Volumetric models of 3D objects have recently been introduced into the reverse engineering (RE) process. Grid-based methods are considered as the major technique for reconstructing surfaces from these volumetric models. This is mainly due to the efficiency and simplicity of these methods. However, these grid-based methods suffer from a number of inherent drawbacks, resulting from the fact that the imposed Cartesian grid in general is not well adapted to the surface, neither in size nor in orientation. In order to overcome the above obstacles a new iso-surface extraction method is proposed for volumetric models. The main idea is first to construct a geometrical field that is induced by the object’s shape. This geometrical field represents the natural directions and a grid cell size for each point in the domain. Then, the imposed volumetric grid is deformed by the produced geometrical field toward the object’s shape. The iso-surface meshes can be extracted from the resulting adaptive grid by any conventional grid-based contouring technique. The proposed method provides better approximation of the unknown surface and exhibits anisotropy, which is present inherently in the surface. Moreover, since the produced meshes are quad-dominant, Catmull-Clark subdivision surfaces are directly constructed from these meshes.