中文摘要：

3维模型的数字水印是数字水印研究的热点之一，鲁棒性、嵌入可读性水印和盲检测是3维模型数字水印的难点所在。从增强3维模型数字水印的鲁棒性出发，提出一种基于局部几何空间的3维模型数字水印算法，它以模型三角网格顶点在其一环邻居顶点为所确定的局部几何空间；通过改变顶点在局部几何空间中的位置来嵌入水印，并以调整其间的夹角来嵌入水印序列的索引，而调整顶点与圆心的距离来嵌入较高比特的二进制数值。本文算法在水印检测时，无需原始模型，且可抵抗平移、旋转、均匀缩放、顶点乱序、剪切及网格简化等攻击。实验结果表明，该水印算法具有很好的鲁棒性、可读水印的不可感知性和盲水印检测的优势。

英文摘要：

Watermarking a 3D mode is one of the hot topics in digital watermark. The.most difficulties of the watermarking model 3D models are mainly on maintaining robustness, embedding readable watermark and blind detecting watermarks. In order to enhance the robustness, this paper proposed a local geometric space based watermarking algorithm for the triangular meshes of 3D models. It is defined as a local geometric space by selected vertex and close neighboring vertices of the triangular meshes in the 3D model, Then the watermarks are embedded through adjusting the position of the selected vertex within their related spaces. The parameter of the central angle is rectified for embedding an index of a series of watermark; The distance between vertex and the central point is rectified for embedding high bit of binary numerical value. The experimental results show that the algorithm guarantees the high performance of the watermark robustness such as translation, rotation, scaling, vertex permutation, model cropping and model simplification with this approach, embedded watermarks can be detected without the original model. And the results also present an evident superiority in non sentience of embedding readable watermark.