CodeParade’s Non-Euclidean Engine

Archive notice: This article was originally published on 6 July 2020. It has been translated into English and lightly edited for clarity while preserving its historical context.

Parallel lines never meet, the shortest route between two points is straight, and a triangle’s angles total 180 degrees. Those rules become less dependable outside Euclidean geometry. Developer CodeParade built a non-Euclidean game engine whose spaces contradict familiar geometric expectations.

The MIT-licensed open-source project created its illusion with a technique related to the portals in Valve’s Portal, but used more portals and hid their transitions. Each portal surface displayed a texture rendered from the perspective of a virtual camera.

The result produces spaces that appear larger, differently connected or otherwise incompatible with ordinary layouts. It is the sort of geometry that makes an IKEA floor plan look reassuringly conventional.

Hyperbolica: a non-Euclidean adventure

CodeParade later tackled the problem in Unity without relying on portals. An early trailer introduced Hyperbolica, with a Steam release and publication of source code planned at the time.

Explaining non-Euclidean geometry

A further video explored the underlying geometry. Developers examining the archived engine should test camera transitions, collision and spatial logic carefully before adapting the technique to production.