[R-sig-Geo] calculate the area of an alpha shape

[Proosdij, Andre van]

Many thanks Ashton!

It does help a lot, but I'm afraid, it's not completely correct yet. One would expect that the area of the alpha shape is larger than the area of the alpha-convex hull (straight line segments instead of arcs). However, applying your suggestion, the area is smaller! If I plot the points and the alpha shape, the plot is correct. The area of the alpha shape seems to be calculated a polygon that includes the point (1.5, 2.0). See the updated example below. I don't know what happens, but apparently, the list of points that defines the polygon is incorrect. Any thoughts of how to adjust this?

Best,

André


x <- c(1,1,1.5,2.8,3,3) # original set of points
y <- c(1,3,2,3,4,1) # original set of points
#x <- c(1,1,2.8,3,3) # points without (1.5, 2.0)
#y <- c(1,3,3,4,1) # points without (1.5, 2.0)
z <- cbind(x,y)
plot(z)

### Calculate the alpha convex hull
library(alphahull)
alpha <- 3 # Define alpha > 0
achull.obj <- ahull(z, alpha = alpha)

### Plot the sampled points and the alpha-convex hull object
plot(achull.obj, add = TRUE, col = "blue")

### Get the length of the alpha-convex hull
achulllength <- achull.obj$length
achulllength

### Get the area of the alpha-convex hull
achullarea <- areaahull(achull.obj)
achullarea

### Plot the alpha shape
plot(achull.obj$ashape.obj, add = TRUE, col = "red")

### Get the length of the alpha shape
ashapelength <- achull.obj$ashape.obj$length
ashapelength

### Get the area of the alpha shape
library(sp)
bds <- achull.obj$ashape.obj$x  # matrix of coordinates in ashape
bds <- rbind(bds, bds[1,]) # close the ring
ashape <- Polygon(bds) # convert to sp Polygon
ashapearea <- ashape at area
ashapearea




Ir. A.S.J. van Proosdij
PhD Student
t   +31 317 48 1198 
e  andre.vanproosdij at wur.nl

Naturalis Biodiversity Center, section NHN
Biosystematics Group, Wageningen University
Gen. Foulkesweg 37, 6703 BL Wageningen, the Netherlands

www.bis.wur.nl

-----Original Message-----
From: Ashton Shortridge [mailto:ashton at msu.edu] 
Sent: maandag 4 november 2013 14:35
To: r-sig-geo at r-project.org
Cc: Proosdij, Andre van
Subject: Re: [R-sig-Geo] calculate the area of an alpha shape

Dear André,

There may be a more elegant solution, but this works fine:
library(sp)
bds <- achull.obj$ashape.obj$x  # matrix of coordinates in ashape
bds <- rbind(bds, bds[1,])          # close the ring
ashape <- Polygon(bds)            # convert to sp Polygon  
print(ashape at area)



On Monday, November 04, 2013 11:58:26 AM Proosdij, Andre van wrote:
> Dear colleagues,
> 
> I wish to calculate the area covered by the alpha shape based on a 
> sample of points in a 2D plane. For the alpha-convex hull this works 
> fine using the function ahull in the alphahull package. However, I 
> want to get the area of the slightly different alpha shape. How can I 
> do this? Below a short example.
> 
> Many thanks in advance for your answers and ideas!
> 
> 
> André