Progressive Curve Representation Based on Reverse Subdivision

A progressive curve representation based on reverse subdivision is introduced. Multiresolution structures for common subdivision rules that have both banded reconstruction and decomposition filters are produced. Multiresolution filters are usually applied to the whole curve uniformly, while progressive curves are based on collapse and split operations that can be applied locally on any portion of a curve. In this work, firstly, small width multiresolution filters are constructed based on the reverse of the cubic B-spline subdivision. The collapse and split operations are replaced by a local decomposition and reconstruction process. Second, an efficient algorithm and data structures are presented to allow for the resulting progressive curve. Third, both a user-controlled and an automatic method to select a portion of the curve for reconstruction or decomposition are described. The technique introduced has various applications such as view-dependent rendering, flexible editing and progressive transmission.