In this article, we build a multi-resolution framework intended to be used for the visualization of continuous piecewise linear functions defined over triangular planar or spherical meshes. In particular , the dataset can be viewed at different level of detail, that's to say as a piecewise linear function defined over any simplification of the base mesh. In his multi-resolution form, the function requires strictly the same volume of data than the original input: It is then possible to go through consecutive levels by the use of so-called detail coefficients, with exact reconstruction if desired. We also show how to choose a decimation sequence that leads to a good compromise between the resulting approximation error and the number of removed vertices. The theoretical tools used here are inspired from wavelet-based techniques and extended in the sense that they can handle non-nested approximation spaces. The reader might also refer to [2], where a similar framework is discussed for piecewise constant functions.