[R] Quadrat counting with spatstat

[Petr Savicky]

On Thu, May 31, 2012 at 08:23:02AM -0700, AMFTom wrote:
> I have photographs of plots that look like so:
> 
> http://r.789695.n4.nabble.com/file/n4631960/Untitled.jpg 
> 
> I need to divide it up so each circle has an equal area surrounding it. So
> into 20 equal segments, each of which contains a circle. Quadratcount is not
> sufficient because if I divide it up into 36 equal quadrats, some quadrats
> do not contain one of the circles. 
> 
> I'm not even sure how to do it mathematically, let alone using R.  

Hi.

Try the following.

  a <- rbind(
  c(-1, -1),
  c(-1,  1),
  c( 1,  1),
  c( 1, -1),
  c(-1, -1))
  plot(a, type="l")

  p <- rbind(
  c(0, 0),
  c(-0.6, 0.6),
  c(-0.6, -0.6),
  c(0.6, 0.6),
  c(0.6, -0.6))
  points(p, col=4, pch=20, cex=4)
 
  v <- sqrt(2/5)
 
  b <- rbind(
  c(-1, 0),
  c( 0,-1),
  c( 1, 0),
  c( 0, 1))
 
  for (i in 1:4) {
      lines(rbind(b[i, ], v*b[i, ]))
      lines(v*rbind(b[i, ], b[(i %% 4) + 1, ]))
  }

This divides a square into 5 equal regions. The area of the
middle square is 2 v^2 = 4/5 and the area of each of the four
remaining parts is 1 - v^2/2 = 4/5.

If the above is repeated in a grid 2 times 2, we get a partition
of a larger square into 20 equal regions. I did not check,
whether they contain the required points, since i do not know
their exact coordinates, but they could.

Hope this helps.

Petr Savicky.