Selection and interpolation of head-related transfer functions for rendering moving virtual sound sources

A variety of approaches have been proposed previously to interpolate
head-related transfer functions (HRTFs). However, relatively
little attention has been given to the way a suitable set of HRTFs is
chosen for interpolation and to the calculation of the interpolation
weights. This paper presents an efficient and robust way to select
a minimal set of HRTFs and to calculate appropriate weights for
interpolation. The proposed method is based on grouping HRTF
measurement points into non-overlapping triangles on the surface
of a sphere by calculating the convex hull. The resulting Delaunay
triangulation maximises minimum angles. For interpolation,
the HRTF triangle that is intersected by the desired sound source
vector is selected. The selection is based on a point-in-triangle
test than can be performed using just 9 multiplications and 6 additions
per triangle. A further improvement of the selection process
is achieved by sorting the HRTF triangles according to their distance
from the sound source vector prior to performing the pointin-
triangle tests. The HRTFs of the selected triangle are interpolated
using weights derived from vector-base amplitude panning,
with appropriate normalisation. The proposed method is compared
to state-of-the-art methods. It is shown to be robust with respect to
irregularities in the HRTF measurement grid and to be well-suited
for rendering moving virtual sources.