On Beauty in Computational Geometry

Computational geometry has always felt unusually honest to me. The objects are abstract, but their failures are visible. If your assumptions are wrong, the shape on the screen folds, intersects, leaks, or explodes. There is very little room to hide behind vague language.

At the same time, geometry rewards exact thinking without becoming sterile. A proof about orientation tests or convex hull structure can feel crisp and inevitable, and then suddenly the implementation forces you to confront degeneracy, precision, and data representation.

That tension is where a lot of the beauty lives. The theorem is elegant. Reality is jagged. Good geometric software respects both.

I am especially drawn to algorithms that reveal hidden order: triangulations, nearest-neighbor structures, arrangements, medial axes. They take a cloud of points or curves and expose a skeleton that was always there waiting to be named.

Some parts of programming feel like bureaucracy. Computational geometry, even when frustrating, still feels like discovery.