refs

paper/paper.bib

@@ -42,16 +42,6 @@ @phdthesis{gosselin2009delaunay
 school = {The University of British Columbia},
 }
 
-@inproceedings{ledoux2005efficient,
-    author = {Hugo Ledoux and Christopher Gold},
-    title = {An efficient natural neighbour interpolation algorithm for geoscientific modelling},
-    booktitle = {Developments in Spatial Data Handling},
-    year = {2005},
-    publisher = {Springer},
-    address = {Berlin, Heidelberg},
-    pages = {97--108},
-}
-
 @article{bezanson2017julia,
   title={Julia: A fresh approach to numerical computing},
   author = {Jeff Bezanson and Alan Edelman and Stefan Karpinski and Viral Shah},
@@ -100,23 +90,6 @@ @inproceedings{yan2008path
   pages={5168--5173},
 }
 
-@inproceedings{sakthivel2022solving,
-  author = {M. Sakthivel and S. Gupta and D. Karras and A. Khang and C. Dixit and B. Haralayya}, 
-  booktitle={2022 International Conference on Knowledge Engineering and Communication Systems (ICKES)}, 
-  title={Solving vehicle routing problem for intelligent systems using {D}elaunay triangulation}, 
-  year={2022},
-  pages={1--5},
-}
-
-@article{zhihai2021dynamic,
-  author={Zhihai Liu and Hanbin Liu and Zhengo Lu and Qingliang Zeng},
-  journal={IEEE Access}, 
-  title={A dynamic fusion pathfinding algorithm using {D}elaunay triangulation and improved {A}-star for mobile robots}, 
-  year={2021},
-  volume={9},
-  pages={20602--20621},
-}
-
 @misc{lairez2024exact,
     title = {{ExactPredicates.jl: Fast and exact geometrical predicates in the Euclidean plane}},
     author = {Pierre Lairez},
@@ -136,15 +109,6 @@ @article{hermann2008delaunay
 author = {Michael {Meyer-Hermann}},
 }
 
-@article{wang2009edge,
-  author={Jie Wang and Lili Ju and Xiaoqiang Wang},
-  journal={IEEE Transactions on Image Processing}, 
-  title={An edge-weighted centroidal {V}oronoi tessellation model for image segmentation}, 
-  year={2009},
-  volume={18},
-  pages={1844--1858},
-}
-
 @article{du1999centroidal,
 author = {Qiang Du and Vance Faber and Max Gunzburger},
 title = {Centroidal {V}oronoi tessellations: {A}pplications and algorithms},
@@ -154,42 +118,6 @@ @article{du1999centroidal
 year = {1999},
 }
 
-@inproceedings{pinho2006voromap,
-  author = {Roberto Pinho and Maria {de Oliveira} and Rosane Minghim and Marinho Andrade},
-  booktitle={Tenth International Conference on Information Visualisation (IV'06)}, 
-  title={Voromap: A {V}oronoi-based tool for visual exploration of multi-dimensional data}, 
-  year={2006},
-  pages={39--44},
-}
-
-@inproceedings{balzer2005voronoi,
-  author={M. Balzer and O. Deussen},
-  booktitle={IEEE Symposium on Information Visualization, 2005. INFOVIS 2005.}, 
-  title={Voronoi treemaps}, 
-  year={2005},
-  pages={49--56},
-}
-
-@article{reddy2012initialisation,
-title = {Initialisation for $k$-means clustering using {V}oronoi diagram},
-author = {Damodar Reddy and Prasanta Jana},
-year = {2012},
-volume = {4},
-pages = {395--400},
-journal = {Procedia Technology},
-}
-
-@inproceedings{schrieber1991voronoi,
-author = {Thomas Schreiber},
-editor={H. Bieri and H. Noltemeier},
-title={A {V}oronoi diagram based adaptive k-means-type clustering algorithm for multidimensional weighted data},
-booktitle={Computational Geometry-Methods, Algorithms and Applications},
-year={1991},
-publisher={Springer},
-address={Berlin, Heidelberg},
-pages={265--275},
-}
-
 @article{wang2024calibration,
     title = {Calibration of agent based models for monophasic and biphasic tumour growth using approximate {B}ayesian computation},
     author = {Xiaoyu Wang and Adrianne Jenner and Robert Salomone and David Warne and Christopher Drovandi},
@@ -198,15 +126,6 @@ @article{wang2024calibration
     volume = {88},
 }
 
-@article{osborne2017comparing,
-    title = {Comparing individual-based approaches to modelling the self-organization of multicellular tissues},
-    year = {2017},
-    journal = {PLOS Computational Biology},
-    author = {James Osborne and Alexander Fletcher and Joe {Pitt-Francis}, and Philip Maini and David Gavaghan},
-    volume = {13},
-    pages = {e1005387},
-}
-
 @incollection{shewchuk1996triangle,
 author = {Jonathan Shewchuk},
 title = {Triangle:  {E}ngineering a {2D} quality mesh generator and
@@ -328,15 +247,6 @@ @article{carr2022mean
 journal = {Journal of Physics A: Mathematical and Theoretical},
 }
 
-@article{kanugo2002efficient,
-  author = {Tapas Kanungo and David Mount and Nathan Netanyahu and Christine Piatko and Ruth Silverman and Angela Wu},
-  journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, 
-  title={An efficient $k$-means clustering algorithm: analysis and implementation}, 
-  year={2002},
-  volume={24},
-  pages={881--892},
-}
-
 @article{arlind2012computing,
 author = {Nocaj, Arlind and Brandes, Ulrik},
 title = {Computing {V}oronoi treemaps: {F}aster, simpler, and resolution-independent},
@@ -346,15 +256,6 @@ @article{arlind2012computing
 year = {2012}
 }
 
-@article{ungor2009off,
-title = {Off-centers: A new type of {S}teiner points for computing size-optimal quality-guaranteed {D}elaunay triangulations},
-journal = {Computational Geometry},
-volume = {42},
-year = {2009},
-pages = {109--118},
-author = {Alper \"Ung\"or},
-}
-
 @inproceedings{hale2009computing,
   author={Erten, Hale and Üngör, Alper},
   booktitle={2009 Sixth International Symposium on Voronoi Diagrams}, 

paper/paper.md

@@ -27,7 +27,7 @@ DelaunayTriangulation.jl is a feature-rich Julia [@bezanson2017julia] package fo
 
 # Statement of Need 
 
-Delaunay triangulations and Voronoi tessellations have applications in a myriad of fields. Delaunay triangulations have been used for point location [@mucke1999fast], solving differential equations [@cheng2013delaunay; @golias1997delaunay; @ju2006adaptive], route planning [@chen2010enhanced; @sakthivel2022solving; @zhihai2021dynamic], etc. Voronoi tessellations are typically useful when there is some notion of _influence_ associated with a point, and have been applied to problems such as geospatial interpolation [@bobach2009natural], image processing [@du2006centroidal; @du1999centroidal], and cell biology [@hermann2008delaunay; @wang2024calibration; @osborne2017comparing].
+Delaunay triangulations and Voronoi tessellations have applications in a myriad of fields. Delaunay triangulations have been used for point location [@mucke1999fast], solving differential equations [@golias1997delaunay; @ju2006adaptive], route planning [@chen2010enhanced; @jan2008path], etc. Voronoi tessellations are typically useful when there is some notion of _influence_ associated with a point, and have been applied to problems such as geospatial interpolation [@bobach2009natural], image processing [@du1999centroidal], and cell biology [@hermann2008delaunay; @wang2024calibration].
 
 Several software packages with support for computing Delaunay triangulations and Voronoi tessellations in two dimensions already exist, such as _Triangle_ [@shewchuk1996triangle], _MATLAB_ [@MATLAB], _SciPy_ [@SciPy], _CGAL_ [@CGAL], and _Gmsh_ [@GMSH]. DelaunayTriangulation.jl is the most feature-rich of these and benefits from the high-performance of Julia to efficiently support many operations. Julia's multiple dispatch [@bezanson2017julia] 
 is leveraged to allow for complete customisation in how a user wishes to represent geometric primitives such as points and domain boundaries, a useful feature for allowing users to represent primitives in a way that suits their application without needing to sacrfice performance. The [documentation](https://juliageometry.github.io/DelaunayTriangulation.jl/stable/) lists many more features, including its ability a wide range of domains, even those that are disjoint and with holes. 
@@ -110,7 +110,7 @@ labels = label.(eachcol(data))
 There are still several features that are intended to eventually be implemented, some of these being:
 
 1. Weighted triangulations and Voronoi treemaps, using the algorithms described in [@cheng2013delaunay; @arlind2012computing].
-2. Support for maximum angle constraints and generalised Steiner points, using algorithms and ideas described in [@ungor2009off; @hale2009quality; hale2009computing].
+2. Support for maximum angle constraints and generalised Steiner points, using algorithms and ideas described in [@hale2009quality; hale2009computing].
 3. Clipped Voronoi tessellations to arbitrary boundaries, possibly using the VoroCrust algorithm [@ahmed2020vorocrust].
 4. Centroidal tessellations with inhomogeneous mass densities, as described in [@du1999centroidal].
 5. Inserting curves into an existing triangulation [@gosselin2009delaunay; @zaide2014inserting].