Error analysis of reparametrization based approaches for curve offsetting

Abstract

This paper proposes an error analysis of reparametrization based approaches for planar curve offsetting. The approximation error in Hausdorff distance is computed. The error is bounded by O ( r sin 2 β ) , where r is the offset radius and β is the angle deviation of a difference vector from the normal vector. From the error bound an interesting geometric property of the approach is observed: when the original curve is offset in its convex side, the approximate offset curve always lies in the concave side of the exact offset, that is, the approximate offset is contained within the region bounded by the exact offset curve and the original curve. Our results improve the error estimation of the circle approximation approaches, as well as the computation efficiency when the methods are applied iteratively for high precision approximation.