Code to identify enclaves and exclaves based on point set topology

The code is related to the paper Identification of enclaves and exclaves by computation based on point-set topology. 

Abstract: Enclaves and exclaves have special roles in geography, and are of particular importance to fields such as (geo)politics and economy. However, enclaves and exclaves have not been defined with sufficient formality for automatic identification yet. To identify enclaves and exclaves more generally by computational means than current definitions existing in the literature, this paper proposes expressive and generalized mathematical definitions of enclaves and exclaves based on point-set topology. A novel Boundary Extended 16-Intersection Model is developed in this paper to identify enclaves, and 74 possible spatial configurations of enclaves are distinguished according to conditions of intersections for polygons in partitions and enclaves. The classic Dimensionally Extended 9-Intersection Model is employed to identify exclaves, and two possible spatial configurations of exclaves are distinguished according to conditions of intersections for polygons in partitions and exclaves. Applications of the proposed definitions are exemplified by the identification of enclaves and exclaves in prototypes and in the real world.

File descriptions:

instructions_enclaves.md is a file which specifies how to run the codes in the Conda environment.

environment.yml is an environment file.

calculating4_4matrix_v05.ipynb is a file which includes the relate16im() function to produce a string of 16-Intersection Matrix.

possible matrix of enclaves_v1.ipynb is a file which employs conditions of intersection for enclaves to get 74 possible spatial configurations of enclaves.

validating_polygon_v3.ipynb is a file which visualizes and validates 74 possible geometric interpretations of enclaves.

data.zip contains the geometries of parts of Baarle-Hertog and Baarle-Nassau, contour lines, and polygons bounded by neighboring contour lines.