Abstract: We introduce a new approach for defining continuous non-oriented gradient fields from discrete inputs, a fundamental stage for a variety of computer graphics applications such as surface or curve reconstruction, and image stylization. Our approach builds on a moving least square formalism that computes higher-order local approximations of non-oriented input gradients. In particular, we show that our novel isotropic linear approximation outperforms its lower-order alternative: surface or image structures are much better preserved, and instabilities are significantly reduced. Thanks to its ease of implementation (on both CPU and GPU) and small performance overhead, we believe our approach will find a widespread use in graphics applications, as demonstrated by the variety of our results.