wbuchanan / stata-delaunay-voronoi

Implementation of the S-Hull Delaunay triangulation algorithm in Stata. The algorithm also generates the convex hull. The Voronoi are recovered as a dual to the Delaunay.

Stata delaunay voronoi

Implementation of the S-Hull Delaunay triangulation algorithm in Stata. The algorithm also generates the convex hull. The Voronoi are recovered as a dual to the Delaunay.

Note: This is a beta release and still needs to be improved. It has been uploaded here for testing purposes only. Feedback is always welcome!

Install the package:

Please install and replace the package everytime you want to use it. Small tweaks are continuously being made. The following command can be used to install it directly in Stata:

net install delaunay, from("https://raw.githubusercontent.com/asjadnaqvi/stata-delaunay-voronoi/main/installation/") replace

The syntax is:

delaunay x y, id(id) [triangles] [hull] [voronoi]

where x and y are coordinates. id is the serial identifier of each point. The last three options export the triangles, hull, and voronoi back to Stata for plotting.

See the help files for details:

help delaunay

Test the package:

You can use the above do file for test the code. A sample code is provided here:

Generate some random data or use your own coordinates:

set obs 2000  // have tested up to 10k observations

gen x = runiform(0,100)
gen y = runiform(0,100)


// create a donut (if you want)
drop if sqrt((x-50)^2 + (y-50)^2) > 50

local obs = _N 
di `obs'
gen id = _n
order id

mat drop _all

Export everything back to Stata:

delaunay x y, id(id) triangles hull voronoi

Plot the triangles and the hull:

	twoway ///
		(area tri_y tri_x, cmissing(n) nodropbase fc(gs14%10) lw(0.04) lc()) ///
		(line hull_y hull_x) ///
		(scatter y x , msize(0.2) mc(black) ) ///
		, ///
		legend(off) aspect(1) xsize(1) ysize(1)

Plot the Voronoi tessellations:

	twoway ///
		(pcspike vor_y1 vor_x1 vor_y2 vor_x2, lw(0.08) lc()) ///
		(scatter y x , msize(0.1) mc(black) ) ///
				, ///
		legend(off)	aspect(1) xsize(1) ysize(1)

Known issues

1. For some point combinations, the last point is being skipped from triangles.
2. For some voronoi lines on the edges, the infinite rays are not being calculated.

In the pipeline

1. The above errors.
2. Add [if] [in] options.
3. Add an option to check and correct indices.
4. Get rid of Mata junk
5. Separate the Mata calculations from export back to Stata.
6. Call the clipline command from within the program, and add box options.
7. Convert Voronoi lines to shapes for more interesting visualizations.
8. Add e-class locals.