  We propose a novel meshless method 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.
