  The grid map, often referred to as the tile map, stands as a vital tool in
geospatial visualization, possessing unique attributes that differentiate it
from more commonly known techniques such as choropleths and cartograms. It
transforms geographic regions into grids, which requires the displacement of
both region centroids and boundary nodes to establish a coherent grid
arrangement. However, existing approaches typically displace region centroids
and boundary nodes separately, potentially resulting in self-intersected
boundaries and compromised relative orientation relations between regions. In
this paper, we introduce a novel approach that leverages the Snake displacement
algorithm from cartographic generalization to concurrently displace region
centroids and boundary nodes. The revised Constrained Delaunay triangulation
(CDT) is employed to represent the relations between regions and serves as a
structural foundation for the Snake algorithm. Forces for displacing the region
centroids into a grid-like pattern are then computed. These forces are
iteratively applied within the Snake model until a satisfactory new boundary is
achieved. Subsequently, the grid map is created by aligning the grids with the
newly generated boundary, utilizing a one-to-one match algorithm to assign each
region to a specific grid. Experimental results demonstrate that the proposed
approach excels in maintaining the relative orientation and global shape of
regions, albeit with a potential increase in local location deviations. We also
present two strategies aligned with existing approaches to generate diverse
grid maps for user preferences. Further details and resources are available on
our project website: https://github.com/TrentonWei/DorlingMap.git.
