发布时间: 2018-12-16 摘要点击次数: 全文下载次数: DOI: 10.11834/jig.180250 2018 | Volume 23 | Number 12 计算机图形学

 收稿日期: 2018-04-17; 修回日期: 2018-07-16 基金项目: 国家自然科学基金项目（61672473，61379080） 第一作者简介: 刘姝玉, 1992年生, 女, 中北大学大数据学院计算机技术专业硕士研究生, 主要研究方向为计算机仿真、虚拟现实技术。E-mail:yulsilence@foxmail.com;贾彩琴, 女, 博士, 主要研究方向为计算机仿真、虚拟现实技术。E-mail:514061118@qq.com. 中图法分类号: TP391.7 文献标识码: A 文章编号: 1006-8961(2018)12-1901-09

# 关键词

3维重组; 网格拼接; 网格融合; 三次B样条; 曲线曲面

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
Supported by: National Natural Science Foundation of China(61672473, 61379080)

# 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.

# Key words

3D restruction; mesh splicing; mesh merging; cubic B-spline; curve and surface

# 1.2 3维模型的选取

3维网格模型以其很好的灵活性成为当前主流的3维离散数字模型的代表。在过去，大部分关于网格拼接的研究为了达到平滑处理拼接结果的目标，其工作都集中于源和目标网格的详细信息中；而现在，随着计算机存储设备的不断发展，可以兼顾网格模型的存储简便与低冗余度，这就使得三角网格模型更易获取和操作。

# 1.3 三次B样条曲线曲面插值

 $\begin{array}{l} {N_{0, 3}}\left( t \right) = \frac{1}{6}( - {t^3} + 3{t^2} - 3t + 1)\\ {N_{1, 3}}\left( t \right) = \frac{1}{6}(3{t^3} - 6{t^2} + 4)\\ {N_{2, 3}}\left( t \right) = \frac{1}{6}( - 3{t^3} + 3{t^2} + 3t + 1)\\ {N_{3, 3}}\left( t \right) = \frac{1}{6}{t^3} \end{array}$ (2)

 $\begin{array}{l} \;\;\;\;\;\;\;\;\;\;\;\;{p_{i, 3}}\left( t \right) = \sum\limits_{k = 0}^3 {{P_{i + k}}{N_{k, 3}}\left( t \right)} = \\ {P_i} \cdot {N_{0, 3}}\left( t \right) + {P_{i + 1}} \cdot {N_{1, 3}}\left( t \right) + {P_{i + 2}} \cdot {N_{2, 3}}\left( t \right) + \\ \;\;\;\;\;\;\;\;\;\;{P_{i + 3}} \cdot {N_{3, 3}}\left( t \right), i = 0, 1, 2, \cdots, m \end{array}$ (3)

 $\begin{array}{l} p\left( {u, v} \right) = \sum\limits_{i = 0}^m {\sum\limits_{j = 0}^n {{P_{i, j}}{N_{i, m}}\left( u \right){N_{j, n}}\left( v \right)} } \\ \;\;\;\;\;\;\;\;\left( {u, v} \right) \in \left[{0, 1} \right] \times \left[{0, 1} \right] \end{array}$ (4)

# 2.2 区域选择

2) B样条曲线插值。对边界点集$\mathit{\boldsymbol{V}}_{11}$$\mathit{\boldsymbol{V}}_{12}利用1.3节中的方法插值三次均匀B样条曲线，便在模型A上形成两条三次均匀B样条曲线\mathit{\boldsymbol{S}}_{11}$$\mathit{\boldsymbol{S}}_{12}$

4) 三角网格化。本文结果是网格模型，为此，要将融合区域网格化。对在第3)步中利用交织而成的簇得到的控制点进行重采样，将之前记录的边界点集和重采样得到的点进行三角网格化，这样，两模型就可以连续地拼接成新的三角网格模型。若新生成的模型未达到预期结果，拼接区域有偏差，可重复上述步骤。否则，进行以下步骤。

5) 光顺处理。为了新生成模型的拼接区域看起来过渡自然，最后，本文采用Laplacian平滑算法对该区域进行光顺处理，使模型光滑拼接。

# 3.2 结果分析与比较

Table 1 The run time of different parameters of algorithms

 模型 源网格 源网格待拼接部分 目标网格 运行时间/s 顶点数 面片数 顶点数 面片数 顶点数 面片数 背部鳍 223 420 0.122 图 6 左侧鳍 5 000 9 992 281 528 5 000 9 996 0.132 右侧鳍 285 543 0.122 图 7 钮 5 600 11 200 450 868 3 000 5 996 0.140 壶嘴 917 1 776 0.167 图 8 1 10 000 19 996 1 222 2 342 5 000 10 000 0.226 2 0.261 图 9 5 000 9 996 1 040 2 000 5 000 10 000 0.213

Table 2 The run time between methods in reference [14] and this paper

 文献[14] 本文 顶点总数 面片总数 运行时间/s 顶点总数 面片总数 运行时间/s 7 483 14 742 0.104 8 600 17 196 0.153 6 430 12 494 0.209 15 000 29 996 0.243 7 483 14 742 0.104 10 000 19 988 0.125

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