一种基于能量函数和矢量场的点集曲面构造方法

doi:10.3901/JME.2018.05.179

机械工程学报 ›› 2018, Vol. 54 ›› Issue (5): 179-184.doi: 10.3901/JME.2018.05.179

一种基于能量函数和矢量场的点集曲面构造方法

刘宇, 侯亮, 席文明

厦门大学机电工程系厦门 361005

收稿日期:2016-12-15 修回日期:2017-11-28 出版日期:2018-03-05 发布日期:2018-03-05
通讯作者: 刘宇(通信作者),男,1977年出生,博士,副教授。主要研究方向为逆向工程、CAD/CAM、数字制造等。E-mail:mseliuyu@xmu.edu.cn
作者简介:侯亮,男,1974年出生,博士,教授。主要研究方向为复杂机电装备产品的大批量定制与创新设计、噪声与振动控制技术等。E-mail:hliang@xmu.edu.cn;席文明,男,1965年出生,博士,教授。主要研究方向为微操作与微装配、机器人、智能控制等。E-mail:wmxi@xmu.edu.cn
基金资助:
国家自然科学基金（51205332）和教育部留学回国人员科研启动基金资助项目。

Point Set Surface Reconstruction Method Based on Energy Functions and Vector Fields

LIU Yu, HOU Liang, XI Wenming

Department of Mechanical and Electrical Engineering, Xiamen University, Xiamen 361005

Received:2016-12-15 Revised:2017-11-28 Online:2018-03-05 Published:2018-03-05

摘要/Abstract

摘要： 点集曲面是直接从离散点构造的光滑曲面，在计算机图形学、计算机视觉、几何建模等领域都有应用。提出一种新的点集曲面构造方法。所构造的点集曲面被称为加权平方极值曲面。该方法采用到二次曲面的代数距离的加权平方和定义能量函数，采用一致法矢量的加权和定义矢量场。然后将加权平方极值曲面定义为能量函数沿矢量场的局部极小点的集合，并给出空间一点向加权平方极值曲面的投影过程。与传统点集曲面相比，加权平方极值曲面能在去除数据噪声的同时更好地逼近理想曲面。

关键词: 点集曲面, 能量函数, 曲面重构, 矢量场

Abstract: Point set surfaces (PSSs) are smooth surfaces defined directly from discrete points, which has been used in fields such as computer graphics, computer vision, geometric modeling, and so on. A novel method for construction of PSSs is presented. The PSSs constructed by the method are called weighted squares extremal (WSE) surface. The method constructs an energy function by weighted summing squared algebraic distances to quadric surfaces and a vector field by weighted summing consistent normal vectors. Then the WSE surface is defined as a set of local minima of the energy function along the vector field. The method also provides a process that projects a point onto the WSE surface. Compared with the traditional PSS, the WSE surface approaches ideal surfaces better and smoothes out data noises at the same time.

Key words: energy functions, point set surfaces, surface reconstruction, vector fields

中图分类号:

TP391

刘宇, 侯亮, 席文明. 一种基于能量函数和矢量场的点集曲面构造方法[J]. 机械工程学报, 2018, 54(5): 179-184.

LIU Yu, HOU Liang, XI Wenming. Point Set Surface Reconstruction Method Based on Energy Functions and Vector Fields[J]. Journal of Mechanical Engineering, 2018, 54(5): 179-184.

参考文献

[1] ZWICKER M,PAULY M,KNOLL O,et al. Pointshop 3D:An interactive system for point-based surface editing[C]//Proceedings of the 29th Annual Conference on Computer Graphics and Interactive Techniques,ACM,2002:322-329.
[2] YANG Pinghai,QIAN Xiaoping. Adaptive slicing of moving least squares surfaces:Toward direct manufacturing from point cloud data[J]. ASME Journal of Computing and Information Science in Engineering, 2008,8(3):031003-1-11.
[3] LIU Yu,XIA Songtao,QIAN Xiaoping. Direct numerical control (NC) path generation:from discrete points to continuous spline paths[J]. ASME Journal of Computing and Information Science in Engineering,2012,12(3):9-30.
[4] LEVIN D. Mesh-independent surface interpolation[C]//Geometric Modeling for Scientific Visualization,2003,Springer Berlin Heidelberg,2003:37-49.
[5] ALEXA M,BEHR J,COHEN-OR D,et al. Computing and rendering point set surfaces[J]. IEEE Transactions on Visualization and Computer Graphics,2003,9(1):3-15.
[6] AMENTA N,KIL Y. Defining point-set surfaces[J]. ACM Transactions on Graphics,2004,23(3):264-270.
[7] ALEXA M,ADAMSON A. Interpolatory point set surfaces-convexity and hermite data[J]. ACM Transactions on Graphics,2007,28(2):20:1-20.
[8] ADAMSON A,ALEXA M. Anisotropic point set surfaces[C]//Proceedings of the 4th International Conference on Computer Graphics,Virtual Reality,Visualization and Interaction in Africa,ACM,2006:7-13.
[9] ÖZTIRELI A C,GUENNEBAUD G,GROSS M. Feature preserving point set surface based on non-linear kernel regression[J]. Computer Graphics Forum,2009,28(2):493-501.
[10] GUENNEBAUD G,GROSS M. Algebraic point set surfaces[J]. ACM Transactions on Graphics,2007,26(3):23.1-23.9.
[11] LIU Yu,QIAN Xiaoping. Computing point-set surfaces with controlled spatial variation of residuals[J]. Computer-Aided Design,2011,43(8):957-970.
[12] WANG H,SCHEIDEGGER C,SILVA C. Optimal bandwidth selection for MLS surfaces[C]//Proceedings of Shape Modelling International,2008:111-120.

一种基于能量函数和矢量场的点集曲面构造方法

Point Set Surface Reconstruction Method Based on Energy Functions and Vector Fields

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