Activity spaces describe the physical area typically encountered by an individual person during his or her routine daily activities. Activity spaces encompass a person’s anchor points – locations that are frequented regularly, such as home, work, school, and recreational areas – and the travel paths that connect them. Activity spaces of criminals are routinely mapped in order to better understand the spatial patterns and processes of crime at the individual level. Although many geographic information system-based methods have been used to map activity spaces over the years, potential path areas are becoming a preferred method since they incorporate both spatial and temporal data, as well as time budget and mobility constraints. This paper extends potential path areas for mapping activity spaces of criminals in two ways. First, time-geographic density estimation (TGDE) is used to estimate individual activity spaces using potential path areas that have associated probability densities. Second, activity spaces of numerous individuals are combined into a single intensity surface that maps areas of a city that are more frequented by offenders and, accordingly, expected to support higher crime rates. The approach is demonstrated using a dataset of home and work addresses of registered sex offenders in the city of St. Louis. The final density surface of their combined activity spaces is related to the locations of reported sex crimes. The results highlight how sex crimes are concentrated in offender activity spaces and suggest the approach might be useful for predictive policing.