% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/ComplexUtils.R
\name{min_enclosing_ball}
\alias{min_enclosing_ball}
\title{Minimum enclosing ball of a finite point set (Welzl's algorithm)}
\usage{
min_enclosing_ball(points)
}
\arguments{
\item{points}{A numeric matrix, one point per row (at least 1 row).}
}
\value{
A list with \code{center} (numeric vector) and \code{radius}.
}
\description{
Used by \code{\link{CechComplex}}: the Cech complex includes a simplex
\eqn{\sigma} at scale \eqn{\epsilon} exactly when the balls of radius
\eqn{\epsilon} centered at its vertices have a common point, which happens
if and only if the minimum enclosing ball of \eqn{\sigma}'s vertices has
radius at most \eqn{\epsilon} (this is the standard reduction used e.g. by
GUDHI's Cech complex; see Cavanna, Jahanseir and Sheehy (2017)).
}
\details{
Randomized, expected linear-time in the number of points; the point sets
passed in here are the vertices of a single simplex, so they are always
small.
}
\keyword{internal}
