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#' @title Calculates the convex hull of X
#'
#' @description \code{calcCvxHullFaces} returns the parameters of the convex
#' hull of X: The indices of points in X that compose the faces of conv(X)
#' (one row per face) as well as the parameters of the hyperplanes that
#' describe these faces.
#'
#' @param X Set of data points (one sample per row)
#' @return A list consisting of parameters describing the convex hull of X:
#' \item{cvh}{A matrix of indices where each row constitutes one face}
#' \item{ACVH}{A matrix where each row constitutes the normal vector of a
#' face} \item{bCVH}{A vector where each entry constitutes the offset of the
#' hyperplane for a face}
calcCvxHullFaces <-function(X) {
d <- dim(X)[2]
# the 1-D case is easy
if (d == 1) {
A <- matrix(c(1,-1), ncol=1)
b <- matrix(c(max(X), -min(X)), ncol=1)
cvh <- matrix(c(which.min(X), which.max(X)), nrow = 1)
} else {
mu <- apply(X, 2, mean)
cvh <- geometry::convhulln(X);
# init param matrix/vector
A <- array(0, c(dim(cvh)[1], d))
b <- array(0, c(dim(cvh)[1], 1))
# iterate over all faces of \conv(X)
for (i in 1:dim(cvh)[1]) {
B <- X[cvh[i,1:d-1], ]-X[cvh[i,2:d], ]
if (d == 2) {
A[i, ] <- MASS::Null(B)
} else {
A[i, ] <- MASS::Null(t(B))
}
# test orientation with sample mean and reverse if necessary
if (A[i, ] %*% (X[cvh[i,1], ] - mu) < 0) {
A[i, ] <- -A[i, ]
}
b[i] <- A[i, ] %*% X[cvh[i,1], ]
}
}
r <- list(
cvh = cvh,
ACVH = A,
bCVH = b
)
return(r)
}
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