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This paper describes the development of a criterion for the quantization of line-drawing data. The criterion provides a guide for selecting the quantization fineness required to assure that the significant features of given line-drawing data will be preserved in the quantization process. The criterion is based on viewing a line drawing as an elastic beam under flexure and selecting a quantization grid size that is fine enough to permit the line drawing to be represented by a beam of minimum strain energy. In this model, regions of sharp curvature of the line drawing correspond to regions of high strain-energy density of the elastic beam. The smoothest possible curve that can be reconstructed from a quantized representation is the minimum-energy curve that satisfies the constraints of the quantized data.