In this paper, we introduce a new formalism for mesh geometry prediction. We derive a class of smooth linear predictors from a simple approach based on the Taylor expansion of the mesh geometry function. We use this method as a generic way to compute weights for various linear predictors used for mesh compression and compare them with those of existing methods. We show that our scheme is actually equivalent to the Modified Butterfly subdivision scheme used for wavelet mesh compression. We also build new efficient predictors that can be used for connectivity-driven compression in place of other schemes like Average/Dual Parallelogram Prediction and High Degree Polygon Prediction. The new predictors use the same neighbourhood, but do not make any assumption on mesh anisotropy. In the case of Average Parallelogram Prediction, our new weights improve compression rates from 3% to 18% on our test meshes. For Dual Parallelogram Prediction, our weights are equivalent to those of the previous Freelence approach, that outperforms traditional schemes by 16% on average. Our method effectively shows that these weights are optimal for the class of smooth meshes. Modifying existing schemes to make use of our method is free because only the prediction weights have to be modified in the code.