2 posts tagged with "mercator"

I was debugging a polygon-overlap test that worked locally and failed on the server. Same code. Same input. Different answer.

The function deciding the answer was small. Three points A, B, C; return the sign of (B - A) cross (C - A). That sign tells you whether a vertex is convex or reflex, whether a diagonal stays inside the polygon, whether a point is above a line or below. On x86, LLVM had folded the multiply and the subtract into a single fma — one rounding step instead of two. On WASM there is no FMA, so two roundings. A vertex sitting in the epsilon neighborhood of zero fell on opposite sides. From one bit of disagreement, the whole decomposition forked.

This wasn't a bug in my code. It was IEEE 754 working as advertised. The standard pins down the storage format. It does not pin down behavior. Reassociation, FMA contraction, x87 registers at 80 bits, denormal flush flags — four separate ways to get a different answer from the same inputs. Tightening tolerances doesn't help: convex decomposition is discrete. A vertex is reflex or it isn't. An epsilon at the input is a binary difference at the output.

So I wrote exact-poly, a 2D geometry library that uses no floats at all.

A 10-vertex star decomposed into 5 convex parts. Vertex labels (v0–v9) match input order; part labels (p0.0–p5.3) are emitted by the cascade. Sum of part areas equals the ring area, exactly.

Imagine a global map simulation, a distributed land registry, or a radio frequency allocator. They all share one unbreakable rule: two people cannot own the exact same space. Polygons must not overlap.

Traditional GIS solved this decades ago. But doing it on-chain—inside a strictly consensus-driven network without external servers—has long been considered impossible. Compute limits were simply too strict.

I wrote Mercator, an open-source spatial indexing library for Sui. It lets you register polygons of any shape directly in a smart contract, mathematically guaranteeing zero overlap.

Registering a 4-vertex polygon in Mercator costs about $0.0065. Registering twenty polygons costs exactly the same. The system scales logarithmically, not linearly. To achieve this, I didn't invent anything new. I just borrowed algorithms from 1990s game engines: the Separating Axis Theorem (SAT) for collision detection, and the Morton Z-curve for indexing.

Why are these classic tools only becoming smart contract primitives now? The answer lies in data model architecture. This code simply will not run on EVM, Solana, or Aptos. Here is why.