  In this paper, we first summarize the existing algorithms for computing all
the generalized asymptotes of a plane algebraic curve implicitly or
parametrically defined. From these previous results, we derive a method that
allows to easily compute the whole branch and all the generalized asymptotes of
a special curve defined in n-dimensional space by a parametrization that is not
necessarily rational. So, some new concepts and methods are established for
this type of curves. The approach is based on the notion of perfect curves
introduced from the concepts and results presented in previous papers.
