In this paper, data hiding on 3D meshes is investigated based on dither modulation. We present two algorithms to embed the data imperceptibly into polygonal meshes by modulating the distance from the mesh surface to mesh centroid and the one from a vertex to the centroid of its traversed neighbors, respectively. In these two algorithms, the embedded data are invariant to rotation, uniformly scaling and translation, as well as slight distortion of the cover mesh to a certain degree. On the other hand, if the cover mesh is maliciously modified, the embedded data will be changed accordingly so that the proposed algorithms can be utilized for authentication applications. Further, to improve the security of using dither modulation, a component is added into the modulation to make the quantization step statistically undetectable. The two algorithms are compared in terms of complexity, capacity and security, and their common characteristics are discussed as well. Experimental results Show their efficacies. Copyright - World Automation Congress (WAC) 2006.