Stereo triangle response

This is a direct-sound point-source model with piston directivity, complex Linkwitz–Riley filters, geometric spreading and propagation phase. It excludes the room, cabinet-edge diffraction and a loudspeaker’s native response.

• The Brown–Duda head-shadow approximation is enabled by default; disabling it makes the ears acoustically transparent pressure probes.
• Rear-facing piston angles are clamped to the 90° directivity value, preventing the circular-piston pattern from mirroring into the rear hemisphere.
• The deterministic movement cloud is uniform by volume inside an ellipsoid with separate horizontal and vertical radii, and always includes the exact center position.
• The console tests assert 0 dB for one on-axis speaker at 1 m below crossover, +6.02 dB for two coherent speakers at 20 Hz, and numerical left/right equality under mirror symmetry.
• The crossover test checks that LR2 is flat on axis with the woofer inverted and produces a deep null at f_c when that polarity is flipped.
• Single-speaker interaural path check: —
• The binaural curve is an energy mean, not a coherent sum of the ears; the theoretical interaural notch is therefore a path check rather than a notch added to that curve.