Personal sound systems have received significant research interest in the past two decades due to their promising applications in a variety of scenarios. Various methods have been proposed to generate personal sound zones, most of which are based on sound pressure manipulation in both the acoustically bright and dark zones. Since sound intensity is closely related to human perception of sound localization, this paper proposes an acoustic contrast control method with a sound intensity constraint to increase the spatial planarity in the bright zone. In the proposed method, the sound intensity in the bright zone is projected to a specific direction while the sound pressure level in the dark zone is minimized. Simulations and experiments are carried out to compare the proposed method with the existing planarity control and pressure matching methods in terms of acoustic contrast, array effort, and planarity. The results demonstrate that the proposed method improves the planarity in the bright zone compared to existing planarity control method, while exhibitig a higher acoustic contrast and a lower array effort than the pressure matching method.