  Herein I present numerical calculations of lightcurves of homogeneous and
structured afterglows with various lateral expansion rates as seen from any
vantage point. Such calculations allow for direct simulation of observable
quantities for complex afterglows with arbitrary energy distributions and
lateral expansion paradigms. A simple, causal model is suggested for lateral
expansion of the jet as it evolves; namely, that the lateral expansion kinetic
energy derives from the forward kinetic energy. As such the homogeneous jet
model shows that lateral expansion is important at all times in the afterglow
evolution and that analytical scaling laws do a poor job at describing the
afterglow decay before and after the break. In particular, I find that lateral
expansion does not cause a break in the lightcurve as had been predicted. A
primary purpose of this paper is to study structured afterglows, which do a
good job of reproducing global relationships and correlations in the data and
thus suggest the possibility of a universal afterglow model. Simulations of
structured jets show a general trend in which jet breaks become more pronounced
with increasing viewing angle with respect to the jet axis. In fact, under
certain conditions a bump can occur in the lightcurve at the jet break time. I
derive scaling relations for this bump and suggest that it may be a source of
some bumps in observed lightcurves such as that of GRB 000301C. A couple of
lateral expansion models are tested over a range of efficiencies and viewing
angles and it is found that lateral expansion can, in some cases, substantially
sharpen the jet break. I show flux surface contour maps and simulated images of
the afterglows which give insight into how they evolve and determine their
lightcurves.
