Multiresolution curves

Abstract

We describe a multiresolution curve representation, based on wavelets, that conveniently supports a variety of operations: smoothing a curve; editing the overall form of a curve while preserving its details; and approximating a curve within any given error tolerance for scan conversion. We present methods to support continuous levels of smoothing as well as direct manipulation of an arbitrary portion of the curve; the control points, as well as the discrete nature of the underlying hierarchical representation, can be hidden from the user. The multiresolution representation requires no extra storage beyond that of the original control points, and the algorithms using the representation are both simple and fast.