Hi everyone,
I wanted to generate random lines between two spatial points (random points
in polygons). The lines should consist of segments (9 segments), after
following suggestions I received to my previous post, I ended up using
trajectories. My aim now is to restrict these random trajectories (see
points in the attachment as an example) to the extent of a polygon (shown
in the attachment in yellow). So the trajectories should lie within the
polygon.
Please find the code I used below:
I first generated a data frame with my start and end point and used it to
generate a trajectory (straight line in attachment). I then generated a
random trajectory and shifted it so that the start and endpoints were equal
to my first trajectory. I transformed the matrices to a Spatial Data frame
to be able to plot it. Does anyone know how I can restrict the extent of
the trajectory that I randomly generate?
#coordinates of start and end point and time steps
x<-c(1649786,-1636500)
y<-c(-2902593,738500)
times<-c(0,9)
start_end_points<-as.data.frame(cbind(x,y,times))
# generate a trajectory between start and endpoint
trj<-TrajFromCoords(point_trj,xCol=1,yCol=2,timeCol=3, spatialUnits="m",
timeUnits="d")
# generate a random trajectory with 9 segments
track<-TrajGenerate(n=9, random=T, stepLength=TrajLength(trj)/9)
# To be able to use StartEndTranslate transform trajectories into matrices
ma1<-as.matrix(trj)
ma2<-as.matrix(track)
# Translate, rotate and scale the points of traj2 using traj1. The new traj
will have the same start and end points as traj1.
p<-StartEndTranslate(ma1,ma2)
# to check if this worked transform into SpatialDataFrame
# the start and end point of the new matrix are the same as the traj1 which
is good, the rest of the points changed as well
p_df<-as.data.frame(p)
# change lat / longs to nummeric
p_df$x<-as.numeric(p_df$x)
p_df$y<-as.numeric(p_df$y)
# generate a spatial dataframe to check if the StartEndTranslate function
worked by plotting it
xy<-p_df[,c(1,2)]
spdf<-SpatialPointsDataFrame(coords=xy, data=p_df, proj4string =
CRS(projection))
Thank you very much!
On Wed, Feb 6, 2019 at 5:42 PM Barry Rowlingson <b.rowling...@gmail.com>
wrote:
> Had another idea which is now implemented...
>
> Consider any segmented path of segments of lengths L_i at angles A_i. Its
> endpoint will be the vector sum of those segments, ie at (x,y) = (sum(L_i
> cos(A_i)), sum(L_i sin(A_i)).
>
> To create a segmented path to a given (x,y), solve that expression for the
> angles A_i. In R you can treat this as an optimisation problem - find a set
> of angles A_i that minimise the distance of the end of the segmented path
> from the target end point.
>
> Here's some code that does that for a path from 0,0 to 0,1:
>
> pathit <- function(segments){
> obj = function(angles){
> dxdy = dxdy(segments, angles)
> xerr = dxdy$dx-1
> yerr = dxdy$dy
> err = sqrt(xerr^2 + yerr^2)
> err
> }
> angles = runif(length(segments), 0 , 2*pi)
> optim(angles, obj)
> }
>
> dxdy = function(segments, angles){
> dx = sum(segments * cos(angles))
> dy = sum(segments * sin(angles))
> list(dx=dx, dy=dy)
> }
>
> plotsegs <- function(segments, angles){
> x = rep(NA, length(segments) +1)
> y = x
> x[1] = 0
> y[1] = 0
> for(i in 2:(length(segments)+1)){
> x[i] = x[i-1] + segments[i-1]*cos(angles[i-1])
> y[i] = y[i-1] + segments[i-1]*sin(angles[i-1])
> }
> cbind(x,y)
> }
>
> This is deliberately written naively for clarity.
>
> To use, set the segment sizes, optimise, and then plot:
>
> s1 = c(.1,.3,.2,.1,.3,.3,.1)
> a1 = pathit(s1)
> plot(plotsegs(s1,a1$par),type="l")
>
> which should show a path of seven segments from 0,0 to 0,1 - since the
> initial starting values are random the model can find different solutions.
> Run again for a different path.
>
> To see what the space of paths looks like, do lots and overplot them:
>
> lots = lapply(1:1000, function(i)plotsegs(s1,pathit(s1)$par))
> plot(c(-.1,1.1),c(-1,1))
> p = lapply(lots, function(xy){lines(xy)})
>
> this should show 1000 paths, and illustrates the "ellipse" of path
> possibles that I mentioned in the previous email.
>
> Sometimes the optimiser struggles to find a solution and so you should
> probably test the output from optim for convergence and to make sure the
> target function is close enough to zero for your purposes. For the example
> above most of the time the end point is about 1e-5 from (1,0) but for
> harder problems such as s = rep(.1, 11) which only has 0.1 of extra "slack"
> length, the error can be 0.02 and failed convergence. Possibly longer optim
> runs would help or constraining the angles.
>
> Anyway, interesting problem....
>
> Barry
>
>
>
>
>
>
>
> On Wed, Feb 6, 2019 at 8:23 PM Barry Rowlingson <b.rowling...@gmail.com>
> wrote:
>
>> Do you want to generate these for input into some statistical process, or
>> to generate some test data that looks a bit like real data? I think
>> generating test data isn't too difficult, but anything that you might want
>> to put into a statistical test (eg testing some hypothesis about the birds
>> maximum deviation from the straight line A-B) needs a lot more care in
>> formulating the path generating process.
>>
>> Here's some thoughts - if you consider one of the red segments in your
>> map as a piece of string (rather than 10 segments) anchored at the points,
>> then you can stretch it taut with a pencil and draw an ellipse with A and B
>> as the foci. Any path created with that string - taut or slack as in your
>> map - has to strictly lie within the ellipse. Now you can wiggle that
>> string inside that ellipse and create an infinity of paths from A to B of
>> the same length. I'm not sure how you can sample uniformly from that
>> infinity such that any path has an equal sampling probability. Your problem
>> is similar but has the additional rigid segment constraint.
>>
>> Any two adjacent segments of a chain, eg 1----2-------3, as long as it
>> isn't taut (ie straight) can be perturbed by holding 1 and 3 still and
>> moving 2 to the "mirror image" point over the straight line from 1 to 3.
>> You can also take three segments 1--2--3--4 and hold 1 and 4 still and
>> perturb 2 and 3 fairly easily. In this way you could set up an initial
>> chain and then run multiple perturbations on the chain to get a "random"
>> chain, but quite what set of all chains it would be a sample from is not
>> clear. It could at least generate reasonable looking paths, but I wouldn't
>> want to test a hypothesis against it.
>>
>> I'm going to generate a path from my office to my home now.
>>
>> Barry
>>
>>
>>
>>
>>
>>
>> On Wed, Feb 6, 2019 at 7:50 PM Hannah Justen <jus...@tamu.edu> wrote:
>>
>>> Hello everyone,
>>>
>>> Thank you very much for the suggestions.
>>>
>>> Regarding more details (please also see attached figure):
>>> I would like to simulate a bird's migration between breeding (starting
>>> polygon - blue in the figure) and wintering grounds (end polygon - green in
>>> the figure). The lines can start from anywhere within the starting polygon
>>> and end anywhere in the end polygon. The lines shall consist of 10
>>> connected segments with variable length between 300 and 1000 km (see red
>>> lines in figure; two examples of possible lines with 10 segments between
>>> the polygons).
>>>
>>> Thank you very much for you help,
>>> Hannah
>>>
>>> ---
>>> PhD Student |Ecology and Evolutionary Biology
>>> Texas A&M University
>>>
>>> On Wed, Feb 6, 2019 at 5:12 AM Barry Rowlingson <
>>> b.rowling...@lancaster.ac.uk> wrote:
>>>
>>>> Interesting, but I think we need more details...
>>>>
>>>> Do the lines have to start and finish at specific locations in the
>>>> polygons - like the centroid, or anywhere?
>>>>
>>>> So one line might be 3 segments of 10km each connecting two polygon
>>>> centroids that are 15km apart? Imagining three rigid rods of length 10
>>>> connected at their ends and with the first and last also connected to two
>>>> fixed points tells me there's an infinite number of possible solutions.
>>>> There's probably also a number of ways of sampling from those solutions.
>>>> Its going to get very complicated with a larger number of segments.
>>>>
>>>> Hmmmmm.....
>>>>
>>>> Barry
>>>>
>>>>
>>>>
>>>>
>>>> On Tue, Feb 5, 2019 at 11:30 PM Hannah Justen <jus...@tamu.edu> wrote:
>>>>
>>>>> Hi everyone,
>>>>>
>>>>> I am studying migratory tracks of birds for my dissertation and I would
>>>>> like to model possible pathways between two polygons. Therefore, I
>>>>> would
>>>>> like to sample random lines between the polygons. These lines can
>>>>> differ in
>>>>> total length but should consist of x - number of fragments of equal
>>>>> length.
>>>>> Each fragment can have slightly different orientation but overall the
>>>>> lines
>>>>> should connect the two polygons.
>>>>>
>>>>> I fail to find the appropriate R package that will allow me to do this
>>>>> type
>>>>> of analysis. Does anyone have a suggestion how to approach analysis?
>>>>>
>>>>> Thank you,
>>>>> Hannah
>>>>>
>>>>> ---
>>>>> PhD Student |Ecology and Evolutionary Biology
>>>>> Texas A&M University
>>>>>
>>>>> [[alternative HTML version deleted]]
>>>>>
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>>>>
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