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Representing digital ink traces as points in a function space has proven useful for online recognition. Ink trace coordinates or their integral invariants are written as parametric functions and approximated by truncated orthogonal series. This representation captures the shape of the ink traces with a small number of coefficients in a form quite compact and independent of device resolution, and various geometric techniques may be employed for recognition. The simplicity and high performance of this method lead us to ask whether the same idea can be applied to another important aspect in online handwriting the compression of digital ink strokes. We have investigated Chebyshev, Legendre and Legendre-Sobolev orthogonal polynomial bases as well as Fourier series and have found that Chebyshev representation is the most suitable apparatus for compressing digital curves. We obtain compression rates of 30× to 50× and have the added benefit that the Legendre-Sobolev form, used for recognition, may be obtained by a single linear transformation.