hr-studioGeometry & Structure · 00
A computational design primer · Geometry & Structure · Overture

The computer never sees the shape.

It sees a representation — a photograph, a grid of pixels, a cloud of points, a mesh, a field, a graph, a toolpath, a vector. Nothing is ever "the geometry." Everything the rest of this chapter does — distance fields, meshes, subdivision, panelization — is an operation on a chosen encoding. Before the deep dives, the map: which lens to pick, what each one costs, and how real workflows chain them together.

Scroll to begin
Now encoded asthe idea
i.
Computers never see objects. They see representations.

Reality and Representation

Here is the shape as an idea — a whole thing you grasp instantly. A computer can't hold that. To store it, we must measure it, and the moment we do, the shape becomes a region of space with the meaning stripped off. Flip between the idea and its measurable shadow: the machine only ever gets the shadow.

Everything else in this chapter happens on the right-hand side of this toggle. The object itself stays out of reach.

the idea
ii.
Different representations answer different questions. There is no universal best.

Choosing the Right Lens

A representation isn't good or bad in the abstract — it's good at a question. Ask "what does it look like?" and a photograph is perfect and a mesh is useless; ask "how do I manufacture it?" and the mesh wins and the photo is worthless. Pick a question and watch the shape snap into the lens that makes it cheap to answer.

The real skill isn't knowing the encodings. It's knowing which question you're actually asking.

slide through the questions →
iii.
Every representation has a cost. Better is never free.

The Price of Representation

A finer lens always costs something — usually memory, sometimes speed, sometimes both. Sample the shape to a grid and you buy accuracy by the cell: double the resolution and the memory quadruples while the error only creeps down. Starve it and thin features fall through the gaps entirely; loss is not gentle.

Drag the resolution and watch the two costs pull against each other. Every computational designer eventually meets this wall.

accuracy costs memory
iv.
Workflows are chains of representation changes. Every algorithm eats one representation and produces another.

Translation Between Worlds

Almost nothing interesting happens inside a single representation. Real pipelines are translations: a photo becomes points, points become a mesh, a mesh becomes a toolpath, a toolpath becomes a physical object. Each arrow is an algorithm — photogrammetry, surface reconstruction, slicing — and each consumes one encoding and emits another.

Play the pipeline. Switch between a scan-to-print chain and a sketch-to-simulation chain, and watch the shape change worlds.

a workflow is a chain of conversions
v.

The Representation Machine

Draw your own shape — or pick one — and it becomes the thing in the middle. Then click any of the nine lenses around it to convert your shape into that encoding; the panel tells you what it keeps, what it loses, what it's good for, and what can come next. Chain conversions and read the pipeline you built along the bottom — click any step to rewind to it. Flip to 3D and orbit a real, lit model of the point cloud, mesh, voxels and distance field. Poke at it — this is the whole overture, as a toy.

Draw a shape, or pick one — then click a lens
Digital geometry is not one thing you store — it's a choice you keep making. Pick the lens for the question, pay its price on purpose, and remember that every algorithm in this chapter is really a translation from one representation to the next. Same shape. Different worlds.