Mathematics, Computation and Geometry of Data

Volume 3 (2023)

Number 2

Blood vessel quadrilateral mesh generation

Pages: 101 – 129

DOI: https://dx.doi.org/10.4310/MCGD.2023.v3.n2.a2

Authors

Zhou Zhao (Stony Brook University, New York, USA)

Siyu Fang (Stony Brook University, New York, USA)

Na Lei (Dalian University of Technology, China)

Yuanpeng Liu (Stony Brook University, New York, USA)

Yiming Zhu (Dalian University of Technology, China)

Chander Sadasivan (Stony Brook University Hospital, New York, USA)

Apostolos Tassiopoulos (Stony Brook University Hospital, New York, USA)

Shikui Chen (Stony Brook University, New York, USA)

Xianfeng Gu (Stony Brook University, New York, USA)

Abstract

Structured mesh generation has fundamental importance, but controlling the qualities of structured meshes remains a challenge. This work proposes a rigorous and practical algorithm to generate quadrilateral meshes on topological poly-annuli with the least number of singularities. It is shown that each quad-mesh with 4$k$ vertex degree induces a holomorphic differential. All the holomorphic differentials form a finite-dimensional linear space. A geometric distortion energy is proposed to measure the local area distortion. One can achieve quad-meshes as uniformly as possible by optimizing the distortion energy in the linear space. Experimental results show the proposed algorithm is able to improve the uniformity of the quad-meshes, and the method has the potential to be generalized to handle quad-meshes with other constraints.

Received 21 May 2023

Published 15 July 2024