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Mathematics > Numerical Analysis

arXiv:2205.14414 (math)
[Submitted on 28 May 2022]

Title:Theoretical Foundation of the Stretch Energy Minimization for Area-Preserving Mappings

Authors:Mei-Heng Yueh
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Abstract:The stretch energy is a fully nonlinear energy functional that has been applied to the numerical computation of area-preserving mappings. However, this approach lacks theoretical support and the analysis is complicated due to the full nonlinearity of the functional. In this paper, we provide a theoretical foundation of the stretch energy minimization for the computation of area-preserving mappings, including a neat formulation of the gradient of the functional, and the proof of the minimizers of the functional being area-preserving mappings. In addition, the geometric interpretation of the stretch energy is also provided to better understand this energy functional. Furthermore, numerical experiments are demonstrated to validate the effectiveness and accuracy of the stretch energy minimization for the computation of square-shaped area-preserving mappings of simplicial surfaces.
Subjects: Numerical Analysis (math.NA); Computational Geometry (cs.CG)
MSC classes: 15B48, 52C26, 65F05, 68U05, 65D18
Cite as: arXiv:2205.14414 [math.NA]
  (or arXiv:2205.14414v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2205.14414

Submission history

From: Mei-Heng Yueh [view email]
[v1] Sat, 28 May 2022 12:24:42 UTC (7,441 KB)
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