Velho, LuizGomes, Jonas2015-02-162015-02-1620001467-8659https://doi.org/10.1111/1467-8659.00457In this paper we introduce variable resolution 4-k meshes, a powerful structure for the representation of geometric objects at multiple levels of detail. It combines most properties of other related descriptions with several advantages, such as more flexibility and greater expressive power. The main unique feature of the 4-k mesh structure lies in its variable resolution capability, which is crucial for adaptive computation. We also give an overview of the different methods for constructing the 4-k mesh representation, as well as the basic algorithms necessary to incorporate it in modeling and graphics applications.10.1111/1467-8659.00457195-212