Understanding Polygon Neighborhoods in Spatial Data Analysis

Polygon neighborhoods are an essential concept in spatial data analysis, particularly when working with geographic information systems (GIS). In this article, we will delve into the world of polygon neighborhoods and explore how to differentiate between polygons with open edges and those that are completely surrounded by neighbors.

The Problem Statement

When working with polygon-shaped objects in a spatial context, it’s essential to understand the concept of neighborhood. A neighbor is another polygon or shapefile that shares some overlap with the central object. However, what constitutes an open edge versus a complete surrounding can be ambiguous.

In this article, we will explore how to define and differentiate between polygons with open edges using R programming language and its associated packages.

Introduction to Spatial Data Analysis

Spatial data analysis is a branch of geospatial science that deals with the study and analysis of geographic data. It involves the use of spatial techniques and tools to extract insights from spatial data, such as location-based relationships, patterns, and trends.

In R programming language, there are several packages available for spatial data analysis, including sp, geosphere, and raster. These packages provide a range of functions and tools for spatial operations, such as buffer creation, shapefile manipulation, and spatial joins.

Buffer Creation

Buffer creation is an essential operation in spatial data analysis. It involves adding a perimeter around a central object or polygon to define its neighborhood. In R, the buffer() function from the geosphere package can be used to create buffers around polygons.

## Create a buffer around a polygon
library(geosphere)
buff <- buffer(one, distance = 10)

In this example, we are creating a buffer around the central object (one) with a distance of 10 meters. The resulting buffer is stored in the buff variable.

Poly2nb()

The poly2nb() function from the spdep package can be used to create a neighborhood matrix from a shapefile or polygon data. This function is useful for creating a spatial join between two datasets based on their geometric overlap.

## Create a neighborhood matrix
library(spdep)
nb <- poly2nb(forest_fc, snap = 0)

In this example, we are creating a neighborhood matrix from the forest_fc shapefile with a snapping distance of 0. The resulting neighborhood matrix is stored in the nb variable.

Defining Open Edge

Defining an open edge versus a complete surrounding requires careful consideration of the spatial relationships between polygons. In R, we can use a combination of spatial operations and conditional statements to achieve this goal.

The defineOpenEdge() function from the provided code demonstrates how to define an open edge using a combination of buffer creation, shapefile manipulation, and spatial joins.

## Define open edge
library(sp)
defineOpenEdge <- function(spdf, treeHeight, distance = 10, pixel.width = 16) {
  
  # Loop through the dataframe
  spdf@data$open_edge <- FALSE
  for (i in seq_along(spdf)) {
    
    # Define stands and leftover forest
    one <- spdf[i, ]
    left <- spdf[-i,]
    
    # Create buffer and intersect with neighbors
    buff <- buffer(one, distance)
    nbrs.buff <- left[which(gOverlaps(sp::geometry(buff), 
                                sp::geometry(left), 
                                byid = TRUE)),]
    
    # Conditions for open edge
    if (nrow(nbrs.buff) == 0) {
      spdf@data[i,]$open_edge <- TRUE  
      
    } else {  # neighbors are smaller than the stands
    
      # Compare the height of the stands:
      height.one <- rep(one@data$treeHeight, nrow(nbrs.buff))
      height.nbrs <- nbrs.buff@data$treeHeight
      
      # Get the differences between the neighboring stands
      difference <- height.one - height.nbrs
      
      # compare here the tree heights of stands
      if(any(difference > 5)) {
        spdf@data[i,]$open_edge <- TRUE
        
      } else {  # check for existence of gap in neighborhood
       
        # Get the difference between two shapefiles???
        int.buff.one <- rgeos::gDifference(buff, nbrs.buff + one)
        
        # Is the size of the opening larger than one pixel (16x16 m)?
        if (!is.null(int.buff.one) ) {
          
          # Calculate area of intersected data
          int.buff.one.area <- gArea(int.buff.one)
          
          if (int.buff.one.area > 16*16) {
            spdf@data[i,]$open_edge <- TRUE
          }
        }
      }
    }
  }
  return(spdf) 
}

This function defines an open edge using a combination of buffer creation, shapefile manipulation, and spatial joins. It checks for the presence of neighbors, compares their heights with the central object’s height, and also checks for the existence of gaps in the neighborhood.

Conclusion

Defining polygons with open edges versus complete surroundings requires careful consideration of spatial relationships between objects. The defineOpenEdge() function demonstrates how to achieve this goal using R programming language and its associated packages. By understanding polygon neighborhoods and applying spatial operations, we can gain valuable insights into our data.

By following the steps outlined in this article, you can develop your own functions for defining open edges in spatial data analysis. Remember to consider the nuances of spatial relationships between objects when working with polygons and buffers.

Last modified on 2024-07-30