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三次B样条插值的网格拼接和融合

刘姝玉,韩燮,贾彩琴(中北大学大数据学院, 太原 030051)

摘 要
目的 网格模型的拼接和融合是3维模型编辑的一个重要方面。为了提高3维模型之间拼接曲面的精度和效率,提出一种基于三次均匀B样条曲线曲面的网格融合方法。方法 首先,利用协变分析和数据驱动方法在目标模型上选定融合区域、确定要融合模型的大小及方向;其次,根据选定的3维网格模型,确定待拼接区域的边界,识别并记录边界点集,利用三次B样条插值边界点集;然后,对边界曲线进行双三次B样条曲面插值得到拼接区域连续曲面,并以此作为两模型拼接时的过渡面;最后,对拼接区域重采样,并对其三角化,以实现网格模型的无缝光滑拼接和融合。结果 为了验证本文方法对3维模型拼接的有效性,选取4组不同的模型,分别对其使用本文提出的融合拼接方法进行实验,对前两组模型的拼接效果进行了对比试验,实验结果表明,本文方法可以达到很好的拼接效果,对于融合区域以外的部分能够保持源模型的细节特征,拼接部分的过渡区域光顺平滑,拼接后的模型完整性佳。在运行时间相差0.05 s内,与数据驱动的建模方法相比,本文方法可以处理的节点数至少多2 000个,面片数至少多5 000个。结论 本文方法能够适用于具有任何边界的模型,在选取模型时,对于模型的形状、大小、拓扑结构等的要求较低,适用于新模型的快速建造,因此,该算法可应用于医学、商业广告、动画娱乐以及几何建模和制造等较为广阔的应用领域。
关键词
Cubic B-spline-interpolation-based mesh splicing and fusion

Liu Shuyu,Han Xie,Jia Caiqin(School of Data Science and Technology, North University of China, Taiyuan 030051, China)

Abstract
Objective 3D reconstruction has attracted considerable attention in the editing operation of 3D models. Various applications, such as 3D model registration, classification and retrieval, segmentation, reconstruction and modeling, guiding model editing, and automatic model synthesis, can benefit from 3D reconstruction. Mesh model is a mainstream 3D model. The editing and transforming of existing 3D models are an important method used to improve the model and to rapidly acquire new models. The technology of mesh mosaic fusion is a commonly used method in acquiring a new model. The fusion and splicing of the mesh can also be called the technology of mesh reconstruction. Graphs and images have widely appeared in daily life with the development of the society. The rapid and easy acquisition of new image models, the rapid reconstruction of existing models, and other issues play a dominant role in the field of graphic processing with the development of corresponding hardware technologies. Spline interpolation is an interpolation method that is commonly used in the industry to obtain a smooth curve. B-spline interpolation is a widely applied method. B-spline interpolation possesses powerful functions in representing and designing curves and surfaces, and is a mainstream method used in mathematical shape description. Therefore, in this study, we utilize the advantage of B-spline interpolation in dealing with boundary curves and surfaces and apply it to the mesh model splicing and interpolate model boundary to achieve the high integrity of grid models with various boundary conditions. In addition, the splicing transition can be sufficient to achieve the high integrity of the new model. The existing 3D model splicing fusion methods, which pursue several certain splicing results, may cause problems, such as large calculation amount, low splicing precision, and program redundancy. To improve the visual appearance of a synthetic model in terms of its continuity and flexibility, the splicing result at the joint is smoothened and the precision and efficiency of the spliced surface between the 3D models are improved. In this study, a mesh fusion method based on three uniform B-spline curves and surfaces is proposed. Method First, the region of interest is selected on the source model, the fusion region is selected on the target model by using the co-variation analysis and data-driven method, and the size and direction of the model to be merged are determined. Second, on the basis of the selected 3D mesh model, the boundary and adjacent curve of the area to be spliced between the source model and target model are determined, respectively. The points of the boundary and adjacent curve are also identified and recorded. In the set, a cubic B-spline is used to interpolate the boundary point and adjacent curve point sets of the source and target models. Subsequently, four cubic B-spline interpolation curves are obtained. Third, the boundary surface curve is interpolated by bi-cubic B-spline surfaces to obtain the continuous surface of the stitched area, which is used as the transition surface when the two models are spliced. Finally, the spliced area is resampled and triangulated by using a Laplacian smoothing algorithm to smooth the spliced regions to achieve seamless smooth splicing and fusion of mesh models. Results To verify the effectiveness of proposed method for the 3D model splicing, four different models were selected for the experiments, and the splicing result of the first two models were selected for comparison. The proposed fusion splicing method was used on the selected models. The experimental results showed that the proposed method can achieve remarkable results. The splicing effect can maintain the detailed features of the other parts of the source model, the spliced model shows good integrity, and a good result of smooth processing of the transition region of the spliced portion can be obtained. Compared with the data-driven modeling method, the proposed method can process at least 2 000 nodes and 5 000 patches within 0.05 s. Conclusion The proposed B-spline curve interpolation model is suitable with any boundary conditions and does not require to deal with the boundary of the model. Thus, considerable attention can be paid on the splicing of the model. The splicing area is resampled using the control points that generate and mesh the cubic B-spline surface. This method can improve the efficiency and reduce the computational complexity. Meanwhile, the proposed method can obtain the smooth splicing area. The shape, size, and topology requirements are low in selecting models. Therefore, the algorithm can be applied to medicine, commercial advertising, animation and entertainment, teaching models, geometric modeling, and manufacturing. This algorithm has a good effect on grid fusion and can be used for the rapid construction of new models.
Keywords
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