`Deldir.deldir`

— Functiondeldir(x::Vector, y::Vector; ...)

Compute the Delaunay triangulation and Voronoi tesselation of the 2D points with x-coordinates `x`

and y-coordinates `y`

.

Optional arguments are

`rw`

: Boundary rectangle specified as a vector with`[xmin, xmax, ymin, ymax]`

. By default,`rw`

is the unit rectangle.`epsilon`

: A value of epsilon used in testing whether a quantity is zeros, mainly in the context of whether points are collinear.

If anomalous errors arise, it is possible that these may averted by adjusting the value of `epsilon`

upward or downward. By default, `epsilon = 1e-9`

.

The output are three `DataFrame`

s:

`delsgs`

- The
`x1`

,`y1`

,`x2`

&`y2`

entires are the coordinates of the points joined by an edge of a Delaunay triangle. - The
`ind1`

and`ind2`

entries are the indices of the two points which are joined.

`vorsgs`

- The
`x1`

,`y1`

,`x2`

&`y2`

entires are the coordinates of the endpoints of one the edges of a Voronoi cell. - The
`ind1`

and`ind2`

entries are the indices of the two points, in the set being triangulated, which are separated by that edge - The
`bp1`

entry indicates whether the first endpoint of the corresponding edge of a Voronoi cell is a boundary point (a point on the boundary of the rectangular window).

Likewise for the `bp2`

entry and the second endpoint of the edge.

- The
`thirdv1`

and`thirdv2`

columns are the indices of the respective third vertices of the Delaunay triangle whose circumcentres constitute the corresponding endpoints of the edge under consideration.

`summary`

- The
`x`

and`y`

entries of each row are the coordinates of the points in the set being triangulated. - The
`ntri`

entry are the number of Delaunay triangles emanating from the point. - The
`del_area`

entry is`1/3`

of the total area of all the Delaunay triangles emanating from the point. - The
`n_tside`

entry is the number of sides — within the rectangular window — of the Voronoi cell surrounding the point. - The
`nbpt`

entry is the number of points in which the Voronoi cell intersects the boundary of the rectangular window. - The
`vor_area`

entry is the area of the Voronoi cell surrounding the point.

`Deldir.deldirwrapper!`

— Methoddeldirwrapper!(da::DeldirArguments)

Wrapper for the Fortran code that returns the output undigested.

`Deldir.edges`

— Method`edges(D) -> Vector, Vector`

Collect the edges of a dataframe in vectors that are ready to be plotted.

`Deldir.remove_duplicates`

— Method`remove_duplicates(x::Vector, y::Vector)`

Remove duplicate tuples `(x[i],y[i])`

from the vectors `x`

and `y`

.

`Deldir.voronoiarea`

— Function`voronoiarea(x::Vector, y::Vector, rw) -> Vector`

Compute the area of each Voronoi cell of the generators `(x[i], y[i])`

in the vectors `x`

and `y`

.

`rw`

is the boundary window.