This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions with jump discontinuities or normal discontinuities across curves, and even across more involved geometries such as a 3-corner. The given data may be uniform or non-uniform, and noisy, and the approximation procedure involves non-linear least-squares minimization. Also included is a basic approximation theorem for functions with jump discontinuity across a smooth curve.

翻译：本文证明了分段光滑函数空间能够由定义在光滑均匀样条上的一组简单(非线性)运算所构成的函数空间很好地逼近。示例涵盖具有沿曲线跳跃间断或法向间断的双变量函数，甚至包括诸如三叉角等更复杂几何形状上的情形。给定数据可以是均匀或非均匀的，并可包含噪声，逼近过程涉及非线性最小二乘极小化。文中还包含一个针对沿光滑曲线具有跳跃间断函数的基本逼近定理。