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1

I have a 4x4 square within which one can draw lines either vertically or horizontally in units of 1. The result would look something like this (as an example).

Given this problem, how would one go about identifying the 3 polygons that construct this image?

I understand that the large square in which the pieces lie is a polygon too, but I'm only interested in the 'base' polygons - not sure if that's the right way to call them.

Clarification: We only know the coordinates of the lines from inputting them, we don't know the polygons in advance.

The solution accordingly would be the polygons themselves (in pseudo-code):

pol[1] = c(0, 0),
 c(1, 0),
 c(1, 1),
 c(2, 1),
 c(2, 2),
 c(1, 2),
 c(1, 3),
 c(0, 3),
 c(0, 0)


pol[2] = c(1, 0),
 c(3, 0),
 c(3, 4),
 c(0, 4),
 c(0, 3),
 c(1, 3),
 c(1, 2),
 c(2, 2),
 c(2, 1),
 c(1, 1),
 c(1, 0)

pol[3] = c(3, 0),
 c(4, 0),
 c(4, 4),
 c(3, 4),
 c(3, 0)

r geometry coordinates

share|improve this question

edited Mar 24 at 1:54

Deuterium

asked Mar 24 at 0:59

DeuteriumDeuterium

4718

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Sorry. What exactly do you want? Do you want people to create an R object that describes the polygons?
  
  – www
  Mar 24 at 1:03
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Looking more for direction regarding the methodology to do so. I wouldn't expect anyone to create an R code for this on my behalf.
  
  – Deuterium
  Mar 24 at 1:05
  

  
  
  
  

add a comment | 

1

I have a 4x4 square within which one can draw lines either vertically or horizontally in units of 1. The result would look something like this (as an example).

Given this problem, how would one go about identifying the 3 polygons that construct this image?

I understand that the large square in which the pieces lie is a polygon too, but I'm only interested in the 'base' polygons - not sure if that's the right way to call them.

Clarification: We only know the coordinates of the lines from inputting them, we don't know the polygons in advance.

The solution accordingly would be the polygons themselves (in pseudo-code):

pol[1] = c(0, 0),
 c(1, 0),
 c(1, 1),
 c(2, 1),
 c(2, 2),
 c(1, 2),
 c(1, 3),
 c(0, 3),
 c(0, 0)


pol[2] = c(1, 0),
 c(3, 0),
 c(3, 4),
 c(0, 4),
 c(0, 3),
 c(1, 3),
 c(1, 2),
 c(2, 2),
 c(2, 1),
 c(1, 1),
 c(1, 0)

pol[3] = c(3, 0),
 c(4, 0),
 c(4, 4),
 c(3, 4),
 c(3, 0)

r geometry coordinates

share|improve this question

edited Mar 24 at 1:54

Deuterium

asked Mar 24 at 0:59

DeuteriumDeuterium

4718

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Sorry. What exactly do you want? Do you want people to create an R object that describes the polygons?
  
  – www
  Mar 24 at 1:03
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Looking more for direction regarding the methodology to do so. I wouldn't expect anyone to create an R code for this on my behalf.
  
  – Deuterium
  Mar 24 at 1:05
  

  
  
  
  

add a comment | 

I have a 4x4 square within which one can draw lines either vertically or horizontally in units of 1. The result would look something like this (as an example).

Given this problem, how would one go about identifying the 3 polygons that construct this image?

I understand that the large square in which the pieces lie is a polygon too, but I'm only interested in the 'base' polygons - not sure if that's the right way to call them.

Clarification: We only know the coordinates of the lines from inputting them, we don't know the polygons in advance.

The solution accordingly would be the polygons themselves (in pseudo-code):

pol[1] = c(0, 0),
 c(1, 0),
 c(1, 1),
 c(2, 1),
 c(2, 2),
 c(1, 2),
 c(1, 3),
 c(0, 3),
 c(0, 0)


pol[2] = c(1, 0),
 c(3, 0),
 c(3, 4),
 c(0, 4),
 c(0, 3),
 c(1, 3),
 c(1, 2),
 c(2, 2),
 c(2, 1),
 c(1, 1),
 c(1, 0)

pol[3] = c(3, 0),
 c(4, 0),
 c(4, 4),
 c(3, 4),
 c(3, 0)

r geometry coordinates

share|improve this question

edited Mar 24 at 1:54

Deuterium

asked Mar 24 at 0:59

DeuteriumDeuterium

4718

pol[1] = c(0, 0),
 c(1, 0),
 c(1, 1),
 c(2, 1),
 c(2, 2),
 c(1, 2),
 c(1, 3),
 c(0, 3),
 c(0, 0)


pol[2] = c(1, 0),
 c(3, 0),
 c(3, 4),
 c(0, 4),
 c(0, 3),
 c(1, 3),
 c(1, 2),
 c(2, 2),
 c(2, 1),
 c(1, 1),
 c(1, 0)

pol[3] = c(3, 0),
 c(4, 0),
 c(4, 4),
 c(3, 4),
 c(3, 0)

share|improve this question

edited Mar 24 at 1:54

Deuterium

asked Mar 24 at 0:59

DeuteriumDeuterium

4718

share|improve this question

edited Mar 24 at 1:54

Deuterium

asked Mar 24 at 0:59

DeuteriumDeuterium

4718

asked Mar 24 at 0:59

DeuteriumDeuterium

4718

asked Mar 24 at 0:59

DeuteriumDeuterium

4718

1 Answer
1

active

oldest

votes

1

Here is an approach to create the spatial object in R. pol_sf is the final output, which is an sf object. This approach needs the sf package. The tidyverse package is not required but work well on the sf object.

library(tidyverse)
library(sf)

# Polygon 1
pol1 <- st_polygon(list(rbind(c(0, 0),
 c(1, 0),
 c(1, 1),
 c(2, 1),
 c(2, 2),
 c(1, 2),
 c(1, 3),
 c(0, 3),
 c(0, 0))))

# Polygon 2
pol2 <- st_polygon(list(rbind(c(1, 0),
 c(3, 0),
 c(3, 4),
 c(0, 4),
 c(0, 3),
 c(1, 3),
 c(1, 2),
 c(2, 2),
 c(2, 1),
 c(1, 1),
 c(1, 0))))

# Polygon 3
pol3 <- st_polygon(list(rbind(c(3, 0),
 c(4, 0),
 c(4, 4),
 c(3, 4),
 c(3, 0))))

# Combine pol1, pol2, and pol3
pol_sfc <- st_as_sfc(list(pol1, pol2, pol3))

# Create an sf object
pol_sf <- tibble(ID = c("a", "b", "c")) %>% 
 mutate(geometry = pol_sfc) %>%
 st_as_sf()

# Plot the data
ggplot(pol_sf) + geom_sf(aes(fill = ID))

share|improve this answer

answered Mar 24 at 1:20

wwwwww

29.1k112345

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Hey www, I feel bad because my original question might not have been clear. The problem is that although we know all the coordinates, we don't know the polygons in advance. The problem is less about showing the polygons in a graph and more about an algorithm that can tell these polygons apart just from coordinates (and then maybe plot them similarly to how you have done it as the cherry on top).
  
  – Deuterium
  Mar 24 at 1:42
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Not clear what do you want. Good luck.
  
  – www
  Mar 24 at 1:44
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  It's cool. Thanks for the attempt.
  
  – Deuterium
  Mar 24 at 1:56
  

  
  
  
  

add a comment | 

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1

Here is an approach to create the spatial object in R. pol_sf is the final output, which is an sf object. This approach needs the sf package. The tidyverse package is not required but work well on the sf object.

library(tidyverse)
library(sf)

# Polygon 1
pol1 <- st_polygon(list(rbind(c(0, 0),
 c(1, 0),
 c(1, 1),
 c(2, 1),
 c(2, 2),
 c(1, 2),
 c(1, 3),
 c(0, 3),
 c(0, 0))))

# Polygon 2
pol2 <- st_polygon(list(rbind(c(1, 0),
 c(3, 0),
 c(3, 4),
 c(0, 4),
 c(0, 3),
 c(1, 3),
 c(1, 2),
 c(2, 2),
 c(2, 1),
 c(1, 1),
 c(1, 0))))

# Polygon 3
pol3 <- st_polygon(list(rbind(c(3, 0),
 c(4, 0),
 c(4, 4),
 c(3, 4),
 c(3, 0))))

# Combine pol1, pol2, and pol3
pol_sfc <- st_as_sfc(list(pol1, pol2, pol3))

# Create an sf object
pol_sf <- tibble(ID = c("a", "b", "c")) %>% 
 mutate(geometry = pol_sfc) %>%
 st_as_sf()

# Plot the data
ggplot(pol_sf) + geom_sf(aes(fill = ID))

share|improve this answer

answered Mar 24 at 1:20

wwwwww

29.1k112345

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Hey www, I feel bad because my original question might not have been clear. The problem is that although we know all the coordinates, we don't know the polygons in advance. The problem is less about showing the polygons in a graph and more about an algorithm that can tell these polygons apart just from coordinates (and then maybe plot them similarly to how you have done it as the cherry on top).
  
  – Deuterium
  Mar 24 at 1:42
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Not clear what do you want. Good luck.
  
  – www
  Mar 24 at 1:44
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  It's cool. Thanks for the attempt.
  
  – Deuterium
  Mar 24 at 1:56
  

  
  
  
  

add a comment | 

1

Here is an approach to create the spatial object in R. pol_sf is the final output, which is an sf object. This approach needs the sf package. The tidyverse package is not required but work well on the sf object.

library(tidyverse)
library(sf)

# Polygon 1
pol1 <- st_polygon(list(rbind(c(0, 0),
 c(1, 0),
 c(1, 1),
 c(2, 1),
 c(2, 2),
 c(1, 2),
 c(1, 3),
 c(0, 3),
 c(0, 0))))

# Polygon 2
pol2 <- st_polygon(list(rbind(c(1, 0),
 c(3, 0),
 c(3, 4),
 c(0, 4),
 c(0, 3),
 c(1, 3),
 c(1, 2),
 c(2, 2),
 c(2, 1),
 c(1, 1),
 c(1, 0))))

# Polygon 3
pol3 <- st_polygon(list(rbind(c(3, 0),
 c(4, 0),
 c(4, 4),
 c(3, 4),
 c(3, 0))))

# Combine pol1, pol2, and pol3
pol_sfc <- st_as_sfc(list(pol1, pol2, pol3))

# Create an sf object
pol_sf <- tibble(ID = c("a", "b", "c")) %>% 
 mutate(geometry = pol_sfc) %>%
 st_as_sf()

# Plot the data
ggplot(pol_sf) + geom_sf(aes(fill = ID))

share|improve this answer

answered Mar 24 at 1:20

wwwwww

29.1k112345

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Hey www, I feel bad because my original question might not have been clear. The problem is that although we know all the coordinates, we don't know the polygons in advance. The problem is less about showing the polygons in a graph and more about an algorithm that can tell these polygons apart just from coordinates (and then maybe plot them similarly to how you have done it as the cherry on top).
  
  – Deuterium
  Mar 24 at 1:42
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Not clear what do you want. Good luck.
  
  – www
  Mar 24 at 1:44
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  It's cool. Thanks for the attempt.
  
  – Deuterium
  Mar 24 at 1:56
  

  
  
  
  

add a comment | 

Here is an approach to create the spatial object in R. pol_sf is the final output, which is an sf object. This approach needs the sf package. The tidyverse package is not required but work well on the sf object.

library(tidyverse)
library(sf)

# Polygon 1
pol1 <- st_polygon(list(rbind(c(0, 0),
 c(1, 0),
 c(1, 1),
 c(2, 1),
 c(2, 2),
 c(1, 2),
 c(1, 3),
 c(0, 3),
 c(0, 0))))

# Polygon 2
pol2 <- st_polygon(list(rbind(c(1, 0),
 c(3, 0),
 c(3, 4),
 c(0, 4),
 c(0, 3),
 c(1, 3),
 c(1, 2),
 c(2, 2),
 c(2, 1),
 c(1, 1),
 c(1, 0))))

# Polygon 3
pol3 <- st_polygon(list(rbind(c(3, 0),
 c(4, 0),
 c(4, 4),
 c(3, 4),
 c(3, 0))))

# Combine pol1, pol2, and pol3
pol_sfc <- st_as_sfc(list(pol1, pol2, pol3))

# Create an sf object
pol_sf <- tibble(ID = c("a", "b", "c")) %>% 
 mutate(geometry = pol_sfc) %>%
 st_as_sf()

# Plot the data
ggplot(pol_sf) + geom_sf(aes(fill = ID))

share|improve this answer

answered Mar 24 at 1:20

wwwwww

29.1k112345

library(tidyverse)
library(sf)

# Polygon 1
pol1 <- st_polygon(list(rbind(c(0, 0),
 c(1, 0),
 c(1, 1),
 c(2, 1),
 c(2, 2),
 c(1, 2),
 c(1, 3),
 c(0, 3),
 c(0, 0))))

# Polygon 2
pol2 <- st_polygon(list(rbind(c(1, 0),
 c(3, 0),
 c(3, 4),
 c(0, 4),
 c(0, 3),
 c(1, 3),
 c(1, 2),
 c(2, 2),
 c(2, 1),
 c(1, 1),
 c(1, 0))))

# Polygon 3
pol3 <- st_polygon(list(rbind(c(3, 0),
 c(4, 0),
 c(4, 4),
 c(3, 4),
 c(3, 0))))

# Combine pol1, pol2, and pol3
pol_sfc <- st_as_sfc(list(pol1, pol2, pol3))

# Create an sf object
pol_sf <- tibble(ID = c("a", "b", "c")) %>% 
 mutate(geometry = pol_sfc) %>%
 st_as_sf()

# Plot the data
ggplot(pol_sf) + geom_sf(aes(fill = ID))

share|improve this answer

answered Mar 24 at 1:20

wwwwww

29.1k112345

answered Mar 24 at 1:20

wwwwww

29.1k112345

answered Mar 24 at 1:20

wwwwww

29.1k112345