Dividing area by distance to certain nodes?

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I am interested in placing several markers/nodes on a map, defining a bounding box and then dividing that bounding box based on closest distance (straight-line) to a node. However, I'm really at a loss how to begin and would really appreciate any tips (using R, arcGIS, or python).

I was thinking of two approaches:

  1. Expand a radius around each node simultaneously; when the circumference from one hits the circumference of another node that point will stop expanding, however the other parts of the circumference will continue until the circumference exceeds the bounding box or hits the edge of another node
  2. Dividing the bounding box into a very fine grid and calculating the Vincenty distance from each point to each node and then keeping only the matching with the closest node. Then if I sort by node, I should get all the points closest to that node and then I can (somehow?) draw a boundary around that
I think method 1 would be the best however I'm not sure how to code that in python GIS libraries or in ArcGIS.



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