#' @export
ring <- function(Tr0, V, Tr, TV, n.layer = 2){
I.tr = c(Tr0)
V1 = c(); T1 = c();
for(i in 1:n.layer){
k = length(I.tr)
J = c()
for(j in 1:k){
J1 = which(TV[, I.tr[j]] != 0)
J = c(J, J1)
}
V2 = Tr[J, ]
I.tr = c(V2)
V1 = c(V1, I.tr)
T1 = c(T1, J)
}
V1 = sort(unique(V1))
I.tr = V1
V1 = V[I.tr, ]
T1 = Tr[sort(unique(T1)), ]
T.sub = T1
nt = nrow(T1)
for(i in 1:nt){
j = T1[i, 1]; nj = which(I.tr == j); T1[i, 1] = nj
j = T1[i, 2]; nj = which(I.tr == j); T1[i, 2] = nj
j = T1[i, 3]; nj = which(I.tr == j); T1[i, 3] = nj
}
j = Tr0[1]; nj = which(I.tr == j); Tr0[1] = nj
j = Tr0[2]; nj = which(I.tr == j); Tr0[2] = nj
j = Tr0[3]; nj = which(I.tr == j); Tr0[3] = nj
ring.tri = list(V1 = V1, T1 = T1, Tr0 = Tr0, I.tr = I.tr, T.sub = T.sub)
}
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