The range of operations on solids supported by current geometric mod elling systems is very limited. Typically, solids represented in a modeller can be transformed by rigid motions and combined by Boolean operations. This paper introduces another family of transformations, called solid offsetting, which map solids into solids.Offset solids are expanded or contracted versions of an original object. Offsetting operations are potentially useful for tolerance analysis, clearance testing, design-rule checking in VLSI, modelling of etching and coating pro cesses, cutter path generation for numerically-controlled machine tools, col lision free path planning for robot motions, and for constant-radius rounding and filleting ("blending") of solids.This paper discusses mathematical properties of solid offsetting, asso ciated representations and algorithms, support of offsetting operations in solid modellers, and applications. Results of an experimental implementa tion are presented.

We present a simple method for compressing very large and regularly sampled scalar fields. Our method is particularlyattractive when the entire data set does not fit in memory and when the sampling rate is high relative to thefeature size of the scalar field in all dimensions. Although we report results for and data sets, the proposedapproach may be applied to higher dimensions. The method is based on the new Lorenzo predictor, introducedhere, which estimates the value of the scalar field at each sample from the values at processed neighbors. The predictedvalues are exact when the n‐dimensional scalar field is an implicit polynomial of degree n− 1. Surprisingly,when the residuals (differences between the actual and predicted values) are encoded using arithmetic coding,the proposed method often outperforms wavelet compression in anL∞sense. The proposed approach may beused both for lossy and lossless compression and is well suited for out‐of‐core compression and decompression,because a trivial implementation, which sweeps through the data set reading it once, requires maintaining only asmall buffer in core memory, whose size barely exceeds a single (n−1)‐dimensional slice of the data. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Compression, scalar fields,out‐of‐core.

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