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Digital watermarking for copyright protection of 3-D meshes cannot be directly applied to point clouds, since we need to derive consistent connectivity information, which might change due to attacks, such as noise addition and cropping. Schemes for point clouds operate only on the geometric data and, hence, are generic and applicable to mesh-based representations of 3-D models. For building generic copyright schemes for 3-D models, this paper presents a robust blind watermarking mechanism for 3-D point-sampled geometry. The basic idea is to find a cluster tree from clusters of 3-D points. Using the cluster tree, watermarks can be embedded and extracted by deriving an order among points at global (intracluster) and local levels (intercluster). The multiple bit watermarks are encoded/decoded inside each cluster based on an extension of the cluster structure-based 3-D quantization index modulation. The encoding mechanism makes the technique robust against uniform affine transformations (rotation, scaling, and transformation), reordering, cropping, simplification, and noise addition attacks. The technique when applied to 3-D meshes also achieves robustness against retriangulation and progressive compression techniques. Customization of the bit-encoding scheme achieves high hiding capacity with embedding rates that are equal to 4 b/point, while maintaining the imperceptibility of the watermark with low distortions. The estimated time complexity is O (n logn), where n is the number of 3-D points.