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Generating Random Transects of Same Length

5 messages · Pierre Racine, Marcelino de la Cruz, Barry Rowlingson +1 more

Original
Pierre Racine
# 
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...

Thanks,

Pierre
Pierre.racine at sbf.ulaval.ca
Barry Rowlingson
# 
2009/2/12 Pierre Racine <Pierre.Racine at sbf.ulaval.ca>:
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
Marcelino de la Cruz
# 
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])
At 19:33 12/02/2009, Barry Rowlingson wrote:
________________________________

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
Barry Rowlingson
# 
2009/2/12 Marcelino de la Cruz <marcelino.delacruz at upm.es>:
Very very nice, but:
generates 128 points on a circle around each point. There's a teeny
tiny chance that none of those points will be in your polygon :)  What
you've done is a rejection method where you generate 128 and throw 127
away!

 I can see the following ways of doing this:

 A:  1. generate first point from CSR on the polygon
      2. generate second point at distance D from first point
      3. goto *2* until second point is in polygon.

 B: 1. generate first point from CSR on the polygon
     2. generate second point at distance D from the first point
     3. goto *1* until second point is in polygon

 C: buffer zone method

your code essentially does A, where the first points are CSR but the
second points arent (I think), and B will have neither first points
nor second points as CSR since it avoids the edges.

the buffer zone method produces CSR in the inner zone for the first
points and non-CSR for the second points.

all depends on what the original questioner wanted - if just a bunch
of segments of length D roughly scattered around inside the polygon
then wham! your lovely spatstat code is exactly that!

Barry