@Article{JCM-41-5,
author = {Wu, Tianqi and Yau, Shing-Tung},
title = {Computing Harmonic Maps and Conformal Maps on Point Clouds},
journal = {Journal of Computational Mathematics},
year = {2023},
volume = {41},
number = {5},
pages = {879--908},
abstract = {<p style="text-align: justify;">We use a narrow-band approach to compute harmonic maps and conformal maps for
surfaces embedded in the Euclidean 3-space, using point cloud data only. Given a surface,
or a point cloud approximation, we simply use the standard cubic lattice to approximate its $\epsilon$-neighborhood. Then the harmonic map of the surface can be approximated by discrete
harmonic maps on lattices. The conformal map, or the surface uniformization, is achieved
by minimizing the Dirichlet energy of the harmonic map while deforming the target surface
of constant curvature. We propose algorithms and numerical examples for closed surfaces
and topological disks. To the best of the authors’ knowledge, our approach provides the
first meshless method for computing harmonic maps and uniformizations of higher genus
surfaces.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2206-m2020-0251},
url = {https://global-sci.com/article/84147/computing-harmonic-maps-and-conformal-maps-on-point-clouds}
}