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This paper presents a robust and blind watermarking algorithm for three-dimensional (3D) meshes. The watermarking primitive is an intrinsic 3D shape descriptor: the analytic and continuous geometric volume moment. During watermark embedding, the input mesh is first normalized to a canonical and robust spatial pose by using its global volume moments. Then, the normalized mesh is decomposed into patches and the watermark is embedded through a modified scalar Costa quantization of the zero-order volume moments of some selected candidate patches. Experimental results and comparisons with the state of the art demonstrate the effectiveness of the proposed approach.