将移动最小二乘法用于3D 点云模型变形，提出一种基于控制曲线的3D 点云模型变形方法. 该方法根据点云数据的形状信息或变形需要设置关键点，利用三维空间三次样条插值拟合生成控制曲线，通过改变曲线两端的偏导数来改变空间曲线的形状，从而更好地拟合物体的轮廓. 基于移动最小二乘法实现3D点云模型的刚性变
形，通过轮廓拟合准确定位变形后的物体轮廓，利用控制曲线可实现多个区域的准确变形. 实验表明，该方法可使3D 点云模型产生比较平滑而真实的变形效果.
This paper proposes a deformation method of 3D point cloud model implemented by controlling curve sets. Compared with deforming a model by controlling point sets, the proposed method makes deformed 3D point cloud model shard to be distorted, and appears more realistic. A moving least squares algorithm is used, in which curves are generated with cubic spline curve fitting. As MLS algorithm is applied to the curves to ensure rigid deformation of the 3D point cloud model. The use of control curves can achieve deformation in multiple areas accurately. Experimental results show that the method can realize smooth and realistic deformation of 3D point cloud models.
[1]谭光华，许秋儿，吴双卿，张三元，张引. 特征保持的大规模点云曲面自由变形[J]. 浙江大学学报：工学版，2010, 44(1): 34-40
TAN Guanghua, XU Quer, WU Shuangqing, ZHANG Sanyuan, ZHANG Yin. Features preserved massive point cloud surfaces freeform. Journal of Zhejiang University: Engineering Science, 2010, 44(1): 34-40. (in Chinese)
[2] SEDERBERG T W, PARRY S R. Free-form deformation of solid geometric models [C]// Proceedings of the 13th Annual Conference on Computer Graphics and Interactive Techniques. New York: ACM Press, 1986, 20(4): 151-160.
[3] 金小刚，彭群生. 基于广义元球的一般约束变形 [J]. 软件学报，1998, 9(9): 677-682.
JIN Xiaogang, PENG Qunsheng. Generalized constraints deformed based on the general dollar ball [J]. Journal of Software, 1998, 9(9): 677-682. (in Chinese)
[4] KOBBELT L, CAMPAGNA S, VORSATZ J, SEIDEL H. Interactive multi-resolution modeling on arbitrary meshes [C]// Proceedings of SIGGRAPH, Orlando, Florida, 1998: 105-114
[5] YU Y, ZHOU K, XU D, SHI X, BAO H, GUO B, SHUM H. Mesh editing with Poisson-based gradient field manipulation[J]. ACM Transactions on Graphics (Proceedings of ACM SIGGRAPH), 2004, 23(3): 644-651.
[6] ALEXA M, COHEN-OR D, LEVIN D. As-rigid-as-possible shape interpolation [C]//SIGGRAPH Conference on Computer Graphics and Interactive Techniques, 2000: 157-164
[7] CUNO A, ESPERANCA C, OLIVEIRA A, CAVALVANTI R. 3D As-rigid-as-possible deformation using MLS [C]// Computer Graphics International Conference, 2007: 1-8
[8] ZHU Y, GORLER S J. 3D deformation using moving least squares[R]. Harvard Computer Science Technical report : TR-10-07, Cambridge, 2007: 1-5
[9] ZHAO Xin, LI Bo, WANG Lei, KAUFMAN Arie. Texture-guided volumetric deformation and visualization using 3D moving least square [J]. IET Comput Vis, 2012, 28: 193-204. DOI 10.1007/s00371-011-0635-2
[10]SCHAEFER S, McPhail T, WARREN J. Image deformation using moving least squares[J]. ACM Transactions on Graphics, 2006, 25 (3): 533-540.
