Multiresolution analysis and wavelets provide useful and efficient tools for representing functions at multiple levels of detail. We are planning to implement a multiresolution curve representation, based on wavelets. The main advantage of such a representation is that it conveniently supports a variety of operations like smoothing a curve, editing the overall sweep of a curve while preserving its character. We present methods to implement continuous levels of smoothing as well as direct manipulation of the sweep of the curve. These manipulations are done based on the control points, which are defined by the user and it is done in such a way that the underlying properties of the curve are preserved. 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.