Geometry · Coq
Circle-Polygon Overlap
The exact overlap area between a circle and any polygon, found by sweeping a signed area along the boundary. Includes a Coq proof of the square-and-circle case.
Art · Maths · Code
I make things where art, maths and programming overlap: interactive simulations, formal proofs, drawings and animation.
Experience
Technical Lead, 3D / VR studio · Nottingham · 2013–2026
I built the real-time 3D and VR layer of industrial digital twins: Unity front ends driven by live process simulation, used to train plant operators for clients including BP, Halliburton, High View Power and Centrica.
I joined as a mathematics graduate working on 2D operator training simulators, moved into the 3D studio as it was set up and became its technical lead.
I managed the Wind Farm training product and did most of its development. On Equipment Explorer I wrote the core system the product is built on, along with its exploded views, virtual handles and label placement. Across the whole portfolio I maintained and debugged every product, which meant keeping a working knowledge of each codebase.
tscsimulation.com
Selected work
Geometry · Coq
The exact overlap area between a circle and any polygon, found by sweeping a signed area along the boundary. Includes a Coq proof of the square-and-circle case.
Maths · JavaScript
Visualising pairing functions, which map pairs of numbers to single numbers.
Maths · Coq
A series of proofs and investigations, many machine-checked in Coq: Kadane's algorithm, Zeckendorf's theorem, Taylor polynomials and more.
Art · Digital
A creature design taken from head studies through to colour variations.
Art · Digital
Digital painting.
Art · Ink
Ink on paper, from a Drink and Draw session in 2023.
About
I'm Nathan. I like art, maths and programming, and most of what I make is some combination of the three.
That tends to mean small interactive things that make an idea visible: a simulation you can poke at, a geometric construction you can drag around, a proof worked through carefully enough for a computer to check it. Alongside that I draw, on paper and digitally.