  The volume-of-tube formula was first introduced by Hotelling (1939), to solve
significance of terms in nonlinear regression models. Since this pioneering
paper, there has been significant work on extending the tube formula to more
general settings, including multidimensional problems, and many new
applications in statistical inference, including confidence bands in regression
and smoothing models; applications to functional data analysis; testing in
mixture models; and spatial scan analysis.
  Implementation of the tube formula requires numerical evaluation of certain
problem-specific geometric constants that appear in Hotelling's formula and its
extensions. The purpose of this note is to describe a software library,
libtube, that performs the calculations. A variety of illustrative examples are
given.
  Source code for the libtube library andexamples can be downloaded from
http://www.herine.net/stat/libtube/.
