Question 1

Producing 5 Different Tesselations from CONUS
Simplifying the County Object

Original County Union: 

## [1] 3229

Simplified Object: 

## [1] 322

Original: 3229 points, simplified object: 322 points, our simplified object removed 2907 points. Consequences of doing this computationally are that we lose accuracy in the shape of our object, however, we do not need to spend as much time or data space on unnecessary points.

Tesselations:

Question 2

Writing a function to Summarize Tesselated Surfaces
Tesselation Summary
Type Number of Features Mean Area (km^2) Standard Deviation Total Area (km^2)
US Counties 3108 2521.745 3404.325 7837583
Voronoi 3107 2522.865 2885.827 7838541
Triangulated 6196 1252.506 1576.110 7760528
Square 3108 2728.126 0.000 8479014
Hexagonal 2271 3763.052 0.000 8545891

Analyzing the tesselation summaries for each type of tesselation, it is notable that the Hexagonal Tesselation has the fewest number of features, and the largest total area. Another thing to note is that both square and hexagonal tesselations have 0 as a value for the standard deviation.

Question 3

Analyzing Data from US Army Corp of Engineers National Dam Inventory (NID)
counties_pip = pip(dams, counties, "geoid") %>% 
  plot_pip("Dams Per County")
v_pip = pip(dams, v_grid, "id") %>% 
  plot_pip("Dams Per Viroinoi Tesselation")
t_pip = pip(dams, t_grid, "id") %>% 
  plot_pip("Dams Per Triangulated Tesselation")
sq_pip = pip(dams, sq_grid, "id") %>% 
  plot_pip("Dams Per Square Coverage")
hex_pip = pip(dams, hex_grid, "id") %>% 
  plot_pip("Dams Per Hexagonal Coverage")

Question 4

Analyzing Distribution and Function of US Dams
## [1] 495