Because of its accuracy, the measurement of a point source throughout the field of view of a PET or SPECT camera has been an attractive approach to derive system response. The procedure however is tedious; Instead, a coarse grid of discrete point source measurements may be experimentally measured while interpolation is used to derive the system response on a finer grid. Existing techniques suffer from the parameterization of the system response to a discrete number of variables. Here we propose an object-space interpolation that imposes no prior knowledge on the the geometric system response and can be widely applied for SPECT imaging systems of any kind. When using graphics hardware, the computational performance of this method enables its use for on-the-fly interpolation in iterative reconstruction, substantially reducing memory and storage requirements.