计算机科学

计算机科学 ›› 2024, Vol. 51 ›› Issue (1): 207-214.doi: 10.11896/jsjkx.230700116

• 计算机图形学&多媒体 • 上一篇    下一篇

逼近误差有界的相容性高阶网格生成

张文祥, 郭佳鹏, 傅孝明   

  1. 中国科学技术大学数学科学学院 合肥230000
  • 收稿日期:2023-07-17 修回日期:2023-09-18 出版日期:2024-01-15 发布日期:2024-01-12
  • 通讯作者: 傅孝明(fuxm@ustc.edu.cn)
  • 作者简介:(zwx111@mail.ustc.edu.cn)
  • 基金资助:
    国家自然科学基金(62272429)

Error-bounded Compatible High-order Remeshing

ZHANG Wenxiang, GUO Jiapeng, FU Xiaoming   

  1. School of Mathematical Sciences,University of Science and Technology of China,Hefei 230000,China
  • Received:2023-07-17 Revised:2023-09-18 Online:2024-01-15 Published:2024-01-12
  • About author:ZHANG Wenxiang,born in 1997,postgraduate.His main research interests include geometric processing and computer graphics.
    FU Xiaoming,born in 1988,Ph.D,associate professor.His main research inte-rests include geometric processing and computer-aided geometric design.
  • Supported by:
    National Natural Science Foundation of China(62272429).

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摘要： 文中提出了一种构造逼近误差有界的高质量相容性高阶网格的方法。给定两个定向的、拓扑同构的三角形网格和一组稀疏的对应点,此方法包含两个步骤:(1)生成满足误差有界的相容性高阶网格;(2)在确保逼近误差总是有界的前提下,降低网格的几何复杂度,并在该过程中通过优化控制顶点来降低相容性网格之间的扭曲以及与原始网格之间的几何近似误差。第一步先生成满足误差有界的相容性线性网格,然后升阶为高阶网格。第二步通过迭代地执行基于边长的重新网格化和增加相容性目标边长场,有效地降低了网格几何复杂度。从切空间的角度,推导出了3DBézier三角形之间映射的雅可比矩阵,从而可以有效地优化扭曲能量。通过对扭曲能量和几何近似误差能量的优化,有效地降低了相容性网格之间的扭曲以及相容性网格与原始网格之间的几何近似误差。通过大量实验,证明了此方法对于构造误差有界的高质量相容性高阶网格的有效性和实用性。

关键词: 相容性网格, 高阶网格, 近似误差有界, Hausdorff距离, 高质量网格, 低网格复杂度

Abstract: This paper proposes a method to construct high-quality and compatible high-order surface meshes with bounded approximation errors.Given two closed,oriented,and topologically equivalent surfaces and a sparse set of corresponding landmarks,the proposed method contains two steps:(1)generate compatible high-order meshes with bounded approximation errors and(2)reduce mesh complexity while ensuring that approximation errors are always bounded,and reduce the distortion between the compatible meshes and approximation errors with the original meshes by optimizing the control vertices.The first step is to generate compatible linear meshes with bounded approximation errors,and then upgrade them to high-order meshes.In the second step,the mesh complexity is effectively reduced by iteratively performing an edge-based remeshing and increasing the compatible target edge lengths.The Jacobian matrix of the mapping between 3D Bézier triangles is derived from tangent space,so that the distortion energy can be effectively optimized.By optimizing the distortion energy and approximation errors energy,the distortion between compatible meshes and approximation errors are effectively reduced.Tests on various pairs of complex models demonstrate the efficacy and practicability of our method for constructing high-quality compatible high-order meshes with bounded approximation errors.

Key words: Compatible mesh, High-order mesh, Bounded approximation errors, Hausdorff distance, High-quality mesh, Low mesh complexity

中图分类号: 

  • TP391
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