Rendering audio using speakers organized as a mesh of arbitrary N-gons

A system for rendering an audio program indicative of at least one source and a trajectory for the source, including by generating speaker feeds for panning the source along the trajectory using an array of speakers, wherein the trajectory comprises a sequence of source locations, said system including:

• a processing subsystem coupled to receive data indicative of the audio program and configured to:
• determine an initial mesh using triangulation of locations of the speakers of the array of speakers;
• wherein faces of the initial mesh are triangular faces, wherein the positions of the vertices of the triangular faces correspond to the locations of the speakers;
• and
• determine a mesh whose faces, Fi, are convex N-gons, where positions of the vertices of the N-gons correspond to locations of the speakers, i is an index in the range 1≦i≦M, M is an integer greater than 2, each of the faces, Fi, is a convex polygon having Ni sides, Ni is any integer greater than 2, and Ni is greater than 3 for at least one of the faces, wherein determining the mesh comprises replacing at least two of the triangular faces of the initial mesh by at least one replacement face which is a non-triangular, convex N-gon, such that the mesh exhibits a greater left-right symmetry and/or such that faces of the mesh are less elongated than faces of the initial mesh, thereby generating the mesh;
• wherein the replacing comprises removing edges which are shared by the at least two of the triangular faces;
• and
• for each of a plurality of source locations of the sequence source locations:
• determine a projection of the source location on a face of the mesh in response to the data indicative of the audio program;
• determine gain values for a subset of the speakers of the array of speakers whose locations correspond to the positions of the vertices of the face of the mesh;
• and
• a speaker feed generation subsystem coupled and configured to generate the speaker feeds in response to the data indicative of the audio program and the gain values.

A non-transitory storage medium containing computer-readable instructions, which, when performed by one or more processors, cause an apparatus to implement a method for rendering an audio program indicative of at least one source, including by generating speaker feeds for causing an array of speakers to pan the source along a trajectory comprising a sequence of source locations, said method comprising:

• determining an initial mesh using triangulation of locations of the speakers of the array of speakers;
• wherein faces of the initial mesh are triangular faces, wherein the positions of the vertices of the triangular faces correspond to the locations of the speakers;
• determining a mesh whose faces, Fi, are convex N-gons, where positions of the vertices of the N-gons correspond to locations of the speakers, i is an index in the range 1≦i≦M, M is an integer greater than 2, each of the faces, Fi, is a convex polygon having Ni sides, Ni is any integer greater than 2, and Ni is greater than 3 for at least one of the faces;
• wherein determining the mesh comprises replacing at least two of the triangular faces of the initial mesh by at least one replacement face which is a non-triangular, convex N-gon, thereby generating the mesh, such that the mesh exhibits a greater left-right symmetry and/or such that faces of the mesh are less elongated than faces of the initial mesh;
• wherein the replacing comprises removing edges which are shared by the at least two of the triangular faces;
• and
• for each of a plurality of source locations of the sequence of source locations:
• determining a projection of the source location on a face of the mesh;
• determining gains for a subset of the speakers of the array of speakers whose locations correspond to the positions of the vertices of the face of the mesh;
• and
• generating speaker feeds for the subset of the speakers, including by applying the gains for the subset of the speakers to audio samples of the audio program.