By Autodesk Technologist for ICM/SWMMWhen Hyperbolic Geometry Meets Urban Drainage: Making Beautiful Subcatchments
](https://www.linkedin.com/in/robertdickinson/)
Helping across the full stormwater spectrum: SWMM (50+ yrs), InfoSWMM/ESRI (20 yrs), InfoWorks ICM (15 yrs), & Autodesk AEC Collection (5 yrs) Grandpa (10 yrs)
December 15, 2025
I've been exploring an unusual intersection: hyperbolic geometry and hydrological modeling. The result is a web-based tool that generates subcatchment tessellations for EPA SWMM5 using Möbius transformations on the Poincaré disc. It looks visually interesting, the exported work as test models in SWMM5 and it is a way to models that tens of thousands of subcatchments easily.
How Does This Even Work?
🔹 Three geometric modes — Elliptic (rotational), Parabolic (translational), and Hyperbolic (stretching) — each producing unique drainage patterns
🔹 Real-time visualization with area-based color gradients
🔹 One-click export to SWMM5 INP format with properly calculated slopes, widths, and rainfall timeseries
🔹 100% browser-based — no installation required
Background
The math behind this goes back to Henri Poincaré's work on non-Euclidean geometry. Each tessellation type corresponds to a different isometry of hyperbolic space, creating drainage networks that are both mathematically elegant and topologically consistent.
Whether you're a hydrologist looking for creative subcatchment layouts, a mathematician curious about applied geometry, or an engineer who appreciates when infrastructure meets art — this tool offers something new.
Try it. Watch the patterns evolve. Export a model. And maybe see stormwater a little differently.
The App Name
https://poincar-swmm-5-subcatchment--robertdickinson.replit.app
All Open Source
Source code is in all apps unless i forget.
Useful for test models