基于最小二乘方法的拟保角网格变形

Gang XU; Li-shan DENG; Wen-bing GE; Kin-chuen HUI; Guo-zhao WANG; Yi-gang WANG

doi:10.1631/jzus.C1400103

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基于最小二乘方法的拟保角网格变形

数字娱乐、艺术与智能CAD专题 | Updated：2022-05-19

- 基于最小二乘方法的拟保角网格变形
- Quasi-angle-preserving mesh deformation using the least-squares approach
- 信息与电子工程前沿（英文） 2014年15卷第9期页码：754-763
- Affiliations：
  
  1.Department of Computer Science, Hangzhou Dianzi University, Hangzhou 310018, China
  2.Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong, China
  3.Department of Mathematics, Zhejiang University, Hangzhou 310027, China
- Author bio：
  
  [ "Gang XU, E-mail:xugangzju@gmail.com" ]
  Yi-gang WANG E-mail:yigang.wang@hdu.edu.cn
- Funds：
  
  Project supported by the National Natural Science Foundation of China (Nos.61472111, 61272300, and 51475309), the Defense Industrial Technology Development Program (No.A3920110002), the Open Project Program of the State Key Lab of CAD & CG, Zhejiang University (No.A1406), the Zhejiang Provincial Natural Science Foundation (No.Z1091077), the Direct Grant from the Chinese University of Hong Kong (No.2050492), and the Research Grants Council of the Hong Kong Special Administration Region, China (No.412913)
- DOI：10.1631/jzus.C1400103
  中图分类号： TP391
- 收稿：2014-03-21，
  
  修回：2014-;8-19，
  
  纸质出版：2014-09
- Accepted：
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基于最小二乘方法的拟保角网格变形[J]. 信息与电子工程前沿（英文）, 2014,15(9):754-763.

Gang XU, Li-shan DENG, Wen-bing GE, et al. Quasi-angle-preserving mesh deformation using the least-squares approach[J]. Frontiers of Information Technology & Electronic Engineering, 2014, 15(9): 754-763.
基于最小二乘方法的拟保角网格变形[J]. 信息与电子工程前沿（英文）, 2014,15(9):754-763. DOI： 10.1631/jzus.C1400103.

Gang XU, Li-shan DENG, Wen-bing GE, et al. Quasi-angle-preserving mesh deformation using the least-squares approach[J]. Frontiers of Information Technology & Electronic Engineering, 2014, 15(9): 754-763. DOI： 10.1631/jzus.C1400103.

摘要

研究目的

网格模型的修改与编辑方法在数字娱乐、数值计算等领域有着重要应用。如何在网格编辑过程中更好地保持模型的几何细节，是网格变形方法中富有挑战性的重要问题。本文利用网格模型蕴涵的内在几何信息，提出基于最小二乘方法的拟保角网格变形方法，在变形过程中有效保持网格模型的几何细节。

创新要点

提出一种基于内在角度信息的离散网格表示方法，具有旋转、平移和均匀缩放不变性，是三角离散网格模型的新型表示方法。基于该网格表示形式和最小二乘方法，建立了拟保持网格角度度量的网格变形框架。与基于拉普拉斯微分坐标方法相比，可有效保持网格模型的几何细节特征。

重要结论

若干三角网格模型变形与编辑实例显示，在数字娱乐领域本文算法有效。

Abstract

We propose an angle-based mesh representation

which is invariant under translation

rotation

and uniform scaling

to encode the geometric details of a triangular mesh. Angle-based mesh representation consists of angle quantities defined on the mesh

from which the mesh can be reconstructed uniquely up to translation

rotation

and uniform scaling. The reconstruction process requires solving three sparse linear systems: the first system encodes the length of edges between vertices on the mesh

the second system encodes the relationship of local frames between two adjacent vertices on the mesh

and the third system defines the position of the vertices via the edge length and the local frames. From this angle-based mesh representation

we propose a quasi-angle-preserving mesh deformation system with the least-squares approach via handle translation

rotation

and uniform scaling. Several detail-preserving mesh editing examples are presented to demonstrate the effectiveness of the proposed method.

关键词

Keywords

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