An experimental R package that performs triangulation & 2D optimal transportation for uniform measure.
In R console, run devtools::install_github("Francis-Hsu/CGALTri").
For Windows user, Makevars.win must be modified to provide correct paths for Boost and CGAL libraries. vcpkg is highly recommended.
CGAL 4.13
library(MASS)
library(CGALTri)
# example given in CGAL document
X = matrix(c(0, 0, 1, 1, 0, 1), 3, 2, byrow = T)
B = c(-1, -1, 2, 2)
TX = Triangulation_2D(X, B)
plot(TX)
# generate some random data
n = 25
X = 2 * mvrnorm(n, rep(0, 2), diag(2))
# uncropped triangulation
TX = Triangulation_2D(X)
plot(TX)
# now crop it
B = c(-2, -2, 2, 2)
TX = Triangulation_2D(X, B)
plot(TX)
# regular triangulation
w = sample(1:3 / 10, n, replace = T)
wX = cbind(X, w)
TwX = Triangulation_2D(wX, type = "Reg")
plot(TwX)CGAL, Computational Geometry Algorithms Library.
Bruno Lévy, Erica L. Schwindt, Notions of optimal transport theory and how to implement them on a computer, Computers & Graphics, Volume 72, 2018, Pages 135-148, ISSN 0097-8493, https://doi.org/10.1016/j.cag.2018.01.009.