Although distance-dependent head-related transfer function (HRTF) databases provide interesting possibilities, e.g., for rendering virtual sounds in the near-field, there is a lack of algorithms and tools to make use of them. Here, a framework is proposed for interpolating HRTF measurements in 3-D (i.e., azimuth, elevation, and distance) using tetrahedral interpolation with barycentric weights. For interpolation, a tetrahedral mesh is generated via Delaunay triangulation and searched via an adjacency walk, making the framework robust with respect to irregularly positioned HRTF measurements and computationally efficient. An objective evaluation of the proposed framework indicates good accordance between measured and interpolated near-field HRTFs.