plotGeodesic: Plot previously computed Wasserstein geodesics
In WSGeometry: Geometric Tools Based on Balanced/Unbalanced Optimal Transport

Description Usage Arguments Value Examples

This function generates either a sequence of images or a gif displaying the input optimal transport geodesic.

plotGeodesic(
  Geodesic,
  method = "default",
  images = FALSE,
  gif = FALSE,
  File = "Geodesic",
  resolution = c(400, 400),
  dotsize = 2,
  gridsize = c(100, 100),
  out.col = grey(0:1000/1000),
  splitrange = c(1, 1),
  turn = FALSE,
  phi = 40,
  theta = 40,
  fps = NULL
)

`Geodesic`	A list of measures in R^2 or R^3 corresponding to the discretized time steps of the geodesic. Each entry in the list must be one of the following: a pp-object; a wpp-object; or a list containing an entry named 'positions' that is an Mxd matrix.
`method`	A string specifying the method used to plot each measure. The input "default" generates a scatterplot where the size of each point corresponds to its mass. The input "bin" maps the data to a grid of prespecified size to plot it as an image. The input "binSplit" also maps the data to a grid, but afterwards the mass of each pixel is split between all pixels in a specified range. This generates smoother output images.
`images`	A boolean specifying whether image files should be generated.
`gif`	A boolean specifying whether a gif should be generated. To use this option the ImageMagick software and the magick R package need to be installed. (see https://cran.r-project.org/web/packages/magick/vignettes/intro.html for details and instructions.)
`File`	A string specifying the prefix of all generated files.
`resolution`	A vector with two elements specifying the resolution of the output images.
`dotsize`	A positive number working as a multiplier on the size of the dots in the output generated by the default method.
`gridsize`	A vector with two elements specifying the size of the grid used for "bin" and "binSplit".
`out.col`	A colour vector, specifying the colour scheme used in the call of the image function when plotting the output of the "bin" and "binSplit" methods. See the documentation of the image function for more details.
`splitrange`	A vector of two positive integers specifying the number of pixels the mass of a point is shared with in the "binSplit" method. The first entry controls the horizontal direction and the second controls the vertical direction.
`turn`	A boolean specifying whether the image should be rotated to account for the output of the image function.
`phi`	A number specifying the viewing direction in the three dimensional method. It gives the colatitude of the plot.
`theta`	A number specifying the viewing direction in the three dimensional setting. It gives the azimuthal direction of the plot.
`fps`	A positive number specifying the number of frames per second in the output gif. The default adjusts the fps to output a gif file of length 10 seconds.

This function does not provide any return value, but instead generates output files in the current working directory.

#2D-Example:
library(transport)
set.seed(420)
N<-2
supp.size<-10^2
L<-sqrt(supp.size)
d<-2
data.list<-vector("list",N)
image.list<-vector("list",N)
for (i in 1:N){
  t.vec<-seq(0,2*pi,length.out=supp.size)
  pos<-cbind(cos(t.vec)*runif(1,0.2,1),sin(t.vec)*runif(1,0.2,1))
  theta<-runif(1,0,2*pi)
  rotation<-matrix(c(cos(theta),sin(theta),-1*sin(theta),cos(theta)),2,2)
  pos<-pos%*%rotation
  pos<-pos+1
  pos<-pos/2
  W<-rep(1/supp.size,supp.size)
  data.list[[i]]<-transport::wpp(pos,W)
}
Geo<-geodesic_pos(data.list[[1]],data.list[[2]],2,seq(0,1,0.1))
## Set the image and/or gif flags to TRUE to run the example. 
## CRAN policy prevents examples from generating files in the working directory,
## so this had to be disabled.
plotGeodesic(Geo,File="TestGeodesicDefault",images=FALSE,gif=FALSE)
plotGeodesic(Geo,method="bin",File="TestGeodesicDefaultBin",images=FALSE,gif=FALSE)
plotGeodesic(Geo,method="binSplit",File="TestGeodesicDefaultBinSPlit",
images=FALSE,gif=FALSE)

#3D-Example:
#Functions to build the example measures
gen_torus<-function(M,R,r){
 theta<-seq(0,2*pi,length.out=M)
 phi<-seq(0,2*pi,length.out=M)
 G<-expand.grid(theta,phi)
 x<-(R+r*cos(G[,1]))*cos(G[,2])
 y<-(R+r*cos(G[,1]))*sin(G[,2])
 z<-r*sin(G[,1])
 return(cbind(x,y,z))
}
sq_norm<-function(v){
 return(sqrt(sum(v^2)))
}
normalize<-function(v){
 return(v/(sq_norm(v)))
}
rotate3D<-function(pos,axis,angle){
 R<-matrix(0,3,3)
 R[1]<-cos(angle)+axis[1]^2*(1-cos(angle))
 R[2]<-axis[1]*axis[2]*(1-cos(angle))+axis[3]*sin(angle)
 R[3]<-axis[3]*axis[1]*(1-cos(angle))-axis[2]*sin(angle)
 R[4]<-axis[1]*axis[2]*(1-cos(angle))-axis[3]*sin(angle)
 R[5]<-cos(angle)+axis[2]^2*(1-cos(angle))
 R[6]<-axis[2]*axis[3]*(1-cos(angle))+axis[1]*sin(angle)
 R[7]<-axis[1]*axis[3]*(1-cos(angle))+axis[2]*sin(angle)
 R[8]<-axis[2]*axis[2]*(1-cos(angle))-axis[1]*sin(angle)
 R[9]<-cos(angle)+axis[3]^2*(1-cos(angle))
 return(t(diag(c(2,3,1))%*%(R%*%t(pos))))
}
## Example
set.seed(123)
M<-40
U<-runif(1,0.5,1)
Torus<-gen_torus(M,U,min(U/2,runif(1)))
v<-normalize(runif(3))
Torus<-rotate3D(Torus,v,runif(1,0,2*pi))
Torus1<-Torus%*%diag(runif(3,1,3))
U<-runif(1,0.5,1)
Torus<-gen_torus(M,U,min(U/2,runif(1)))
v<-normalize(runif(3))
Torus<-rotate3D(Torus,v,runif(1,0,2*pi))
Torus2<-Torus%*%diag(runif(3,1,3))
L<-length(Torus)/3
Torus1<-transport::wpp(Torus1,rep(1/L,L))
Torus2<-transport::wpp(Torus2,rep(1/L,L))
geo<-geodesic_pos(Torus1,Torus2,p=2,seq(0,1,0.1))
## Set the image and/or gif flags to TRUE to run the example. 
## CRAN policy prevents examples from generating files in the working directory,
## so this had to be disabled.
plotGeodesic(geo,File="3dGeodesic",images=FALSE,gif=FALSE)