Abstract: We describe a simple mechanism for bounding the portion of the plane lying between a quadratic Bézier curve segment and its offset curve at distance d. Instead of comprising one or more partial bounding polygons, our representation consists of only a single approximate offset curve segment, also in quadratic Bézier form. Evaluated on a corpus of real-world curves, this technique avoids 68-99% of antialias-distance queries and 41-96% of brushparameter queries. A proof of correctness is provided.