Two multiresolution analyses (MRA) intended to be used in scientiic visualization, and that are both based on a non-nested set of approximating spaces, are presented. The notion of approximated r eenement is introduced to deal with non nested spaces. The rst MRA scheme, referred to as BLaC (Blending of Linear and Constant) wavelets is based on a one parameter family of wavelet bases that realizes a blend between the Haar and the linear wavelet bases. The approximated reenement is applied in the last part to build a second MRA scheme for data deened on an arbitrary planar triangular mesh.