With the increase of three-dimensional (3D) printing applications in many areas of life, a large amount of 3D printing data is copied, shared, and used several times without any permission from the original providers. Therefore, copyright protection and ownership identification for 3D printing data in communications or commercial transactions are practical issues. This paper presents a novel watermarking algorithm for 3D printing models based on embedding watermark data into the feature points of a 3D printing model. Feature points are determined and computed by the 3D slicing process along the Z axis of a 3D printing model. The watermark data is embedded into a feature point of a 3D printing model by changing the vector length of the feature point in OXY space based on the reference length. The x and y coordinates of the feature point will be then changed according to the changed vector length that has been embedded with a watermark. Experimental results verified that the proposed algorithm is invisible and robust to geometric attacks, such as rotation, scaling, and translation. The proposed algorithm provides a better method than the conventional works, and the accuracy of the proposed algorithm is much higher than previous methods.
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