We present the detailed construction and analysis of the most complete map to
date of the circumstellar environment around SN 1987A, using ground and
space-based imaging from the past 16 years. PSF-matched difference-imaging
analyses of data from 1988 through 1997 reveal material between 1 and 28 ly
from the SN. Careful analyses allows the reconstruction of the probable
circumstellar environment, revealing a richly-structured bipolar nebula. An
outer, double-lobed ``Peanut,'' which is believed to be the contact
discontinuity between red supergiant and main sequence winds, is a prolate
shell extending 28 ly along the poles and 11 ly near the equator. Napoleon's
Hat, previously believed to be an independent structure, is the waist of this
Peanut, which is pinched to a radius of 6 ly. Interior to this is a cylindrical
hourglass, 1 ly in radius and 4 ly long, which connects to the Peanut by a
thick equatorial disk. The nebulae are inclined 41\degr south and 8\degr east
of the line of sight, slightly elliptical in cross section, and marginally
offset west of the SN. From the hourglass to the large, bipolar lobes, echo
fluxes suggest that the gas density drops from 1--3 cm^{-3} to >0.03 cm^{-3},
while the maximum dust-grain size increases from ~0.2 micron to 2 micron, and
the Si:C dust ratio decreases. The nebulae have a total mass of ~1.7 Msun. The
geometry of the three rings is studied, suggesting the northern and southern
rings are located 1.3 and 1.0 ly from the SN, while the equatorial ring is
elliptical (b/a < 0.98), and spatially offset in the same direction as the
hourglass.Comment: Accepted for publication in the ApJ Supplements. 38 pages in
apjemulate format, with 52 figure