In geometric and topological reconstruction of compact length spaces embedded in some metric space, one needs an appropriate notion of distortion of the embedding. We consider variants of the classical notion of distortion, by controlling the coarseness of the distance scale of the ambient space and the discreteness of the coarse paths used to generate the length structure. In addition to discussing the stability and convergence of these notions of distortion, we compare them with existing notions of sampling parameters used in shape reconstruction and show some applications of our approach. This is based on joint work with Rafal Komendarczyk and Sushovan Majhi.