Cosmatesque Geodesics

Year: 2024 Authors: Steve Pomerantz

Core claim

Clairaut’s relation enables a simple algorithm for drawing geodesics on surfaces of revolution and using them as a basis for ornamental grids and tessellations.

Topics

geodesics, surfaces of revolution, Cosmatesque ornament, tessellation

Domains

differential geometry, surface geometry, numerical integration, Clairaut relation, ornament, pattern design, Byzantine motifs, textile-like tessellation

Methods

finite difference algorithm, Euler method, Runge-Kutta, rotational replication

Media

MATLAB, surface renderings, polygonal tilings, guilloche patterns

Source status

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