Software comparison (#191)

Author: DanielVandH

README.md

@@ -144,3 +144,34 @@ This is not the only Delaunay triangulation package available. Some others are:
 - [GMT.jl](https://github.com/GenericMappingTools/GMT.jl): A wrapper of [GMT](https://github.com/GenericMappingTools/gmt), allowing for [unconstrained Delaunay triangulations in two dimensions](https://www.generic-mapping-tools.org/GMTjl_doc/documentation/modules/triangulate/index.html#triangulate), and for [spherical triangulation, i.e. triangulation of points lying on a sphere](https://www.generic-mapping-tools.org/GMTjl_doc/documentation/modules/sphtriangulate/index.html#sphtriangulate).
 - [Quickhull.jl](https://github.com/augustt198/Quickhull.jl): A pure Julia library for unconstrained triangulations, Voronoi tessellations, and convex hulls in $N$ dimensions.
 
+In addition to these Julia packages, software packages in other programming languages are available, such as:
+
+- [Triangle](https://www.cs.cmu.edu/~quake/triangle.html): A C library for generating (constrained) Delaunay triangulations, Voronoi tessellations, and refined meshes. Also supports weighted triangulations. As mentioned above, there is a Julia interface to this library through TriangleMesh.jl, Triangulate.jl, or Triangle.jl. 
+- [CGAL](https://www.cgal.org/): A C++ library which, among many other features relevant in computational geometry, supports Delaunay triangulations, spherical triangulations, periodic triangulations, constrained triangulations, 3D Delaunay triangulations, Voronoi tessellations, mesh refinement, surface triangulations, and more.
+- [Gmsh](https://gmsh.info/): Gmsh is a finite element mesh generator with many features, providing constrained Delaunay triangulations (or, in addition to triangles, elements can also be mixed with e.g. squares) and mesh refinement with many options. Provides a set of meshing algorithms to choose from. Supports both 2D and 3D meshing. In addition to simple segments, you can also provide curves for boundaries and surfaces in the 3D case. Has interfaces in several languages, including [Gmsh.jl](https://github.com/JuliaFEM/Gmsh.jl).
+- [SciPy](https://docs.scipy.org/doc/scipy/tutorial/spatial.html): A Python library providing Delaunay triangulations, Voronoi tessellations, and convex hulls in $\mathbb R^N$. Does not support constrained triangulations or mesh refinement.
+- [MATLAB](https://uk.mathworks.com/help/matlab/computational-geometry.html?s_tid=CRUX_lftnav): MATLAB has built-in functions for Delaunay triangulations and Voronoi tessellations in two and three dimensions. Additionally, it supports constrained triangulations and mesh refinement.
+- [Qhull](http://www.qhull.org/): A C library for computing Delaunay triangulations, Voronoi tessellations, and convex hulls in $\mathbb R^N$. No support is provided for constrained triangulations or mesh refinement, but it does provide furthest-site Delaunay triangulations and furthest-site Voronoi tessellations. The packages MiniQhull.jl and DirectQhull.jl wrap Qhull for use in Julia.
+- [Delaunator](https://github.com/mapbox/delaunator): A JavaScript library that provides support for fast construction of two-dimensional unconstrained Delaunay triangulations.
+- [Spade](https://github.com/Stoeoef/spade): A Rust library providing support for Delaunay triangulations and constrained Delaunay triangulations, mesh refinement, and Voronoi tessellations in the plane. 
+- [Acute](https://www.cise.ufl.edu/~ungor/aCute/index.html): A C library that builds on top of Shewchuk's Triangle library, being the first of its kind to not only allow for minimum angle constraints in mesh refinement, but also for maximum angle constraints.
+- [Tinfour](https://github.com/gwlucastrig/Tinfour): A Java library for Delaunay triangulations and constrained Delaunay triangulations in the plane, with a lot of features for interpolation.
+- [JTS](https://github.com/locationtech/jts): A Java library which, among many other features for working with vectory geometries, supports Delaunay triangulations, constrained Delaunay triangulations, mesh refinement (at least to make a conformal triangulation), and Voronoi tessellations.
+- [Voro++](https://math.lbl.gov/voro++/): A C++ library for constructing Voronoi tessellations, power diagrams, and clipped tessellations. 
+- [Stellar](https://people.eecs.berkeley.edu/~jrs/stellar/): A C library for constructing three-dimensional Delaunay triangulations, providing the ability to efficiently refine the mesh.
+
+Compared to all these other libraries, and only in the context of planar triangulations, DelaunayTriangulation.jl is one of the most developed in terms of the features provided, except possibly with the exception of CGAL and Gmsh who provide many features although neither are in the public domain (CGAL being GPL v3+ and Gmsh being GPL v2+), unlike DelaunayTriangulation.jl which is MIT licensed. A tabular comparison of all these packages is given below (focusing only on two dimensional meshing). If there are any errors in this comparison, please let me know. Also please note that the features listed are not intended to be exhaustive, but rather to give a general idea of the capabilities of each package, and certainly not all software packages are listed here. 
+
+<!--
+<div style="font-size: 14px; background-color: white;">
+<table><thead><tr><th></th><th></th><th></th><th colspan="10">Delaunay Triangulations</th><th colspan="5">Voronoi</th><th></th><th></th><th></th></tr></thead><tbody><tr><td>Package</td><td>Language</td><td>Open Source License</td><td>Unconstrained</td><td>Constrained</td><td>Weighted</td><td>Refinement<br></td><td>Curve-Bounded</td><td>Dynamic Updates</td><td>Convex Polygons</td><td>Periodic</td><td>Spherical</td><td>Furthest-site</td><td>Standard</td><td>Clipped (Rect. or Hull)</td><td>Generic Clipped</td><td>Centroidal</td><td>Power</td><td>Point Location</td><td>Robust Predicates</td><td>Customisable Interface</td></tr><tr><td>DelaunayTriangulation.jl</td><td>Julia</td><td>✅ (MIT)</td><td>✅</td><td>✅</td><td>✅</td><td>✅</td><td>✅</td><td>✅</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>✅</td><td>✅</td><td>✅</td><td>✅</td><td>✅</td><td>✅</td><td>✅</td></tr>
+<tr><td>VoronoiDelaunay.jl</td><td>Julia</td><td>✅ (MIT)</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>✅</td><td>❌</td></tr><tr><td>VoronoiCells.jl</td><td>Julia</td><td>✅ (MIT)</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr><tr><td>Delaunay.jl</td><td>Julia</td><td>✅ (MIT)</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr><tr><td>MiniQhull.jl</td><td>Julia</td><td>✅ (MIT)</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr>
+<tr><td>DirectQhull.jl</td><td>Julia</td><td>✅ (MIT)</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr><tr><td>Delaunator.jl</td><td>Julia</td><td>✅ (MIT)</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr><tr><td>TriangleMesh.jl</td><td>Julia</td><td>✅ (MIT)</td><td>✅</td><td>✅</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr><tr><td>Triangulate.jl</td><td>Julia</td><td>✅ (MIT)</td><td>✅</td><td>✅</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr>
+<tr><td>Triangle.jl</td><td>Julia</td><td>✅ (MIT)</td><td>✅</td><td>✅</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr><tr><td>GMT.jl</td><td>Julia</td><td>✅ (MIT)</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr><tr><td>Quickhull.jl</td><td>Julia</td><td>✅ (MIT)</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr><tr><td>Triangle</td><td>C</td><td>❌ (Non-standard)</td><td>✅</td><td>✅</td><td>✅</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>✅</td><td>❌</td></tr>
+<tr><td>CGAL</td><td>C++</td><td>❌ (GPL v3+)</td><td>✅</td><td>✅</td><td>✅</td><td>✅</td><td>❌</td><td>✅</td><td>❌</td><td>✅</td><td>✅</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>✅</td><td>✅</td><td>❌</td></tr><tr><td>Gmsh</td><td>Own/C++</td><td>❌ (GPL v2+)</td><td>✅</td><td>✅</td><td>❌</td><td>✅</td><td>✅</td><td>❌</td><td>❌</td><td>✅</td><td>✅</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr><tr><td>SciPy</td><td>Python</td><td>✅ (BSD 3-Clause)</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr><tr><td>MATLAB</td><td>MATLAB</td><td>❌ (Commercial)</td><td>✅</td><td>✅</td><td>❌</td><td>✅</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>✅</td><td>❌</td></tr>
+<tr><td>Qhull</td><td>C</td><td>✅ (Permissive)</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr><tr><td>Delaunator</td><td>JavaScript</td><td>✅ (ISC)</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr><tr><td>Spade</td><td>Rust</td><td>✅ (MIT/Apache 2.0)</td><td>✅</td><td>✅</td><td>❌</td><td>✅</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr><tr><td>Acute</td><td>C</td><td>❌ (Non-standard)</td><td>✅</td><td>✅</td><td>✅</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>✅</td><td>❌</td></tr>
+<tr><td>Tinfour</td><td>Java</td><td>✅ (Apache 2.0)</td><td>✅</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>✅</td><td>❌</td></tr><tr><td>JTS</td><td>Java</td><td>✅ (EPL 2.0/EDL 1.0)</td><td>✅</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>❌</td><td>✅</td><td>❌</td></tr></tbody></table>
+</div>
+-->
+
+![Comparison](softwarecomparison.png)