The document proposes a new algorithm called Virtual Surrounding Face Geocasting (VSFG) to improve geocasting in wireless ad hoc and sensor networks. VSFG combines greedy face routing, face traversal, and restricted flooding using a dominating set to deliver messages to all nodes within a target region with guaranteed delivery, low transmission cost, and reduced collisions. It works in three steps: 1) forwarding the message to the boundary of a virtual surrounding face, 2) traversing the face boundaries bidirectionally, and 3) restricted flooding within the region using a dominating set.