How to partition (discretize) the space around points using Voronoi Diagram?

I have a problem:

The plot shows a 399 cities locations and the Voroni Diagram (in latitude and longitude coordinates).

The question is, if a have a new coordinate pair and I want to assign it to some os the 399 cities how to find out which Voronoy cell it is in?

The coordinates file are attached.

Thanks in advance!

Answer 1

[Sean de Wolski]

• Create a polyshape for each voronoi cell.
• Loop over cells and test isinterior for each, you can short circuit when you find a match. To be even smarter, you could calculate distance to each cell's centroid using pdist or hypot, sort it ascending, and start testing isinterior in that order.

NOTE: You should really project your lat/lon data into a cartesian coordinate system. Lat/Lon are measured on the surface of a sphere so the lengths of the voronoi cell edges are not in a linear unit. Look at mfwdtran or https://www.mathworks.com/help/map/ref/map.rasterref.geographiccellsreference.geographictointrinsic.html

[David Franco]

Thank you Sean!

[HG]

https://www.mathworks.com/matlabcentral/answers/855885-color-voronoi-diagram-and-coresponding-matrix?s_tid=prof_contriblnk

please answer my question if it's possible for you.