Audio Rendering Using Convex N-gon Speaker Meshes
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Solution Overview
Problem
Conventional audio panning methods are not optimal for implementing sound pans with arbitrarily positioned speakers, leading to unstable gain variations and timbral degradation, especially when the source trajectory crosses the speaker mesh near the listener's sweet spot, and do not efficiently handle arbitrary speaker arrays or trajectories.
Innovation Solution
The method involves determining a mesh of loudspeakers with convex N-gon faces, where each face is a polygon with vertices corresponding to speaker locations, and calculating gains for subsets of speakers to accurately position sound sources along trajectories, using generalized barycentric coordinates to ensure stable and uniform panning across the speaker array.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If conventional panning methods (VBAP) are used with speakers arranged in triangular meshes, then the system can handle arbitrary speaker positions, but the gain variations become unstable and timbral degradation occurs when source trajectories cross near the listener's sweet spot
Solution Approach 1:
The speaker array is segmented into multiple convex N-gon faces that partition the spatial domain. Each face independently handles panning for sources within its region, preventing the instability that occurs when sources cross triangular mesh boundaries in conventional VBAP. This segmentation allows stable gain calculation using generalized barycentric coordinates for each N-gon face without the reliability issues of triangular meshes.
Solution Approach 2:
The invention changes the fundamental geometric parameter of the mesh structure from triangles (3-gons) to convex N-gons with N>3. This parameter change enables more speakers to be included in each panning calculation while maintaining stability, as the generalized barycentric coordinate system can handle arbitrary convex polygons. This resolves the contradiction by allowing arbitrary speaker positions while maintaining gain stability.
2Measurement precision
If more speakers are simultaneously activated to improve spatial accuracy, then the precision of sound source positioning improves, but the complexity of the system increases and timbral fidelity may degrade
Solution Approach 1:
The system dynamically determines the number of speakers to activate based on the source position relative to each N-gon face. By using convex N-gons with N>3, the system can include more speakers in each active subset than traditional triangular meshes, improving spatial precision. The dynamic gain calculation using generalized barycentric coordinates ensures that the appropriate number of speakers are activated without excessive complexity.
3Ease of manufacture
If conventional triangular mesh panning is used, then the implementation is simpler, but the uniformity of speaker activation is poor leading to timbral degradation
Solution Approach 1:
The generalized barycentric coordinate system serves as a universal mathematical framework that works for any convex N-gon configuration. This universal approach maintains implementation simplicity while improving uniformity, as the same mathematical principles apply regardless of the specific N-gon geometry. The system can handle various speaker arrangements and trajectories uniformly, resolving the contradiction between simplicity and uniformity.
Data Source
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AI summary
In some embodiments, a method for rendering an audio program indicative of at least one source, including by panning the source along a trajectory comprising source locations using speakers organized as a mesh whose faces are convex N-gons, where N can vary from face to face, and N is not equal to three for at least one face of the mesh, including steps of: for each source location, determining an intersecting face of the mesh (including the source location's projection on the mesh), thereby determining a subset of the speakers whose positions coincide with the intersecting face's vertices, and determining gains (which may be determined by generalized barycentric coordinates) for speaker feeds for driving each speaker subset to emit sound perceived as emitting from the source location corresponding to the subset. Other aspects include systems configured (e.g., programmed) to perform any embodiment of the method.