The paper presents an a priori procedure to control the element size and shape variation for meshing algorithms governed by anisotropic sizing specifications. The field of desired element size and shape is represented by a background structure. The procedure consists in replacing the initial field with a smoothed one that preserves anisotropic features and smaller element sizes. The smoothness of the resulting field can be controlled by a prescribed threshold value γ0. Examples are included to show the application in three dimensional anisotropic adaptive simulation, as well as the effect of γ0.