We generalize the local-feature size definition of adaptive sampling used in surface reconstruction to relate it to an alternative metric on Euclidean space. In the new metric, adaptive samples become uniform samples, making it simpler both to give adaptive sampling versions of homological inference results and to prove topological guarantees using the theory of critical points to distance functions.

@inproceedings{cavanna16adaptive,
	Author = {Nicholas J. Cavanna and Donald R. Sheehy},
	Booktitle = {Proceedings of the Canadian Conference on Computational Geometry},
	Title = {Adaptive Metrics for Adaptive Samples},
  Pages = {128--132},
	Year = {2016}}