Added refs

paper/paper.bib

@@ -1217,4 +1217,28 @@ @Article{Kirveslahti2023
   publisher     = {Springer Science and Business Media LLC},
 }
 
+@InCollection{Diaconis2013,
+  author       = {Persi Diaconis and Susan Holmes and Mehrdad Shahshahani},
+  booktitle    = {Advances in Modern Statistical Theory and Applications: A Festschrift in honor of Morris L. Eaton},
+  publisher    = {Institute of Mathematical Statistics},
+  title        = {Sampling from a Manifold},
+  year         = {2013},
+  pages        = {102--125},
+  creationdate = {2017-11-03T00:00:00},
+  doi          = {10.1214/12-imscoll1006},
+  file         = {:Diaconis2013.pdf:PDF},
+}
+
+@Book{Mardia1999,
+  author    = {Mardia, Kanti V. and Jupp, Peter E.},
+  publisher = {Wiley},
+  title     = {Directional Statistics},
+  year      = {1999},
+  isbn      = {9780470316979},
+  month     = jan,
+  doi       = {10.1002/9780470316979},
+  issn      = {1940-6347},
+  journal   = {Wiley Series in Probability and Statistics},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}

paper/paper.md

@@ -85,7 +85,11 @@ The main functionality of the `ECT` package is to be able to compute the ECT mat
 
 ## Extension to higher dimensional embedding
 
-**TODO: If we're going to have 3D stuff implemented, we need the version for that descibed.**
+In theory, the ECT can be defined for a space embedded in $\R^d$ for any $d$. 
+In practice, for applications geared toward encoding shapes seen in the physical world, this is largely limited to the cases $d=2$ or $d=3$. 
+Still, issues arise in applications in the case of $d=3$ where the choice for discretizing the directions chosen on the sphere $\mathbb{S}^2$ is not canonical like the case of $d=2$ and the circle $\mathbb{S}^1$ [@Mardia1999]. 
+
+
 
 ## Extension to higher dimensional cells