hr-studioSearch · 02
A computational design primer · Constraints & Feasibility

The shape of what’s allowed.

A brief never gives you the whole design space. Codes cap the height, budgets floor the area, physics forbids the twist — and every such rule takes a knife to the map. What survives all the cuts is the feasible region: the actual territory a search is allowed to walk. It has a geography — coasts, straits, islands — and knowing it is half the battle.

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i.

One rule, one cut

A constraint is an inequality — height ≤ limit, area ≥ minimum — and on the map of designs it draws a boundary: allowed on one side, forbidden on the other. The design doesn’t stop existing when it crosses; it just stops being buildable. Drag yours over the line and watch the verdict flip.

Drag the design dot across the boundary.

Warm side allowed · past the line, violated
ii.

Rules intersect

Real briefs stack rules, and each one only ever shrinks what remains — the feasible region is the intersection of every cut. Stack enough of them and the map can close entirely: an overconstrained brief, where no design exists and something has to give. The area counter below never goes up.

Toggle the rules on and off; try to close the map.

Each rule can only shrink the region
iii.

Islands and straits

When rules curve, the feasible set can split into islands — pockets of valid designs with a forbidden sea between them. That geography matters enormously for search: a step-by-step improver born on one island may never discover the other, however good it is. Try walking your design from left to right without touching red.

Drag the dot; the forbidden strait blocks the way.

Two feasible islands · no legal bridge
iv.

Repair by projection

What do you do with a violating design? The gentlest answer: project it — slide it to the nearest point that obeys, changing it as little as possible. If that sounds familiar, it should: it’s exactly how the cloth solver enforced its distance constraints, applied to design instead of fabric. Drop your design anywhere illegal and let the map pull it home.

Drag anywhere; release, and it snaps to the nearest legal design.

Release to repair · smallest possible change
v.

The site test

The tower returns, and now it has to pass planning. Four live rules — a height cap, a daylight plane that trades height against taper, a minimum floor area, and a twist-comfort limit that tightens as the tower slims — carve the height × taper map in real time. The twist slider reshapes the region from off-axis, the readout names exactly which rules a violating design breaks, and Repair projects it to the nearest tower that passes. Red means rejected; get it warm.

Drag the map · watch which rules object · repair to comply
Every rule is a cut, every brief an intersection, and the survivor is the ground a search may stand on — sometimes wide, sometimes an archipelago, sometimes nothing at all. Next: onto this allowed ground, we pour a landscape of better and worse.