How to plot the Voronoi diagram in MATLAB?

How to plot the Voronoi diagram in MATLAB?

voronoi (x,y,T) uses the Delaunay triangulation T to plot the Voronoi diagram. voronoi (TO) uses the delaunayTriangulation object TO to plot the Voronoi diagram. [vx,vy] = voronoi (___) returns the 2-D vertices of the Voronoi edges.

How is the Voronoi diagram used in science?

Voro++ is an open source software library for the computation of the Voronoi diagram, a widely-used tessellation that has applications in many scientific fields. For a set of points in a domain, the tessellation is defined by associating a cell of space to each point, consisting of the part of the domain closer to that point than any other.

Which is the best library for Voronoi tessellation?

Several mature software libraries exist for computing the Voronoi tessellation (such as Qhull, used by MATLAB, and CGAL) but these typically compute the Voronoi diagram as a single object: given a set of points they will return the complete mesh that divides those points into cells.

How is the Voronoi library structured in C + +?

The library is structured around several C++ classes. The voronoicell class encapsulates all of the routines for representing a Voronoi cell as an irregular convex polyhedron (Fig. 1 (a)). This class is then employed by the container class, which represents a system of particles (Fig. 1 (b)), and can carry out a wide variety of computations.

Why does a weighted Voronoi diagram have a weight?

In weighted Voronoi diagrams, each site has a weight that influences the distance computation. The idea is that larger weights indicate more important sites, and such sites will get bigger Voronoi cells.

How to create a 2 d Voronoi diagram?

Create a matrix of 2-D points and compute the Voronoi vertices and diagram cells. v = 10×2 Inf Inf 0.7000 -1.6500 -0.0500 -0.0500 -0.0500 -0.5250 -1.4500 0.6500 -1.7500 0.7500 0 0.2875 0.3833 0.3833 0.2875 0 0 0 Points, specified as a matrix whose columns contain the coordinates for the corresponding dimension.

How to calculate voronoin for a matrix P?

[v,c] = voronoin (P) returns the Voronoi vertices v and the Voronoi cells c of the Voronoi diagram for the N-D points in a matrix P. [v,c] = voronoin (P,opts) also specifies the Qhull options used to compute the Voronoi diagram.

What is the boundary of a Voronoi diagram?

This boundary defines a single Voronoi polygon. The collection of all Voronoi polygons for every point in the set is called a Voronoi diagram. You can plot individual bounded cells of an N-D Voronoi diagram.

Which is the easiest algorithm of Voronoi diagram to implement?

The Bowyer-Watson algorithm is quite easy to understand. Here is an implementation: http://paulbourke.net/papers/triangulate/. It’s a delaunay triangulation for a set of points but you can use it to get the dual of the delaunay,i.e. a voronoi-diagram.