  The variable continuum emission of an active galactic nucleus (AGN) produces
corresponding responses in the broad emission lines, which are modulated by
light travel delays, and contain information on the physical properties,
structure, and kinematics of the emitting gas region. The reverberation mapping
technique, a time series analysis of the driving light curve and response, can
recover some of this information, including the size and velocity field of the
broad line region (BLR). Here we introduce a new forward-modeling tool, the
Broad Emission Line MApping Code (BELMAC), which simulates the
velocity-resolved reverberation response of the BLR to any given input light
curve by setting up a 3D ensemble of gas clouds for various specified
geometries, velocity fields, and cloud properties. In this work, we present
numerical approximations to the transfer function by simulating the
velocity-resolved responses to a single continuum pulse for sets of models
representing a spherical BLR with a radiatively driven outflow and a disk-like
BLR with Keplerian rotation. We explore how the structure, velocity field, and
other BLR properties affect the transfer function. We calculate the
response-weighted time delay (reverberation "lag"), which is considered to be a
proxy for the luminosity-weighted radius of the BLR. We investigate the effects
of anisotropic cloud emission and matter-bounded (completely ionized) clouds
and find the response-weighted delay is only equivalent to the
luminosity-weighted radius when clouds emit isotropically and are
radiation-bounded (partially ionized). Otherwise, the luminosity-weighted
radius can be overestimated by up to a factor of 2.
