This paper presents a method for classifying pen strokes in an on-line sketching system. The method, based on linear least squares fitting to a conic section equation, proposes using the conic equation’s natural classification property to help classify sketch strokes and identify lines, elliptic arcs, and corners composed of two lines with an optional fillet. The hyperbola form of the conic equation is used for corner detection. The proposed method has proven to be fast, suitable for real-time classification, and capable of tolerating noisy input, including cusps and spikes. The classification is obtained in o(n) time in a single path, where n is the number of sampled points. In addition, an improved adaptive method for clustering disconnected end-points is proposed. The notion of in-context analysis is discussed, and examples from a working implementation are given.