Delay Lines and Effects
69
Vector Base Panning
Room within a Room
· If the virtual source is located at a loudspeaker position only that loud-
speaker has nonzero gain;
· If the virtual source is located on a line connecting two loudspeakers only
those two loudspeakers have nonzero gain;
· If the virtual source is located on the triangle delimited by three adjacent
loudspeakers only those three loudspeakers have nonzero gain.
The formulation of VBAP given here is consistent with the low frequency
formulation of directional psychoacoustics. The extension to high frequencies
have been also proposed with the name Vector Base Panning (VBP) [68].
Room within a room
A different approach to spatialization using loudspeakers can be taken by con-
trolling the relative time delay between the loudspeaker feeds. A model sup-
porting this approach was introduced by Moore [60], and can be described as
a physical and geometric model. The metaphor underlying the Moore model is
that of the Room within a Room, where the inner room has holes in the walls,
corresponding to the positions of loudspeakers, and the outer room is the vir-
tual room where sound events have to take place (fig. 13). The simplest form of
1
2
3
4
Figure 13: Moore's Room in a Room Model
spatialisation is obtained by drawing direct sound rays from the virtual sound
source to the holes of the inner room. If the outer room is anechoic these are
the only paths taken by sound waves to reach the inner room. The loudspeakers
will be fed by signals delayed by an amount proportional to the length of these
paths, and attenuated according to relationship of inverse proportionality valid
for propagation of spherical waves. In formulas, if l
i
is the path length from the
source to the i-th loudspeaker, and c is the speed of sound in air, the delay in
seconds is set to
d
i
= l
i
/c ,
(37)
and the gain is set to
g
i
=
1
l
i
, l
i
> 1
1, l
i
< 1
.
(38)