Support for QuadRegion in VBAP

[galanhir]

Problem to Solve

Currently, a Left-Right symmetric loudspeaker geometry may end up in an AllRAD designed decoder without Left-Right symmetry. As far as I understand, this may happen during the VBAP phase, during the triangulation, when 4 loudspeakers, e.g. {L1, L2, R2, R1} happens to be coplanar. In such case, the actual triangulation ends up choosing one of the two triangles configuration, e.g. {L1, L2, R2} and {R1, R2, L1}, and eventually produces a matrix that have lost the Left-Right symmetry.

Current Workaround

The best work-around, so far, is to add a virtual loudspeaker, Z, in such a way that the triangulation of {L1, L2, R2, R1,Z} produces 4 triangles and eventually, to downmix Z onto L1, L2, R2, R1.

Proposed Solution

One possible way forward is to adapt VBAP in a way similar to 6.1.2.3 QuadRegion from ITU-R BS.2127-1, i.e. by allowing quadrilateral to be handled and to create its panning accordingly.

Additional Information

In order to reproduce explicitly the issue, consider for instance an AllRAD design given those 4 side loudspeakers {L1, L2, R2, R1} : {110, 0}, {90, 60}, {-90, 60}, {-110, 0}. Add for instance 3 front loudspeaker to complete the sphere coverage: {30, 0}, {-30,0} and {0,0}. Note also that in that case, adding a 8th loudspeaker in e.g. {180, 30} re-establishes the symmetry of the decoder.