Spherical Density-Equalizing Map

• Spherical density-equalizing map (SDEM): Compute a spherical density-equalizing map of a genus-0 closed surface using the method in [1].

• Landmark-aligned spherical density-equalizing map (LSDEM): Compute a landmark-aligned spherical density-equalizing map of a genus-0 closed surface using the method in [1].

Any comments and suggestions are welcome.

If you use this code in your work, please cite the following paper:

[1] Z. Lyu, L. M. Lui, and G. P. T. Choi, "Spherical Density-Equalizing Map for Genus-0 Closed Surfaces." Preprint, arXiv:2401.11795, 2024.

Copyright (c) 2024, Zhiyuan Lyu, Lok Ming Lui, Gary P. T. Choi

https://github.com/garyptchoi/spherical-density-equalizing-map

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Usage:

• map = SDEM(v,f,population,S,dt,epsilon,max_iter)
• map = LSDEM(v,f,population,S,landmark,target,alpha,beta,gamma,dt,epsilon,max_iter)

Input:

• v: nv x 3 vertex coordinates of a genus-0 triangle mesh
• f: nf x 3 triangulations of a genus-0 triangle mesh
• population: nf x 1 positive quantity
• S: nv x 3 vertex coordinates of the initial spherical conformal parameterization
• dt: step size
• epsilon: stopping parameter
• max_iter: maximum number of iterations
• landmark: k x 1 vertex indices of the landmarks
• target: k x 3 target positions of the landmarks on the unit sphere
• alpha: nonnegative weighting parameter for the density-equalizing term
• beta: nonnegative weighting parameter for the harmonic term
• gamma: nonnegative weighting parameter for the landmark mismatch term

Output:

• map: nv x 3 vertex coordinates of the spherical parameterization