I have been researching methods to compute the Laplacian/Laplace-Beltrami operator, but I’ve found that R lacks built functions for these purposes. There is actually a package that allows for normalization of such operator ::matrixLaplacian.

I am interested in deriving the Laplace-Beltrami operator using a discrete approach, preferably Delaunay triangulation.

The main steps are: 1) Create a mesh using the Delaunay triangulation 2) Compute the area matrix and cotangent weight matrix (which is the Laplace-Beltrami discrete operator). To do it so, the cotangent is used.

I am also open to receive any other approaches.

#Just for starters
vertices <- matrix(runif(30), ncol = 10)
colnames(vertices) <- c("x", "y", "z")
tri_mesh <- geometry::delaunayn(vertices) #creating a mesh?

#Possible solution using igraph ? (not sure this might be correct)
library(igraph)
g <- graph_from_data_frame(tri_mesh, directed = FALSE, vertices = 1:10)
L <- laplacian_matrix(g,normalized = T, weights = NA)