Minimax curve simplification with guaranteed L∞ error

This paper proposes a curve simplification/approximation method that, for a fixed budget of primitives m, minimizes the maximum geometric error (one-sided Hausdorff or Euclidean distance to segments). The core idea is to find the minimal admissible ε (error bound) via binary search together with a fast feasibility check: can a consecutive block of points be covered by a single segment so that all points lie within an ε-wide “tube” around that segment? In addition, segments are locally adjusted so that the error within each segment is as uniform as possible, avoiding large spikes. Experiments show that, for the same segment budget, our method achieves a smaller maximum error than the Ramer–Douglas–Peucker heuristic. We also provide a clear evaluation protocol and a working Python prototype.