Is there a way to compute a triangulation of points (e.g. triangles that approximate the surface of a 2-sphere) from a pairwise distance matrix in n-dimensions?
So far, what I've found is from Building a graph from pairwise distances:
I'm aware that you can take the distance matrix and obtain (or attempt to obtain) a layout in however many dimensions you like by taking the eigenvectors (by say the power iteration) of the all pairs shortest path matrix computed by the Floyd-Warshall algorithm from that distance matrix.
These two articles should cover this well enough.
(1) Boissonnat, J. D.; Dyer, R.; Ghosh, A.; Oudot, S. Y. Only Distances Are Required to Reconstruct Submanifolds. Computational Geometry: Theory and Applications 2017, 66, 32–67. https://doi.org/10.1016/j.comgeo.2017.08.001.
(2) Connor, R.; Vadicamo, L.; Rabitti, F. High-Dimensional Simplexes for Supermetric Search. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 2017, 10609 LNCS, 96–109. https://doi.org/10.1007/978-3-319-68474-1_7.