A physics-based low-order filter approximation for scattering from a rigid sphere

Efficient simulation of object scattering is crucial in virtual and room acoustics, particularly for interactive scenarios where time-varying diffraction must be evaluated repeatedly in real-time. In this context, the rigid sphere is commonly used as a simple geometric representation of more complex three-dimensional objects. Although the analytical solution for rigid sphere scattering is well known, its computation is too involved for interactive audio rendering. In this paper, we propose a physically informed, low-order digital filter approximation of rigid sphere scattering for arbitrary source and receiver positions. For the low-frequency range, the first three terms of the spherical harmonics analytical solution are directly expressed by combined first-order low- and high-pass filters. For high-frequencies, the basic properties of rigid sphere scattering are approximated by modelling the shortest and longest paths reflected or bent around the sphere. Both approximations are combined using a blending function to obtain the wideband result. The magnitude of the low-frequency approximation matches the analytical solution well, yielding mean root mean square errors below 0.5 dB for source and receiver distances greater than twice the sphere radius and about 1.5 dB at smaller distances. For the high-frequency range, the mean error in magnitude is overall larger and is about 2 dB.