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In this paper, two novel methods suitable for blind 3D mesh object watermarking applications are proposed. The first method is robust against 3D rotation, translation, and uniform scaling. The second one is robust against both geometric and mesh simplification attacks. A pseudorandom watermarking signal is cast in the 3D mesh object by deforming its vertices geometrically, without altering the vertex topology. Prior to watermark embedding and detection, the object is rotated and translated so that its center of mass and its principal component coincide with the origin and the z-axis of the Cartesian coordinate system. This geometrical transformation ensures watermark robustness to translation and rotation. Robustness to uniform scaling is achieved by restricting the vertex deformations to occur only along the r coordinate of the corresponding (r, θ, φ) spherical coordinate system. In the first method, a set of vertices that correspond to specific angles θ is used for watermark embedding. In the second method, the samples of the watermark sequence are embedded in a set of vertices that correspond to a range of angles in the θ domain in order to achieve robustness against mesh simplifications. Experimental results indicate the ability of the proposed method to deal with the aforementioned attacks.