Voronoi tessellations (#47)

Author: DanielVandH

.gitignore

@@ -16,3 +16,4 @@ docs/src/triangulations/waste.jl
 docs/animation.jl
 test/animation.jl
 test/tassy.txt
+lloyd_animation.mp4

Project.toml

@@ -1,7 +1,7 @@
 name = "DelaunayTriangulation"
 uuid = "927a84f5-c5f4-47a5-9785-b46e178433df"
 authors = ["Daniel VandenHeuvel <[email protected]>"]
-version = "0.5.2"
+version = "0.6.0"
 
 [deps]
 DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"

README.md

@@ -18,6 +18,8 @@ This is a package for constructing Delaunay triangulations of planar point sets.
 - [Fully customisable interface](https://danielvandh.github.io/DelaunayTriangulation.jl/dev/interface/interface/) for defining geometric primitives.
 - [Simple iteration over mesh elements, including points, edges, or triangles](https://danielvandh.github.io/DelaunayTriangulation.jl/dev/data_structures/triangulation/).
 - Computation of [statistics](https://danielvandh.github.io/DelaunayTriangulation.jl/dev/data_structures/statistics/) over individual triangular elements and over a complete triangulation.
+- [Computation of Voronoi tessellations](https://danielvandh.github.io/DelaunayTriangulation.jl/dev/tessellations/voronoi.md), including [clipping of polygons to the convex hull]((https://danielvandh.github.io/DelaunayTriangulation.jl/dev/tessellations/clipped.md)). I hope to get this working for constrained triangulations, but it's difficult.
+- Computation of [centroidal Voronoi tessellations](https://danielvandh.github.io/DelaunayTriangulation.jl/dev/tessellations/lloyd.md) using Lloyd's algorithm.
 
 Much of the work in this package is derived from the book *Delaunay Mesh Generation* by Cheng, Dey, and Shewchuk (2013). 
 
@@ -27,5 +29,4 @@ Just as a nice demonstration of the incremental behaviour of the algorithms in t
 
 https://user-images.githubusercontent.com/95613936/232210266-615e08bd-d4f2-4a40-849e-e832778a4b71.mp4
 
-
-
+Here is also a nice animation showing the computation of a centroidal Voronoi tessellation.

docs/make.jl

@@ -24,14 +24,21 @@ makedocs(;
             "Plotting" => "triangulations/plotting.md",
             "Convex Polygons" => "triangulations/convex.md"
         ],
+        "Voronoi Tessellations" => [
+            "Voronoi Tessellations" => "tessellations/voronoi.md",
+            "Clipped Voronoi Tessellations" => "tessellations/clipped.md",
+            "Centroidal Voronoi Tessellation" => "tessellations/lloyd.md",
+            "Plotting" => "tessellations/plotting.md"
+        ],
         "Boundary Handling" => "boundary_handling.md",
         "Data Structures" => [
             "Adjacent" => "data_structures/adjacent.md",
             "Adjacent2Vertex" => "data_structures/adjacent2vertex.md",
             "Graph" => "data_structures/graph.md",
             "Convex Hull" => "data_structures/convex_hull.md",
             "Triangulation" => "data_structures/triangulation.md",
-            "Statistics" => "data_structures/statistics.md"
+            "Statistics" => "data_structures/statistics.md",
+            "Voronoi Tessellation" => "data_structures/voronoi.md"
         ],
         "Operations" => "operations.md",
         "Other Features" => [

docs/src/data_structures/statistics.md

@@ -77,6 +77,7 @@ Delaunay Triangulation Statistics.
 All the relevant docstrings for working with these structs are below.
 
 ```@docs 
+get_all_stat
 num_vertices(::TriangulationStatistics)
 num_solid_vertices(::TriangulationStatistics)
 num_ghost_vertices(::TriangulationStatistics)

docs/src/data_structures/voronoi.md

@@ -0,0 +1,104 @@
+```@meta
+CurrentModule = DelaunayTriangulation
+```
+
+# Voronoi Tessellation 
+
+The data structure for a Voronoi tessellation is reasonably simple. The data structure here is probably not as exhaustive as it could be, but it is sufficient.
+
+```@docs 
+VoronoiTessellation 
+```
+
+Each field has its own accessor:
+
+```@docs 
+get_triangulation(::VoronoiTessellation) 
+get_generators(::VoronoiTessellation) 
+get_polygon_points(::VoronoiTessellation)
+get_polygons(::VoronoiTessellation) 
+get_circumcenter_to_triangle(::VoronoiTessellation)
+get_triangle_to_circumcenter(::VoronoiTessellation) 
+get_unbounded_polygons(::VoronoiTessellation) 
+get_cocircular_circumcenters(::VoronoiTessellation) 
+get_adjacent(::VoronoiTessellation) 
+get_boundary_polygons(::VoronoiTessellation) 
+```
+
+There are several useful methods available for working with this data structure. We list some of these below; for functions that actually construct the tessellation, see the dedicated tessellation section in the sidebar.
+
+## Type queries 
+
+```@docs 
+edge_type(::VoronoiTessellation{Tr,P,I,T,S,E}) where {Tr,P,I,T,S,E}
+number_type(::VoronoiTessellation{Tr,P}) where {Tr,P}
+integer_type(::VoronoiTessellation{Tr,P,I}) where {Tr,P,I}
+triangle_type(::VoronoiTessellation{Tr,P,I,T}) where {Tr,P,I,T}
+```
+
+## Getters 
+
+```@docs 
+get_generator(::VoronoiTessellation, ::Any)
+get_polygon_point(::VoronoiTessellation, ::Any)
+get_polygon(::VoronoiTessellation, ::Any)
+get_circumcenter_to_triangle(::VoronoiTessellation, ::Any)
+get_triangle_to_circumcenter(::VoronoiTessellation, ::Any)
+get_polygon_coordinates 
+get_neighbouring_boundary_edges 
+```
+
+## Nums 
+
+```@docs 
+num_polygons 
+num_polygon_vertices 
+num_generators 
+``` 
+
+## Adders 
+
+```@docs
+add_polygon! 
+push_polygon_point! 
+add_unbounded_polygon! 
+delete_unbounded_polygon! 
+add_boundary_polygon! 
+```
+
+## Iterators 
+
+```@docs 
+each_generator 
+each_polygon_vertex 
+each_unbounded_polygon 
+each_polygon 
+each_polygon_index 
+```
+
+## Adjacent 
+
+```@docs 
+get_adjacent(::VoronoiTessellation, ::Any)
+add_adjacent!(::VoronoiTessellation, ::Any, ::Any)
+delete_adjacent!(::VoronoiTessellation, ::Any, ::Any)
+delete_polygon_adjacent!
+add_polygon_adjacent!
+```
+
+## Features 
+
+```@docs 
+polygon_features(::VoronoiTessellation, ::Any)
+get_area
+get_centroid 
+polygon_bounds(::VoronoiTessellation, ::Any)
+jump_and_march(::VoronoiTessellation, ::Any)
+```
+
+## Utilities 
+
+```@docs 
+get_surrounding_polygon(::VoronoiTessellation, ::Any)
+convert_to_boundary_edge(::VoronoiTessellation, :Any)
+```

docs/src/index.md

@@ -6,7 +6,9 @@ CurrentModule = DelaunayTriangulation
 
 Documentation for [DelaunayTriangulation](https://github.com/DanielVandH/DelaunayTriangulation.jl).
 
-This is a package for computing Delaunay triangulations of planar point sets. We support both unconstrained and constrained Delaunay triangulations, as well as mesh refinement with Rupper's algorithm. An interface for computing  constrained Delaunay triangulations with Gmsh is also available if needed; see the Gmsh discussion in the sidebar. Unconstrained Delaunay triangulations are computed with the Bowyer-Watson algorithm, and constrained Delaunay triangulations are computed with the incremental algorithm given by [https://doi.org/10.1016/j.comgeo.2015.04.006](https://doi.org/10.1016/j.comgeo.2015.04.006).
+This is a package for computing Delaunay triangulations of planar point sets. We support both unconstrained and constrained Delaunay triangulations, as well as mesh refinement with Rupper's algorithm. We also support Voronoi tessellations, clipped Voronoi tessellations, and central Voronoi tessellations; for these latter two cases, the triangulation is treated as constrained with the convex hull edges, but we do not support general boundary constraints for tessellations - if you do know about this, get in touch!
+
+An interface for computing  constrained Delaunay triangulations with Gmsh is also available if needed; see the Gmsh discussion in the sidebar. Unconstrained Delaunay triangulations are computed with the Bowyer-Watson algorithm, and constrained Delaunay triangulations are computed with the incremental algorithm given by [https://doi.org/10.1016/j.comgeo.2015.04.006](https://doi.org/10.1016/j.comgeo.2015.04.006).
 
 To ensure that the triangulations are robust to degeneracies, we use ExactPredicates.jl for all geometrical predicates. The results from these predicates are handled through a Certificate module, as outlined in the predicates section in the sidebar.
 

docs/src/interface/edges.md

@@ -19,6 +19,7 @@ terminal
 ```@docs 
 edge_indices 
 reverse_edge
+compare_unoriented_edge
 ```
 
 ## Collection of Edges 

docs/src/interface/figs/interface_example.png

@@ -33,12 +33,14 @@ num_points
 number_type 
 push_point!
 pop_point!
+set_point!
 ```
 
 ### Generic Methods 
 
 ```@docs 
 get_point 
 points_are_unique 
-lexicographic_order 
+lexicographic_order
+mean_points 
 ```