Th the recorded watermark to authenticate the physical aspect.Appl. Sci. 2021, 11, x FOR PEER REVIEW3 ofAppl. Sci. 2021, 11,in the geometric model. When the target is usually a physical part, we illuminate the object by using three of 15 light rays to uncover the watermark. Then, the revealed watermark is compared with the recorded watermark to authenticate the physical aspect. The rest of this article is organized as follows. Section two describes the embedding and detecting procedures. The test results are offered in Section three. Discussion and evaluation of the rest of this short article is organized as follows. Section 2 describes the embedding and this investigation are presented in Section 4. Comparisons with others’ techniques and future detecting procedures. The test results are offered in Section three. Discussion and evaluation of this work are also included in Section 4. This short article ends using a conclusion in Section 5. study are presented in Section four. Comparisons with others’ methods and future function are also integrated in Section 4. This short article ends using a conclusion in Section five. two. Components and Methods2. Supplies and Procedures proposed watermarking process is illustrated in Figure 1. It The flowchart from the includesflowchart with the proposed watermarkingtransformation, region-of-interest creaThe the measures of voxelization, distance field procedure is illustrated in Figure 1. It tion, watermark embedding, and G-codefield transformation, region-of-interest creation, incorporates the methods of voxelization, distance generation. Information of these computations are presented within this section. In addition to generation. Particulars of those computations are presented watermark embedding, and G-code the encoding process, we also design many verification procedures for digital and physical contents. These algorithms are also formulated in in this section. Besides the encoding process, we also design and style several verification procedures this section. for digital and physical contents. These algorithms are also formulated in this section.Figure 1. Flowchart in the watermarking strategy. Figure 1. Flowchart of the watermarking strategy.2.1. voxelization and Distance Field Computation two.1. Voxelization and Distance Field Computation Inside the proposed watermarking technique, the input model is presumed to become contained in Inside the proposed watermarking system, the input model is expressed to be contained a Tiaprofenic acid web volumetric space, composed of voxels. In case that the model is presumed in a standard in a volumetric space, composed of voxels. In case that thetriggered to decomposea tradipolygonal representation, a voxelization computation [18] is model is expressed in it into tional To achieve this aim, we enclose the model by using an [18] is triggered to decomvoxels. polygonal representation, a voxelization computation axis-aligned bounding box pose it Then, the AABB is divided purpose, we enclose the model by utilizing the following (AABB).into voxels. To achieve this into voxels by using a typical grid. Atan axis-aligned bounding box (AABB). Then, the two sorts: model voxels and using a common grid. At step, the voxels are classified intoAABB is divided into voxels byvoid voxels. A voxel will be the following step, voxel if it would be the interior of two kinds: model voxels and void voxels. regarded as a model the voxelsis in classified into the model or intersected with all the model’s A voxel is regarded as model voxel as a void voxel. Just after the model or intersected the boundaries. Otherwise,ait is regarded if it can be in the interior.