Sounds like you want spatialization on a plane through 8 speakers positioned on a circle?
So you need to convert any cartesian locations to polar coords first. For an approximate 3D sound effect you really only need a function to create distance (and Doppler?) effects, and then feed that output, and the angle into the planner.
The Doppler effects are the trickiest obviously. Last time I checked, real time pitch shifting as a function of change in distance was best done in the Fourier domain. Not sure how real time that is these days.
Distance effects are just inverse square of distance (or 1/ d^1.5 according to some). Then add filters for high and low frequencies. Constant power panning and variants popular and easy for speakers on a circle.
There's pseudo code in this book from memory: Dodge, Charles; Jerse, Thomas A. 1997 Computer music : synthesis, composition,
and performance. 2nd ed. New York : Schirmer Books ; London : Prentice
Hall International.
Cheers