Geodesic Boards

The Mathematics

A geodesic is the straightest possible path across a surface, the route a taut string would take. Carved as families into these boards, they make curvature tangible: where the surface curves positively, nearby geodesics are pulled together, and where it curves negatively they spread apart. The physical grooves also let you feel the extrinsic behavior directly — a geodesic has zero acceleration within the surface, so as you run a finger down a groove neither side drags or pushes you off course; you simply track straight ahead.

Technique

A collaborative project. I wrote software that takes a surface in ℝ³ and initializes a parallel family of geodesics along one edge — parallel-translating a given tangent vector across that edge — then solves the geodesic equation to trace each curve across the surface. It exports a description of the surface together with sequences of positions and surface normals along every curve. This feeds into Edmund Harriss’ custom CNC software, which converts it into tool paths and mills the result out of a block of wood.