We calculate the probability (``quenching weight'') that a hard parton
radiates an additional energy fraction due to scattering in spatially extended
QCD matter. This study is based on an exact treatment of finite in-medium path
length, it includes the case of a dynamically expanding medium, and it extends
to the angular dependence of the medium-induced gluon radiation pattern. All
calculations are done in the multiple soft scattering approximation
(Baier-Dokshitzer-Mueller-Peign\'e-Schiff--Zakharov ``BDMPS-Z''-formalism) and
in the single hard scattering approximation (N=1 opacity approximation). By
comparison, we establish a simple relation between transport coefficient, Debye
screening mass and opacity, for which both approximations lead to comparable
results. Together with this paper, a CPU-inexpensive numerical subroutine for
calculating quenching weights is provided electronically. To illustrate its
applications, we discuss the suppression of hadronic transverse momentum
spectra in nucleus-nucleus collisions. Remarkably, the kinematic constraint
resulting from finite in-medium path length reduces significantly the
transverse momentum dependence of the nuclear modification factor, thus leading
to consistency with the data measured at the Relativistic Heavy Ion Collider
(RHIC).Comment: 45 pages LaTeX, 20 eps-figure