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摘 要
目的 网格模型的拼接和融合是三维模型编辑的一个重要方面。为了提高三维模型之间拼接曲面的精度和效率,本文提出了一种基于三次均匀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,根据选定的三维网格模型,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 为了验证本文提出的方法对三维模型拼接的有效性,选取四组不同的模型,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,本文提出的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秒内,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2000个,面片数至少多5000个。结论 本算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应用领域。
A cubic B-spline-interpolation-based mesh splicing and fusion

Liu Shuyu,Han Xie,Jia Caiqin(North University of China)

Objective As a research hot spot in the editing operation of 3D models, 3D reconstruction has become more and more important. A variety of applications can benefit from it such as 3D model registration, classification and retrieval, segmentation, reconstruction and modeling, guiding model editing and automatic model synthesis. Mesh model is one of the mainstream 3D models. Editing and transforming existing 3D models are not only an important method to improve the model, but also an important means to acquire new models quickly. When acquiring a new model, the most commonly used method is the technology of mesh mosaic fusion. The fusion and splicing of the mesh can also be called the technology of mesh reconstruction. With the development of society, graph and image have appeared widely in daily life. As the corresponding hardware technology develops, how to acquire new image models quickly and easily, how to reconstruct existing models quickly and other issues play a popular role in the field of graphics processing. Spline interpolation is an interpolation method which is commonly used in industry to obtain a smooth curve. And the B-spline interpolation is the one that are more widely applied. It has powerful functions in representing and designing curves and surfaces, and it is one of the mainstream methods of mathematical description of shape. Therefore, in this paper, we take advantage of it in dealing with boundary curves and surfaces, and apply it to the mesh model splicing and interpolate model boundary to achieve the goal of high integrity of grid models with various boundary conditions. Besides this, with the advantages, the splicing transition can be good enough to achieve the goal of higher integrity of the new model. As for the existing 3D model splicing fusion methods, which pursue some certain result of splicing, they may cause problems such as large calculation amount, low splicing precision, and program redundancy. In order to improve the visual appearance of the synthetic model, considering the continuity and flexibility of the appearance of the model, preventing the splicing result from not being smooth enough at the joint, and improving the precision and efficiency of the spliced surface between the 3D models, in this paper, 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, and the fusion region is selected on the target model by using the co-variation analysis and the data-driven method, and the size and direction of the model to be merged are determined. Secondly, according to the selected 3D mesh model, determine the boundary and adjacent curve of the area to be spliced between the source model and the target model, respectively, and the points of the boundary and the adjacent curve are identified and recorded. In the set, a cubic B-spline is used to interpolate the boundary point set and the adjacent curve point set of the source model and the target model. After this, four cubic B-spline interpolation curves got. Then, 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, using Laplacian smoothing algorithm to smooth the spliced regions to achieve seamless smooth splicing and fusion of mesh models. Results In order to verify the effectiveness of the method presented in this paper for the 3D model splicing, four different models were selected for experiments, and the splicing result of the first two models were selected for contrast test. The fusion splicing method proposed in this paper was used on them respectively. The experimental results show that the proposed method can achieve great results. The splicing effect can maintain the detailed features of the other parts of the source model, and the spliced model shows good integrity, and there can also get a good result of the smooth processing of the transition region of the spliced portion. Compared with the data-driven modeling method, the method in this paper can process at least 2000 nodes and 5000 patches within 0.05 seconds. Conclusion The use of the B-spline curve interpolation model boundary in this paper makes the model with any boundary conditions applicable, and does not need to deal with the boundary of the model too much. And thus, we can pay more attention on splicing of the model. The splicing area is resampled by using the control points that generate the cubic B-spline surface and mesh it. This method can not only improve the efficiency but also reduce the computational complexity. Meanwhile, it can get an effect of smooth splicing area as well. When selecting models, the requirements for the shape, size, and topology of the model are low. Therefore, the algorithm can be applied to medicine, commercial advertising, animation and entertainment, and teaching models, as well as geometric modeling and manufacturing and etc. And this algorithm has good effect on grid fusion and can be used for the rapid construction of new models.