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

Question

David Franco 2020 年 4 月 24 日

コメント済み: HG 2021 年 6 月 14 日

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 2020 年 4 月 24 日

編集済み: Sean de Wolski 2020 年 4 月 24 日

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