plot_tess(pip_counties, "Original")

plot_tess(pip_counties_grid, "Square Grid")

plot_tess(pip_counties_hexgrid, "Hexagon Grid")

plot_tess(v_grid_final, "Voroni Coverage") + 
  geom_sf(data = pip_counties_u, col = "darkred", size = .2)

plot_tess(t_grid_final, "Triangulated Coverage") + 
  geom_sf(data = pip_cent, col = "darkred", size = .3)

knitr::kable(tess_summary,
             col.names = c("Type", "Number of Features", "Mean Area", "St. Dev", "Total Area"),
             caption = "Summary of Our 5 Tesselations")%>% 
  kableExtra::kable_styling("striped", full_width = TRUE, font_size = 10)
Summary of Our 5 Tesselations
Type Number of Features Mean Area St. Dev Total Area
Original 3107 2522.499 3404.614 7837404
Square Grid 2242 3819.376 0.000 8563041
Hexagon Grid 2271 3763.052 0.000 8545891
Triangulated Coverage 6194 1252.183 1575.912 7756021
Voroni Coverage 3107 2522.499 2887.307 7837404

Differences in each tesselation

-Original: Visually, it is represented the best. The downfall is that it differs the most in standard deviation, which doesn’t help when trying to do something with equal area.

-Square/Hexagon: These tesselations have the least standard deviation and because they are displayed to be equally represented, it results in the least amount of features.

-Voronoi: This tesselation has the greatest variance in the sizes, but is the closest to the original tesselation

-Triangulation: This tesselation provides twice as much features which improves it accuracy, but process slower.