[GIS] How to find the minimum perimeter oriented bounding box

cextentsgeosrectangle

I would like to know an algorithm to calculate the minimum perimeter oriented bounding box of a point set or polygon. I know that if I use the rotating calipers, I am able to get the minimum area oriented bounding box. However, I would like the bounding box considering the perimeter, or the width.

An example of this is given in ArcGIS.

Best Answer

Here is Python Code to determine the MBR by minimum Area. It seems easy to change the criteria to minimum Width or Perimeter. https://github.com/dbworth/minimum-area-bounding-rectangle/blob/master/python/min_bounding_rect.py

Related Solutions

R Language – Creating Minimum Bounding Geometry Using the Convex Hull Method

I have a hidden function for calculating the Alpha Convex Hull (Pateiro-Lopez & Rodriguez-Casal 2009) in the development version of spatialEco. The reason this function is not in the CRAN release is due to licensing issues in the alphahull package.

Please note that this statistic only works for [x,y] data. Polygons are tricky because the bounding geometry is based on the vertices of each polygons, functionally making it based on points ([x,y] vertices). Because of this, if you want an alpha hull, it takes some extra data prep to get points representing the polygon boundaries.

Please install alphahull and remotes packages from CRAN and then install the development version of spatialEco using remotes::install_github.

remotes::install_github("jeffreyevans/spatialEco")
library(sp)
library(sf)
library(spatialEco)
library(dplyr)

Here we add some example data and create your polygons

data(meuse)
  sp::coordinates(meuse) = ~x+y
  meuse <- as(meuse, "sf")
  meuse_poly <- sf::st_buffer(meuse, dist = meuse$elev*15)

Now, we can get [x,y] data from the polygons using the sf::st_segmentize function.

poly_points <- sf::st_segmentize(meuse_poly, dfMaxLength = 5) %>% 
  sf::st_coordinates() %>% 
  as.data.frame() %>% 
  dplyr::select(X, Y) %>% 
  sf::st_as_sf(coords = c("X", "Y"))

We can then pass the points the the convexHull function

a <- spatialEco::convexHull(poly_points,alpha = 100000, sp=FALSE)
 plot(sf::st_geometry(a), cex=1.5, col="red") 
    plot(sf::st_geometry(meuse_poly), add=TRUE)

Let's test multiple alpha values to find an optima.

  par(mfcol=c(2,2))
    for (a in c(500, 1500, 5000, 100000)) {
    ch <- spatialEco::convexHull(poly_points, alpha = a, sp = FALSE)
      plot(sf::st_geometry(ch), cex=1.5, col="red") 
        plot(sf::st_geometry(meuse_poly), add=TRUE)
         title(paste0("alpha=", a))      
    }

References

Pateiro-Lopez & Rodriguez-Casal (2009) Generalizing the Convex Hull of a Sample: The R Package alphahull. Journal of Statistical Software 34(5):1-28 http://www.jstatsoft.org/v34/i05/paper

Best Answer

Related Solutions

R Language – Creating Minimum Bounding Geometry Using the Convex Hull Method

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