MESHGRID is a novel, compact, multi-scalable and animation-friendly 3D object representation method, which is part of MPEG-4, and which resides in the Animation Framework Extensions (AFX) toolset. The paper introduces the novel concept of local error control for arbitrary mesh encoding. In this sense, the paper proposes a new wavelet-based L-infinity-constrained coding technique for MESHGRID models, generating a fully scalable L-infinity-oriented bit-stream. The advantages of scalable L-infinity-oriented coding over L2 coding are experimentally demonstrated.