Abstract
Previous work has made use of a parameterized plane curve polynomial representation for mathematical handwriting, with the polynomials represented in a Legendre or Legendre-Sobolev graded basis. This provides a compact geometric representation for the digital ink. Preliminary results have also been shown for Chebyshev and Chebyshev-Sobolev bases. This article explores the trade-offs between basis choice and polynomial degree to achieve accurate modeling with a low computational cost. To do this, we consider the condition number for polynomial evaluation in these bases and bound how the various inner products give norms for the variations between symbols.
Abstract (translated)
先前的工作利用了参数化平面曲线多项式表示法来描述数学手写，其中多项式用Legendre或Legendre-Sobolev分层基表示。这种方法为数字墨水提供了一种紧凑的几何表示方式。初步结果显示，Chebyshev和Chebyshev-Sobolev基底也适用。本文探讨了在选择不同基底和多项式次数之间进行权衡，以实现精确建模并降低计算成本的方法。为此，我们考虑了这些基底中多项式评估的条件数，并界定了各种内积如何给出符号间差异的范数。
URL
https://arxiv.org/abs/2509.10815
