  We study pursuit-evasion differential games between a faster pursuer moving
in 3D space and an evader moving in a plane. We first extend the well-known
Apollonius circle to 3D space, by which we construct the isochron for the
considered two players. Then both cases with and without a static target are
considered and the corresponding optimal strategies are derived using the
concept of isochron. In order to guarantee the optimality of the proposed
strategies, the value functions are given and are further proved to be the
solution of Hamilton-Jacobi-Isaacs equation. Simulations with comparison
between the proposed strategies and other classical strategies are carried out
and the results show the optimality of the proposed strategies.
