Generating Random Transects of Same Length

As an spatstat aficionado, I would use the following code:

Enjoy!

Marcelino


library(spatstat)

# Define polygon, length of transect and number of (points)transects
data(letterR)
mywindow <- letterR
ltransect <- 0.3
npoints <- 100
s<- 1:npoints

# Generate random origin points
cosa <- runifpoint(npoints, w=mywindow)
plot(cosa)


cosaxy <- data.frame(cosa$x,cosa$y)

#compute a circle around each point
cosadisc<- apply(cosaxy,1, function(x) disc(r=ltransect, x))

# Test if every circle point is inside polygonal boundary
cosadisc.df <- lapply(cosadisc, function(W){
                          inside.owin(W$bdry[[1]]$x,W$bdry[[1]]$y 
,w=mywindow)})

#function to sample circle points within the window
samplea2 <- function(cosaxy, l1=cosadisc, l2=cosadisc.df){
result<-c(0,0)
for (i in 1:length(l1)){
                  truinside<-sum(l2[[i]])
                  inside 
<-cbind(l1[[i]]$bdry[[1]]$x,l1[[i]]$bdry[[1]]$y)[l2[[i]],]
                  result<-rbind(result,  inside[sample(1:truinside, size=1),])
}
result<-result[-1,]
result<-cbind(cosaxy,result)
return(result)
}

#the result is a matrix with x0,y0, x1, y1 for each transect
#Plot the random transects:

segmentos<-samplea2(cosaxy)
segments(segmentos[,1][s], segmentos[,2][s],segmentos[,3][s], segmentos[,4][s])

2009/2/12 Pierre Racine <Pierre.Racine at sbf.ulaval.ca>:

Hi,

Anybody knows a tool or algorythm (R, GRASS or ArcGIS Script, anything!)
to generate a number of random same length transects (e.g. 1000) within
the extent of a given polygon or raster?

I can't just create random point in the extent and joint hem two by two.
This would result in different length transects.

A simple algorythm would be:

-create a transect of a certain length from a random point and a random
angle
-reject any transect having an end falling outside the given extent

But there is chances that this takes years to run...

 What do you mean by 'random' transects?

 You could define a buffer line of distance d around the inside your
polygon. This divides space into three regions - the outside area, the
buffer zone area, and the inside area. The buffer zone area and the
inside area make up your original polygon.

 Then choose your first point from a spatial uniform distribution on
the inside area. Then pick another point at a random U(0,2*pi) angle
and distance d. This is guaranteed to be in the original polygon, so
there's no rejection step. However, you'll never get transects with
start and end both within the buffer zone. But they would still, in
some sense of the word, be 'random'.

 If this isn't clear then I think a picture would make it so! I think
you can do buffer operations in R... Grass certainly can!

Barry

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________________________________

Marcelino de la Cruz Rot

Departamento de  Biolog?a Vegetal
E.U.T.I. Agr?cola
Universidad Polit?cnica de Madrid
28040-Madrid
Tel.: 91 336 54 35
Fax: 91 336 56 56
marcelino.delacruz at upm.es