Tolerance, and what it deletes

The algorithm does not know what matters

Every simplification algorithm works by comparing vertices to a threshold — a tolerance distance. Any vertex closer to the simplified line than that distance is removed; anything farther stays. The geometry gets smaller. The files get lighter. The rendering gets faster. And something, always something, gets deleted.

The problem is that the algorithm measures geometric significance, which is a poor proxy for cartographic significance. A tiny jog in a coastline that falls inside the tolerance disappears. But that jog might be the harbour mouth, the estuary throat, the headland that gives the bay its name. The algorithm has no way to know. It is measuring millimetres, not meaning.

This is the central tension in simplification: the features that make a place recognisable are often small relative to the features that establish the shape. A river's meanders, a city's peninsula, an island's defining notch — each is geometrically minor and cartographically essential. Apply a loose enough tolerance and you erase precisely the things that let a reader orient.

Tolerance is not one number for all situations

The choice of tolerance is inseparable from the scale at which the simplified geometry will be displayed. A threshold of fifty metres is catastrophic at 1:10 000, where it is five millimetres on the sheet, and conservative at 1:50 000, where the same fifty metres is only about a millimetre. The practical rule is to set the tolerance at roughly the visual resolution of the target scale — the minimum distance a reader's eye can resolve on the output. Below that distance, detail is invisible anyway; above it, you are deleting things the map should show.

But that rule applies to a single target scale. Serving one dataset across a zoom pyramid means each zoom level needs its own simplified version. A tolerance tuned for a regional overview will collapse coastal inlets and ox-bow lakes entirely; those features must survive in the version served at the larger scale. Applying one universal tolerance — often done because it is simpler to maintain — guarantees that either the coarse levels carry unnecessary complexity or the detailed levels have already lost features they need.

Plate 2

Every drawn grid is an agreement about where things sit — on tracing paper as much as on a screen.

Photo: Ksenia Chernaya / Pexels

There is a subtler issue, too: different geometry types tolerate the same threshold differently. A long, gently curving shoreline loses relatively little character when vertices are thinned; a complex, indented fjord coast loses a great deal. Equal tolerance applied to both geometries produces unequal results. The smooth coast looks fine. The fjord coast looks like it was drawn with a crayon.

What survives, and what you must protect

The Ramer–Douglas–Peucker algorithm — the one most tools use by default — is a recursive divide-and-conquer method. It keeps the endpoints of a line, finds the vertex farthest from the straight segment between them, retains it if it exceeds the tolerance, and repeats on each sub-segment. This tends to preserve large deviations and discard small ones, which sounds correct until you notice that a critical feature can be small in the global geometry and large in local meaning.

The practical answer is constraint. Many workflows allow certain vertices or segments to be marked as protected — not subject to removal regardless of tolerance. Harbour entrances, island peaks, named capes, administrative boundary intersections: wherever a point carries a name or a function, it earns protection. This requires editorial judgment that no algorithm supplies automatically. Someone has to decide which geometry is load-bearing.

That judgment is also what separates a simplified map from a generalised one. Simplification is a mechanical operation on coordinates. Generalisation is a cartographic decision about what a map at a given scale should communicate. The tolerance is a parameter; the map is an argument. Setting the parameter without making the argument produces geometry that is technically smaller and cartographically poorer — lines that bend less, coastlines that breathe less, places that begin to look like somewhere else.

The algorithm removes what is geometrically minor. The cartographer's job is to notice, before the threshold runs, which minor things cannot be spared.