When using a gesture-based interface for pointing to targets on a wide screen, displaying a large pointer instead of a typical spot pattern reduces disturbance caused by measurement errors of user's pointing posture. However, it remains unclear why a large pointer helps facilitate easy pointing. To examine this issue, in this study we propose a mathematical model that formulates human pointing motions affected by a large pointer. Our idea is to describe the effect of the large pointer as human visual perception, because the user will perceive the pointer-target distance as being shorter than it actually is. We embedded this scheme, referred to as non-linear distance filter (NDF), into a typical feedback loop model designed to formulate human pointing motions. We also proposed a method to estimate NDF mapping from pointing trajectories, and used it to investigate the applicability of the model under three typical disturbance patterns: small vibration, smooth shift, and step signal. Experimental results demonstrated that the proposed NDF-based model could accurately reproduced actual pointing trajectories, achieving high similarity values of 0.89, 0.97, and 0.91 for the three respective disturbance patterns. The results indicate the applicability of the proposed method. In addition, we confirmed that the obtained NDF mappings suggested rationales for why a large pointer helps facilitate easy pointing.