Pursuit-evasion games in complex environments have a rich but disconnected history. Continuous or differential pursuit-evasion games focus on optimal control methods, and rely on very intense computations in order to provide locally optimal controls. Discrete pursuit-evasion games on graphs are algorithmically much more appealing, but completely ignore the physical dynamics of the players, resulting in possibly infeasible motions. In this paper, we present a provable and algorithmically feasible solution for visibility-based pursuit-evasion games in simply-connected environments, for players with dynamic constraints. This is achieved by combining two recent but distant results.