How to Approximate Curves Using Bézier and Euler Spiral Segments

Curve flattening and arc approximation are key in graphics and computational geometry for transforming complex curves into simpler, error-bounded segments. This article examines techniques for minimizing subdivision while maintaining accuracy, focusing on invertible error metrics for cubic Bézier and Euler spiral curves. It compares traditional “cut-and-measure” approaches to analytical methods, showing how invertible formulas enable near-optimal flattening with fewer computations.