2D WAVELET TRANSFORM DATA COMPRESSION WITH ERROR LEVEL GUARANTEE FOR Z-MAP MODELS

A-DEWS 2016 - Innovation of Life in Asia - Asian Design Engineering Workshop

Year: 2016
Editor: Umeda, Y.; Nomaguchi, Y.; Koga, T.; Kishita, Y.
Author: Yokota, Keisuke; Umezu, Nobuyuki; Inui, Masatomo
Institution: Ibaraki University, Japan
Section: CAD/CAM and Computer Graphics
Page(s): 117-126

Abstract

Computer simulations are generally used to find any potential problems prior to the actual manufacturing process of workpieces. Most of the workpiece shape is in a Z-map representation, which requires a large amount of data to accurately record a high resolution model. To solve this problem, an irreversible compression algorithm for Z-map models has been proposed using one-dimensional wavelet transform with a specified maximum error. In the present study, we propose a higher performance algorithm using two-dimensional wavelet transform. The input shape data is transformed by using 2D wavelet, and the maximum errors caused by virtual pruning of highfrequency components are recorded simultaneously. We reduce the amount of shape data by truncating the diagonal components in the wavelet synopsis tree. The errors generated at a certain node are calculated by accumulating all errors recorded at the node's children and the effects of the virtually truncated diagonal components at that node. Our algorithm retains the maximum errors at nodes in the positive and negative directions because the same errors appear in the diagonal directions at the leaf nodes and the same values are accumulated in the errors recorded at the node’s children. Nodes in the wavelet tree are pruned if the absolute value of its error by the virtual truncation is within a tolerance value specified by the user, and the remaining tree nodes are compressed reversibly using gzip compression library. Our method guarantees, without the repetitive compress-decompress-compare loop, that all the differences from the original model is less than a specified limit. Experimental results confirmed that the reduction rate of 90.4% on the average in 0.020 seconds for 12 sample shape models on a 512x512 grid under a maximum tolerance of 10x10^-6 m.

Keywords: Irreversible data compression, Gzip, Haar wavelet, Z-Map, NC milling simulation, Error range tree