Human reaching in a 3D environment is an interesting matter of research due to its application to workplace or vehicle-interior design. We introduce a 3D environment where a virtual human performs reaching tasks over 3D objects in the world. This environment also provides tools to generate and visualize reachable volumes. Reachable spaces are approximated using adjacent box-shaped voxels. We define several strategies in order to model different types of reaching, and we employ our system to construct and analyze reachable spaces for these strategies. In general, different strategies do have reachable spaces that share a common region of intersection. Therefore, goals exists that can be reached using two or more strategies. For those goals, a high-level layer is responsible for selecting the most appropriate given a certain reaching task. As a practical application, this paper presents a comparison of two usual strategies to model standing and seated reaching. The generated reach spaces show that, for each of them, a strategy is clearly more adequate than the other