结合重心坐标的泊松网格编辑算法
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摘要
综合考虑泊松网格编辑在保细节特征方面的优势和重心坐标插值的光滑性两方面,提出基于重心坐标的泊松网格编辑算法。首先确定待变形区域网格模型的包围网格,以包围网格所确定的重心坐标生成控制网格,然后任意操纵控制网格,将对应重心坐标变化的信息映射为网格模型的梯度场变化,最后通过求解泊松方程的系数矩阵进行网格重构,得到变形后模型。通过实验验证,该算法克服了传统泊松网格变形算法难以保持变形结果光顺自然的缺陷,并有效的保留了模型变形的细节特征。
Considering the advantages of Poisson mesh editing in preserving the geometric details and the smoothness of the barycentric coordinates in the parallel operation, a Poisson mesh editing algorithm based on the barycentric coordinates is proposed. Firstly, a bounding mesh of the deformable model is constructed, and then the deformation control surface is obtained with the barycentric coordinates which is determined by the bounding mesh. Secondly, when the control surface is modified according to the desired deformation result, the information of the corresponding barycentric coordinates is transformed into the alteration of the mesh gradient field. Finally, the deformed model is reconstructed by solving the mesh matrix of the Poisson equation. The algorithm overcomes the shortcomings of the traditional Poisson mesh deformation algorithm which is difficult to keep the deformation result smooth and effectively retains the details of the deformation of the model.
Considering the advantages of Poisson mesh editing in preserving the geometric details and the smoothness of the barycentric coordinates in the parallel operation, a Poisson mesh editing algorithm based on the barycentric coordinates is proposed. Firstly, a bounding mesh of the deformable model is constructed, and then the deformation control surface is obtained with the barycentric coordinates which is determined by the bounding mesh. Secondly, when the control surface is modified according to the desired deformation result, the information of the corresponding barycentric coordinates is transformed into the alteration of the mesh gradient field. Finally, the deformed model is reconstructed by solving the mesh matrix of the Poisson equation. The algorithm overcomes the shortcomings of the traditional Poisson mesh deformation algorithm which is difficult to keep the deformation result smooth and effectively retains the details of the deformation of the model.
引文
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[2] CHEN C H, TSAI M H, LIN C I, et al. Skeleton-driven surface deformation through lattices for real-time character animation[J]. The Visual Computer, 2013, 29(4):241-251.
[3] MANSON J, LI K, SCHAEFER S. Positive Gordon-Wixom coordinates[J]. Computer- Aided Design, 2011, 43(11): 1422-1426.
[4] SUN S, CHEN B. An Algebraic Deformation Approach for Moving Grid Based on Barycentric Coordinates[C]// International Conference on Computational Intelligence & Software Engineering. Wuhan: IEEE Wuhan Branch, 2010.
[5] XIAN C H, LIN H W, GAO S M. Automatic generation of coarse bounding cages from dense meshes[C]//IEEE International Conference on Shape Modeling and Applications. Beijing: IEEE Computer Society Press, 2009.
[6] 杜正君,张慧. 体积图控制的近似刚性的网格变形[J]. 计算机辅助设计与图形学学报,2016,28(2):218-227.
[7] 张辉鑫. 基于广义重心坐标的三角网格模型变形方法研究和应用[D]. 吉林大学,2015.
[8] 张湘玉,李明,马希青.基于细分的网格模型骨架驱动变形技术[J].计算机应用, 2015,35(3):811-815.
[9] 许斌,李忠科,吕培军,等. 保持细节的网格曲面局部变形算法[J].计算机应用与软件, 2013,10(30):81-84.
[10] LIPAMN Y, LEVIN D, COHEN-OR D. Green coordinates[J]. ACM Transactions on Graphics, 2008,27(3):78-87.