Understanding Euler Spirals and Their Parallel Curves

This article explores how Euler spirals—curves with linearly varying curvature—can outperform traditional Bézier curves in modeling and flattening parallel curves. By leveraging their clean mathematical properties and stable handling of inflection points, Euler spirals simplify stroke rendering and improve geometric precision. The piece also details an empirical approximation for subdivision density integrals, balancing computational speed and visual accuracy.