Wavelet-based multiresolution representation and editing of closed b-spline curves

A multiresolution curve representation, based on wavelets, provides more flexibility for curve smoothing, data compressing, and editing at different resolution levels. It requires no extra storage apart from that of the original control points. This paper presents the technique for wavelet-based multiresolution representations of C2 continuous closed cubic B-spline curves. Due to the requirement on continuity at the start/end point, closed B-spline curves need special processing when wavelets are applied to decompose or reconstruct them. The method for multiresolution editing of closed B-spline curves is also introduced. Users can edit the overall shape of a closed curve while preserving its details, or change its details without affecting its overall shape. The corresponding algorithms have been implemented and some examples are given to illustrate the editing of C2 continuous closed cubic B-spline curves at multiresolution levels.