Wavelet Transform Data Compression with an Error Level Guarantee for Z-Map Models

Abstract

This paper proposes an algorithm to compress CAD models in a grid-based Z-map representation while keeping the compression artifacts within a specified value (the maximum difference allowed by the user). A wavelet transform is used for decomposing the input shape into lower and higher frequency patterns. A significant reduction in the data size can be achieved by deleting higher frequency components. We employ a tree structure called the error range (ER) tree to manage error occurrences and determine where to prune branches without increasing the resulting errors in the data compression. The widely used reversible compression method, gzip, is then used to obtain the final compressed model data output. We conducted a series of experiments with 12 sample shape models on a 512 × 512 grid. With a maximum error of 10 μm (a typical value specified for NC milling), the proposed method reduces the data by 90.9% on average and the computational cost of 19 ms is extremely low. The proposed method can be extended to larger CAD models in real applications.