trim

paper/paper.bib

@@ -70,18 +70,6 @@ @article{ju2006adaptive
 year = {2006},
 }
 
-@inproceedings{chen2010enhanced,
-author = {Jun Chen and Chaomin Luo and Mohan Krishnan and Mark Paulik and Yipeng Tang},
-title = {An enhanced dynamic {D}elaunay triangulation-based path planning algorithm for autonomous mobile robot navigation},
-volume = {7539},
-booktitle = {Intelligent Robots and Computer Vision XXVII: Algorithms and Techniques},
-editor = {David P. Casasent and Ernest L. Hall and Juha R{\"o}ning},
-organization = {International Society for Optics and Photonics},
-publisher = {SPIE},
-year = {2010},
-url = {https://doi.org/10.1117/12.838966}
-}
-
 @misc{lairez2024exact,
     title = {{ExactPredicates.jl: Fast and exact geometrical predicates in the Euclidean plane}},
     author = {Pierre Lairez},

paper/paper.md

@@ -27,12 +27,12 @@ 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 [@golias1997delaunay; @ju2006adaptive], route planning [@chen2010enhanced; @yan2008path], 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].
+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], path planning [@yan2008path], 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 to represent a wide range of domains, even those that are disjoint and with holes. 
 
-DelaunayTriangulation.jl has already seen use in several areas. DelaunayTriangulation.jl was used for mesh generation in @vandenheuvel2023computational and is used for the `tricontourf`, `triplot`, and `voronoiplot` routines inside Makie.jl [@danisch2021makie]. The packages [FiniteVolumeMethod.jl](https://github.com/SciML/FiniteVolumeMethod.jl) [@vandenheuvel2024finite] and [NaturalNeighbours.jl](https://github.com/DanielVandH/NaturalNeighbours.jl) [@vandenheuvel2024natural] are also built directly on top of DelaunayTriangulation.jl. The design of boundaries in DelaunayTriangulation.jl has been motivated especially for the efficient representation of boundary conditions along different parts of a boundary for solving differential equations, and this is heavily utilised by FiniteVolumeMethod.jl.  
+DelaunayTriangulation.jl has already seen use in several areas. DelaunayTriangulation.jl was used for mesh generation in @vandenheuvel2023computational and is used for the `tricontourf`, `triplot`, and `voronoiplot` routines inside Makie.jl [@danisch2021makie]. The packages [FiniteVolumeMethod.jl](https://github.com/SciML/FiniteVolumeMethod.jl) [@vandenheuvel2024finite] and [NaturalNeighbours.jl](https://github.com/DanielVandH/NaturalNeighbours.jl) [@vandenheuvel2024natural] are also built directly on top of DelaunayTriangulation.jl. 
 
 # Examples
 
@@ -49,7 +49,7 @@ T(x, y) & = & 0 & (x, y) = (x_s, y_s), \\
 $$
 Here, $T(x, y)$ denotes the mean exit time of a particle exiting $\Omega$ with diffusivity $D$ starting at $(x, y)$ [@redner2001guide; @carr2022mean], $\hat{\boldsymbol n}(x, y)$ is the unit normal vector field on $\Gamma_r$, $(x_s, y_s) = (0, 0)$, and the domain $\Omega$ with boundary $\partial\Omega = \Gamma_a \cup \Gamma_r$ is shown in \autoref{fig:1}(a). This setup defines a mean exit time where the particle can only exit through $\Gamma_a$ or through the sink $(x_s, y_s)$, and it gets reflected off of $\Gamma_r$.
 
-The code to generate a mesh of the domain is given below. We use curves to define the boundary so that curve-bounded refinement can be applied [@gosselin2009delaunay]. The resulting mesh is shown in \autoref{fig:1}, together with a solution of the mean exit time problem with $D = 6.25 \times 10^{-4}$; FiniteVolumeMethod.jl [@vandenheuvel2024finite] is used to solve this problem, and the code for this can be found [here](https://github.com/JuliaGeometry/DelaunayTriangulation.jl/blob/paper/paper/paper.jl).
+The code to generate a mesh of the domain is given below. We use curves to define the boundary so that curve-bounded refinement can be applied using the algorithm of @gosselin2009delaunay. The resulting mesh is shown in \autoref{fig:1}, together with a solution of the mean exit time problem with $D = 6.25 \times 10^{-4}$; FiniteVolumeMethod.jl [@vandenheuvel2024finite] is used to solve this problem, and the code for this can be found [here](https://github.com/JuliaGeometry/DelaunayTriangulation.jl/blob/paper/paper/paper.jl).
 
 ```julia
 # The outer circle
@@ -99,6 +99,6 @@ label = p -> get_nearest_neighbour(cvor, p)
 labels = label.(eachcol(data))
 ```
 
-![Example of $k$-means clustering. The polygons are the clusters, and each point is coloured according to which cluster it belongs to, computed using `get_nearest_neighbour`.\label{fig:2}](figure2.png){width=50%}
+![Example of $k$-means clustering. The polygons are the clusters, and each point is coloured according to which cluster it belongs to, computed using `get_nearest_neighbour`.\label{fig:2}](figure2.png){width=60%}
 
 # References