Compared with non-blind algorithms, blind algorithms are more widely used because they do not need to transmit the original carrier during watermark detection. Although the robustness of blind watermarking algorithms is slightly weaker, there is still room for improvement. This paper proposes a 3D grid blind watermarking algorithm, which uses pseudo-random numbers to generate a straight line passing through the centroid of the model, selects a spherical neighborhood with the intersection of the straight line and the model as the sphere center as the embedding object, and embeds the watermark information by modulating the centroid of the vertices in the neighborhood by jitter. Because the centroid depends on the coordinates of all vertices in the spherical neighborhood, it is necessary to solve the problem of inversely estimating the coordinates of the vertices in the neighborhood from the adjusted centroid, and the corresponding algorithm is given in this paper. In addition to being immune to vertex rearrangement, the watermarking algorithm also associates each bit of watermark to multiple intersections of the straight line and the model and groups of vertices in the spherical neighborhood of multiple intersections, which can better resist shear attacks and random noise. Experimental data show the robustness of the algorithm.
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