Computer Science ›› 2024, Vol. 51 ›› Issue (1): 207-214.doi: 10.11896/jsjkx.230700116

• Computer Graphics & Multimedia • Previous Articles     Next Articles

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).

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

CLC Number: 

  • TP391
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