A large range of computer graphics applications such as data visualization or virtual movie production require users to position and move viewpoints in 3D scenes to effectively convey visual information or tell stories. The desired viewpoints and camera paths are required to satisfy a number of visual properties (e.g. size, vantage angle, visibility, and on-screen position of targets). Yet, existing camera manipulation tools only provide limited interaction methods and automated techniques remain computationally expensive. In this work, we introduce the Toric space, a novel and compact representation for intuitive and efficient virtual camera control. We first show how visual properties are expressed in this Toric space and propose an efficient interval-based search technique for automated viewpoint computation. We then derive a novel screen-space manipulation technique that provides intuitive and real-time control of visual properties. Finally, we propose an effective viewpoint interpolation technique which ensures the continuity of visual properties along the generated paths. The proposed approach (i) performs better than existing automated viewpoint computation techniques in terms of speed and precision, (ii) provides a screen-space manipulation tool that is more efficient than classical manipulators and easier to use for beginners, and (iii) enables the creation of complex camera motions such as long takes in a very short time and in a controllable way. As a result, the approach should quickly find its place in a number of applications that require interactive or automated camera control such as 3D modelers, navigation tools or 3D games.