Head-related transfer functions (HRTFs) explore the spatial auditory characteristics of human and can be used in various applications such as spatial audio and 3D games. Since non-individualized HRTFs cause high elevation localization error and front/back confusion, individualizing HRTFs are required for more precise three-dimensional localization. However, HRFTs measurement for each individual is expensive and time-consuming. In this paper, we use ray tracing techniques to simulate individualized HRTFs. Ray tracing techniques, however, show limited performance in simulating diffraction of sound. In order to solve such problem, Kirchhoff-Helmholtz integral is applied to ray tracing, so called Multiple Source Ray Tracing. We conducted experiments using binaural and spectral cues as performance measurement, and verified that the proposed method yields performance comparable to the measured HRFTs.
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