Estimating the neural activity fields of biological neurons is an important aspect of computational neuroscience research. Unfortunately, the experimental data is usually characterized by very high noise levels and follows a sparse and uneven spatial distribution, complicating the task of obtaining a reliable estimate. A technique is introduced in this article that integrates computational geometry methods with radial basis function networks to obtain reliable estimates of activity fields of individual neurons. The specific problem of extrapolating the spatio-temporal movement fields of neurons in the superior colliculus during saccadic eye movements is then addressed.