction, so it tends to split between layers under load, and you must orient the part with that in mind. A worked example: print a hook lying flat and it may snap along the layers at a fraction of the load it survives when the layers run along the pull. Additive is not a synonym for digital fabrication; it is the family you reach for when the geometry genuinely cannot be reached any other way.

ADDITIVE - LAYERS, SUPPORTS, ANISOTROPYsupportfor overhangbuild Zstrong ALONG layersweak BETWEEN layerssplits hereSlow, but it makes geometry no tool could reach - waste is low.
Zoom
Additive builds a part in layers from the bottom up. Two constraints follow directly: an overhang beyond a critical angle needs throwaway support structure, and the part is anisotropic - markedly weaker between layers than along them. Orient the part so the load runs along the layers, not across the bond lines.

Layers = anisotropy. A print is weakest between its layers - orient for the load.

Formative - reshape without adding or removing

Formative processes keep the same volume of material and simply reshape it. The family includes bending and folding (sheet metal on a press brake, acrylic on a line bender), thermoforming (heating a plastic sheet and pulling it over a mould with vacuum), moulding and casting (pouring or pressing material into a cavity - resin, plaster, concrete, injection-moulded plastic), and vacuum-forming signage and trays. Digital fabrication rarely does the forming directly; instead it makes the tooling - the mould, jig, buck or die - by CNC or 3D printing, and formative then reproduces that form quickly and cheaply.

Formative shines at repetition and material efficiency: once a mould exists, each part is fast and near-waste-free, which is why the whole mass-production world is formative. But it carries two honest limits. It needs tooling, which is an upfront cost and time, so formative rewards quantity and punishes true one-offs. And materials fight back - a bent metal sheet springs back by a few degrees when released, so you overbend to compensate; a thermoformed sheet thins over deep draws; a casting shrinks as it cures. The digitally fabricated mould is where the designer's control lives, but the material has the final say on the form. Recognising a job as formative early tells you the real deliverable is often not the part at all - it is the mould.

This is also why formative and the other families are so often paired. A designer CNC-mills or 3D-prints a positive or a mould once, then casts, presses or vacuum-forms a run of identical parts from it - marrying the geometric freedom of a digital tool to the speed and repeatability of forming. A concrete example from architecture: milling a reusable formwork mould, then casting dozens of matching facade panels. The digital step happens once, up front, and the formative step multiplies it cheaply - a pattern worth recognising because it turns an expensive bespoke shape into an affordable series.

In formative, the mould is the real deliverable. Watch springback and shrinkage.

Joining and assembly - the fourth activity

No family makes everything in one piece, so a fourth activity stitches parts together: joining and assembly. It spans mechanical fasteners (bolts, screws, dowels), integral joints designed into the geometry (finger joints, mortise-and-tenon, laser-cut slots and tabs, snap fits, the flexible living hinge cut into a single sheet), adhesives, and welding or solvent bonding. The digital-fabrication move is to design the joint into the file so parts self-locate and self-align - a slotted rib that only fits one way is worth more than a page of assembly instructions.

Assembly is also where robotics increasingly enters the field. A six-axis robot arm with the right end-effector can place, glue, weld, nail or stack components with a reach and repeatability no other machine offers - stacking bricks to a computed pattern, assembling timber frames, weaving fibre. That is the whole subject of Modules 6 and 7. For now, the point is that real projects almost never sit in one family: a typical build is laser-cut ribs (subtractive) that slot into a thermoformed skin (formative) with 3D-printed connectors (additive), all bolted or robot-assembled (joining). Fluency is knowing how the families combine, and designing the joins so the assembly is obvious, strong and forgiving.

Design the joint INTO the file. Parts that self-locate beat a page of instructions.

How to pick a family

With the families clear, choosing between them becomes a short interrogation of the job. Geometry first: is the shape essentially flat sheet, or a solid with reachable surfaces? That points to subtractive. Does it have internal cavities, lattices or undercuts no tool can reach? That points to additive. Is it a form a sheet or a cast can take? That points to formative. Then quantity: one or a few unique parts favour subtractive or additive, where the setup is the file; hundreds of identical parts favour formative, where a mould amortises across the run.

After that, weigh material (a laser loves acrylic and ply but not thick metal; a waterjet cuts almost anything; FDM is limited to thermoplastics), scale (desktop printer versus a gantry that prints a wall), tolerance and finish (milling and SLA are fine; FDM is coarser), and waste - a real design criterion in a circular-economy world, where subtractive offcuts and additive supports are both losses to minimise. There is rarely a single right answer, and the best makers combine families deliberately. The discipline is to ask these questions before modelling, because the family you choose reshapes the geometry you should draw - a part destined for a 3-axis mill must avoid undercuts, and a part destined for FDM must respect overhang angles. Choose the family first; let it inform the form.

PICK A FAMILY - GEOMETRY FIRSTWhat is the shape?flat / reachableSUBTRACTIVElaser, mill, waterjetinternal / undercutADDITIVEFDM, SLA, SLSformable / manyFORMATIVEbend, mould, castthen refine by: quantity - material - scale - tolerance - wasteThe honest answer is often a deliberate combination + joining.
Zoom
A quick way to pick a family. Ask geometry first (flat or reachable solid, unreachable internal shape, or a form a sheet or cast can take), then let quantity, material, scale, tolerance and waste refine the answer. The honest result is often a deliberate combination, not a single machine.
Processes & terms you will meet in this lesson

CNC milling / router

Subtractive - a spinning tool carves stock

Precise on wood, plastic and metal, but a 3-axis machine cannot reach undercuts or enclosed cavities. Watch cutter reach and clamping.

Kerf

The width of material a cut removes

Roughly 0.1-0.5 mm on a laser, wider on router or waterjet. Ignore it and slotted joints come out loose; compensate in the file.

FDM / FFF

Additive - molten filament laid in beads

Cheap and robust but anisotropic - weakest between layers. Orient the part for the load and mind overhang angles that need support.

SLA / SLS

Additive - cured resin / laser-fused powder

SLA gives fine detail and smooth surfaces; SLS supports the part in its own powder, enabling complex geometry with no separate supports.

Thermoforming / moulding

Formative - reshape a sheet or cast a form

Fast and near-waste-free once tooling exists, but needs a mould and fights springback, thinning and shrinkage. Rewards quantity.

Living hinge

Joining - a flexible hinge cut into one sheet

A pattern of laser-cut slots lets a rigid sheet fold. A neat example of designing the joint straight into the file.

Hands-on workshop

Workshop — sort a shelf of objects into families

The fastest way to internalise the taxonomy is to classify real things and argue the edge cases. This trains the judgement you will use every time you choose a process.

None required - objects and a notebook. A fablab visit to see a laser, a CNC and a printer side by side makes the tells vivid, but the reasoning comes first.

Given & goal
Goal: read objects into families and justify a process choice
Inputs: 5-6 varied objects and a notebook (a bottle, a bracket, a laser-cut card, a bent-metal clip, a cast handle)
Time: ~30 minutes
  1. 1Gather five or six objects made in obviously different ways. For each, decide its dominant family: was material removed, added, or reshaped? Look for the tells - kerf and offcuts, layer lines and support scars, mould seams and springback.
  2. 2For at least one object, identify the joining used - fasteners, integral slots, snap fit, adhesive, weld - and note whether the joint was designed into the geometry or added afterwards.
  3. 3Pick one object and imagine remaking it in a different family. What would have to change about its geometry? (An undercut that must vanish for milling; an overhang that needs support for FDM; draft that a mould requires.)
  4. 4For a small imagined product - say a custom bracket - write a two-line decision: which family, and why, working through geometry, quantity, material, scale, tolerance and waste in that order.
  5. 5Where a job seems to need two families, say which does what (for example, CNC the mould, then cast the parts) - the combination is usually the honest answer.

You’ll walk away with
A classified list of your objects with the family, the tells you spotted, and one worked family-choice for an imagined part - your first real process-selection reasoning, on paper.

The worked example

Three altitudes on the same idea

Read the band that fits you — or all three.

For the architectFrom design to made object

The family you choose reshapes the detail you draw. A cladding panel milled from a solid must avoid undercuts; the same panel thermoformed needs draft and a mould; printed, it can carry cavities but must respect overhang and layer strength. Knowing the families lets you rationalise ambitious geometry into something a real shop can build - and specify it without over-promising.

For the interior designerBespoke fabrication, furniture & detail

Match the piece to the process and bespoke becomes affordable. A screen or reception desk is usually subtractive (laser, CNC); a run of identical light shades is formative (one mould, many casts); an intricate one-off fitting is additive. Reading a job into a family up front tells you the cost, the finish and the joints before you commit a client to a look.

For the studentMaking skills, portfolio & jobs

Learn the three families and every machine slots into place. Instead of memorising a laser, a mill and a printer as separate mysteries, you see remove / add / reshape - and their tells: kerf and offcuts, layer lines and supports, mould seams and springback. In a portfolio review, being able to justify why you chose a family for a made object reads as real making intelligence.

Misconception check

3D printing can make anything, so it is the most capable family - the others are just older technology it will replace.

Each family has geometry it owns and geometry it simply cannot do well, and none replaces the others. Additive makes internal cavities and lattices no tool can reach, but it is slow, anisotropic (weak between layers), needs supports for overhangs, and is limited in materials and finish. Subtractive is faster and more precise on sheet and solid stock but cannot machine undercuts. Formative is unbeatable for quantity and material efficiency but demands tooling and fights springback and shrinkage. Real projects combine all three plus joining. The capable maker is not the one who prints everything; it is the one who reads a job into the right family - and most of the time that is not the printer.
Try it

Do it yourself

No machine - reason through the families.

  1. 1Name the three families and what each one does to material.
  2. 2Why can a 3-axis mill not make an undercut, and which family solves that?
  3. 3What is anisotropy in an FDM print, and how should it change how you orient a part?
  4. 4When does formative beat additive and subtractive - and what is the catch?
  5. 5Give the first two questions you would ask to choose a family for a new part.
Take this with you

The one line to carry out

You can only remove, add, or reshape material - then join the results. Read every job into a family before you model, because the family decides the speed, the waste, the geometry limits and the very shape you should draw. And the honest answer is usually a deliberate combination, not one machine.
Take it further
References & further reading

Peer-reviewed journals & authoritative standards

  1. 013D printing / additive manufacturingWikipedia, 2026.
  2. 02Milling (machining)Wikipedia, 2026.
  3. 03Laser cuttingWikipedia, 2026.
  4. 04Molding (process)Wikipedia, 2026.
  5. 05Living hingeWikipedia, 2026.
Related lessons
Recap
Subtractive removes material from stock (milling, laser, waterjet) - precise and fast, but blocked by tool reach and undercuts, and it wastes offcuts and kerf. Additive builds in layers (FDM, SLA, SLS, concrete) - unmatched for complex geometry, but slow, anisotropic and support-hungry. Formative reshapes a fixed volume (bending, thermoforming, moulding) - superb for quantity, but needs tooling and fights springback and shrinkage. Joining stitches families together and is where robotics enters. Pick the family from geometry, quantity, material, scale, tolerance and waste - before you model.
Carry forward →

Whichever family a job lands in, the machine still needs its instructions in a form it can read. Next we get concrete about that: what a machine actually needs from a file - vectors, meshes or solids; layers and colours; units and origin - and how to sanity-check it before you press go.

A

The author

Amogh N P

Architect, interior designer, and creative polymath. Studio Matrx began in his notebooks — his vision of design made honest, useful, and open to everyone. Its Academy is written and taught in his memory, and free, forever.

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