+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Interpolating, smoothing, and simulating trajectories
+
+
+create some data
+t0 = as.POSIXct(as.Date("2013-09-30",tz="CET"))
+# person A, track 1:
+x = c(7,6,5,5,4,3,3)
+y = c(7,7,6,5,5,6,7)
+n = length(x)
+set.seed(131)
+t = t0 + cumsum(runif(n) * 60)
+library(sp)
+require(rgdal)## Loading required package: rgdal## rgdal: version: 1.2-15, (SVN revision 691)
+## Geospatial Data Abstraction Library extensions to R successfully loaded
+## Loaded GDAL runtime: GDAL 2.1.2, released 2016/10/24
+## Path to GDAL shared files: /usr/share/gdal/2.1
+## GDAL binary built with GEOS: TRUE
+## Loaded PROJ.4 runtime: Rel. 4.9.3, 15 August 2016, [PJ_VERSION: 493]
+## Path to PROJ.4 shared files: (autodetected)
+## Linking to sp version: 1.2-5crs = CRS("+proj=longlat +ellps=WGS84") # longlat
+
+library(spacetime)
+stidf = STIDF(SpatialPoints(cbind(x,y),crs), t, data.frame(co2 = rnorm(n)))
+
+library(trajectories)
+A1 = Track(stidf)
+# person A, track 2:
+x = c(7,6,6,7,7)
+y = c(6,5,4,4,3)
+n = length(x)
+t = max(t) + cumsum(runif(n) * 60)
+stidf = STIDF(SpatialPoints(cbind(x,y),crs), t, data.frame(co2 = rnorm(n)))
+
+A2 = Track(stidf)
+# Tracks for person A:
+A = Tracks(list(A1=A1,A2=A2))
+# person B, track 1:
+x = c(2,2,1,1,2,3)
+y = c(5,4,3,2,2,3)
+n = length(x)
+t = max(t) + cumsum(runif(n) * 60)
+stidf = STIDF(SpatialPoints(cbind(x,y),crs), t, data.frame(co2 = rnorm(n)))
+B1 = Track(stidf)
+# person B, track 2:
+x = c(3,3,4,3,3,4)
+y = c(5,4,3,2,1,1)
+n = length(x)
+t = max(t) + cumsum(runif(n) * 60)
+stidf = STIDF(SpatialPoints(cbind(x,y),crs), t, data.frame(co2 = rnorm(n)))
+B2 = Track(stidf)
+# Tracks for person A:
+B = Tracks(list(B1=B1,B2=B2))
+Tr = TracksCollection(list(A=A,B=B))
+stplot(Tr, scales = list(draw=TRUE))
stplot(Tr, attr = "direction", arrows=TRUE, lwd = 3, by = "direction")
stplot(Tr, attr = "direction", arrows=TRUE, lwd = 3, by = "IDs")
plot(Tr, col=2, axes=TRUE)
dim(Tr)## IDs tracks geometries
+## 2 4 24dim(Tr[2])## tracks geometries
+## 2 12dim(Tr[2][1])## geometries
+## 6u = stack(Tr) # four IDs
+dim(u)## IDs tracks geometries
+## 4 4 24dim(unstack(u, c(1,1,2,2))) # regroups to original## IDs tracks geometries
+## 2 4 24dim(unstack(u, c(1,1,2,3))) # regroups to three IDs## IDs tracks geometries
+## 3 4 24dim(unstack(u, c(1,2,2,1))) # regroups differently## IDs tracks geometries
+## 2 4 24as(Tr, "data.frame")[1:10,] # tracks separated by NA rows## x y sp.ID time endTime timeIndex
+## A.A1.1 7 7 1 2013-09-30 02:00:12 2013-09-30 02:00:12 1
+## A.A1.2 6 7 2 2013-09-30 02:00:19 2013-09-30 02:00:19 2
+## A.A1.3 5 6 3 2013-09-30 02:00:37 2013-09-30 02:00:37 3
+## A.A1.4 5 5 4 2013-09-30 02:01:00 2013-09-30 02:01:00 4
+## A.A1.5 4 5 5 2013-09-30 02:01:50 2013-09-30 02:01:50 5
+## A.A1.6 3 6 6 2013-09-30 02:02:22 2013-09-30 02:02:22 6
+## A.A1.7 3 7 7 2013-09-30 02:02:53 2013-09-30 02:02:53 7
+## A.A1.8 NA NA NA <NA> <NA> NA
+## A.A2.1 7 6 1 2013-09-30 02:03:31 2013-09-30 02:03:31 1
+## A.A2.2 6 5 2 2013-09-30 02:04:09 2013-09-30 02:04:09 2
+## co2 Track IDs
+## A.A1.1 -0.71322105 A1 A
+## A.A1.2 1.37185185 A1 A
+## A.A1.3 -0.39982855 A1 A
+## A.A1.4 -0.47880016 A1 A
+## A.A1.5 -0.54870456 A1 A
+## A.A1.6 0.48757652 A1 A
+## A.A1.7 -0.06981164 A1 A
+## A.A1.8 NA A1 A
+## A.A2.1 1.40377616 A2 A
+## A.A2.2 0.79969808 A2 Aas(Tr, "segments")[1:10,] # track segments as records## x0 y0 x1 y1 time co2 distance duration
+## A.A1.1 7 7 6 7 2013-09-30 02:00:12 -0.7132211 110495.2 7.49653
+## A.A1.2 6 7 5 6 2013-09-30 02:00:19 1.3718518 156407.3 17.59639
+## A.A1.3 5 6 5 5 2013-09-30 02:00:37 -0.3998285 110583.3 22.54678
+## A.A1.4 5 5 4 5 2013-09-30 02:01:00 -0.4788002 110898.7 50.78081
+## A.A1.5 4 5 3 6 2013-09-30 02:01:50 -0.5487046 156547.2 31.75229
+## A.A1.6 3 6 3 7 2013-09-30 02:02:22 0.4875765 110587.4 31.11752
+## A.A2.1 7 6 6 5 2013-09-30 02:03:31 1.4037762 156547.2 37.52483
+## A.A2.2 6 5 6 4 2013-09-30 02:04:09 0.7996981 110579.9 24.03699
+## A.A2.3 6 4 7 4 2013-09-30 02:04:33 -0.7110605 111050.1 34.96193
+## A.A2.4 7 4 7 3 2013-09-30 02:05:08 -1.5005960 110577.2 19.64212
+## speed direction Track IDs
+## A.A1.1 14739.515 270.06094 A1 A
+## A.A1.2 8888.604 224.87295 A1 A
+## A.A1.3 4904.618 180.00000 A1 A
+## A.A1.4 2183.870 270.04358 A1 A
+## A.A1.5 4930.266 315.17903 A1 A
+## A.A1.6 3553.863 0.00000 A1 A
+## A.A2.1 4171.830 224.91682 A2 A
+## A.A2.2 4600.407 180.00000 A2 A
+## A.A2.3 3176.316 89.96512 A2 A
+## A.A2.4 5629.598 180.00000 A2 ATr[["distance"]] = Tr[["distance"]] * 1000
+Tr$distance = Tr$distance / 1000
+Tr$distance## A.A11 A.A12 A.A13 A.A14 A.A15 A.A16 A.A21 A.A22
+## 110495.2 156407.3 110583.3 110898.7 156547.2 110587.4 156547.2 110579.9
+## A.A23 A.A24 B.B11 B.B12 B.B13 B.B14 B.B15 B.B21
+## 111050.1 110577.2 110579.9 156757.4 110575.2 111252.1 156827.6 110579.9
+## B.B22 B.B23 B.B24 B.B25
+## 156757.4 156827.6 110573.8 111302.6# work with custum TrackStats function:
+MyStats = function(track) {
+ df = apply(coordinates(track@sp), 2, diff) # requires sp
+ data.frame(distance = apply(df, 1, function(x) sqrt(sum(x^2))))
+}
+crs = CRS(as.character(NA))
+stidf = STIDF(SpatialPoints(cbind(x,y),crs), t, data.frame(co2 = rnorm(n)))
+B2 = Track(stidf) # no longer longlat;
+B3 = Track(stidf, fn = MyStats)
+all.equal(B3$distance, B2$distance)## [1] TRUE
+
+Interpolating trajectories
+opar = par()
+par(mfrow = c(1, 2))
+plot(B2, ylim = c(.5, 6))
+plot(B2, pch = 16, add = TRUE)
+title("irregular time steps")
+i = index(B2)
+B3 = approxTrack(B2, seq(min(i), max(i), length.out = 50))
+plot(B3, col = 'red', type = 'p', add = TRUE)
+B4 = approxTrack(B2, seq(min(i), max(i), length.out = 50), FUN = spline)
+plot(B4, col = 'blue', type = 'b', add = TRUE)
+# regular time steps:
+t = max(t) + (1:n) * 60 # regular
+B2 = Track(STIDF(SpatialPoints(cbind(x,y),crs), t, data.frame(co2 = rnorm(n))))
+plot(B2, ylim = c(.5, 6))
+plot(B2, pch = 16, add = TRUE)
+title("constant time steps")
+i = index(B2)
+B3 = approxTrack(B2)
+plot(B3, type = 'p', col = 'red', add = TRUE)
+B4 = approxTrack(B2, FUN = spline)
+plot(B4, type = 'p', col = 'blue', add = TRUE)
par(opar)## Warning in par(opar): graphical parameter "cin" cannot be set## Warning in par(opar): graphical parameter "cra" cannot be set## Warning in par(opar): graphical parameter "csi" cannot be set## Warning in par(opar): graphical parameter "cxy" cannot be set## Warning in par(opar): graphical parameter "din" cannot be set## Warning in par(opar): graphical parameter "page" cannot be set
+
+Smoothing trajectories
+smth = function(x,y,xout,...) predict(smooth.spline(as.numeric(x), y), as.numeric(xout))
+data(storms)
+plot(storms, type = 'p')## Warning in axis(side, at = at, labels = labels, ...): graphical parameter
+## "type" is obsolete
+
+## Warning in axis(side, at = at, labels = labels, ...): graphical parameter
+## "type" is obsolete## Warning in title(...): graphical parameter "type" is obsoletestorms.smooth = approxTracksCollection(storms, FUN = smth, n = 200)## Warning in validityMethod(object): tracks with overlapping time intervals:
+## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18## Warning in validityMethod(object): tracks with overlapping time intervals:
+## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19## Warning in validityMethod(object): tracks with overlapping time intervals:
+## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20## Warning in validityMethod(object): tracks with overlapping time intervals:
+## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10plot(storms.smooth, add = TRUE, col = 'red')
+
+Simulating random trajectories
+x = rTrack()
+dim(x)## geometries
+## 100plot(x)
x = rTracks(sd1 = 120)
+dim(x)## tracks geometries
+## 20 2000plot(as(x, "SpatialLines"), col = 1:dim(x)[1], axes=TRUE)
x = rTracksCollection() # star
+dim(x)## IDs tracks geometries
+## 10 200 20000plot(x)
x = rTracksCollection(sd2 = 200)
+plot(x, col=1:dim(x)[1])