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pd-vbap 1.1-2
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A Pd port of the VBAP object for Max/MSP

Written by Ville Pulkki
Helsinki University of Technology
Laboratory of acoustics and audio signal processing

http://www.acoustics.hut.fi/research/cat/vbap/

 This is a library for Pure Data for sound spatialization using the
 vector base amplitude panning (VBAP) method.  VBAP is an amplitude
 panning method to position virtual sources in arbitrary 2-D or 3-D
 loudspeaker setups. In amplitude panning the same sound signal is
 applied to a number of loudspeakers with appropriate non-zero
 amplitudes. With 2-D setups VBAP is a reformulation of the existing
 pair-wise panning method. However, differing from earlier solutions
 it can be generalized for 3-D loudspeaker setups as a triplet-wise
 panning method. A sound signal is then applied to one, two, or three
 loudspeakers simultaneously. VBAP has certain advantages compared to
 earlier virtual source positioning methods in arbitrary
 layouts. Previous methods either used all loudspeakers to produce
 virtual sources, which results in some artefacts, or they used
 loudspeaker triplets with a non-generalizable 2-D user interface.

 The directional qualities of virtual sources generated with VBAP can
 be stated as follows. Directional coordinates used for this purpose
 are the angle between a position vector and the median plane (θcc),
 and the angle between a projection of a position vector to the median
 plane and frontal direction (Φcc). The perceived θcc direction of a
 virtual source coincides well with the VBAP panning direction when a
 loudspeaker set is near the median plane. When the loudspeaker set is
 moved towards a side of a listener, the perceived θcc direction is
 biased towards the median plane. The perceived Φcc direction of an
 amplitude-panned virtual source is individual and cannot be predicted
 with any panning law.