  We compare various approaches to find the most efficient method for the
practical computation of the lightcurves (integrated brightnesses) of
irregularly shaped bodies such as asteroids at arbitrary viewing and
illumination geometries. For convex models, this reduces to the problem of the
numerical computation of an integral over a simply defined part of the unit
sphere. We introduce a fast method, based on Lebedev quadratures, which is
optimal for both lightcurve simulation and inversion in the sense that it is
the simplest and fastest widely applicable procedure for accuracy levels
corresponding to typical data noise. The method requires no tessellation of the
surface into a polyhedral approximation. At the accuracy level of 0.01 mag, it
is up to an order of magnitude faster than polyhedral sums that are usually
applied to this problem, and even faster at higher accuracies. This approach
can also be used in other similar cases that can be modelled on the unit
sphere. The method is easily implemented in lightcurve inversion by a simple
alteration of the standard algorithm/software.
