Direct manipulation can be used as an intuitive interface for spatial interaction with multiple objects in virtual environments. However, users often have difficulties in precisely manipulating objects in the 3D space; this is mainly because the user is not provided with enough visual information to sufficiently recognize the spatial relationships among objects. We present a new method for improving the preciseness of object manipulation in the 3D space by providing the user with an auxiliary view that is consistently retargeted to closely highlight the spatial relationship between the manipulated object and the object nearest to it. Both the target and the position of the auxiliary camera are computed efficiently using the bisector surface of the two involved objects. The viewing target is set to the center of the closest area between the two objects, and the camera position is optimized under an objective function primarily measuring the visual clarity of the auxiliary view. We demonstrate the usefulness of our method through various experiments based on practical usage scenarios.

Popular virtual reality systems today allow us to experience highly immersive applications in which virtual objects are realistically perceived via stereoscopic displays and can be directly manipulated based on hand-eye coordination in a very similar way as in the real world. However, the insufficiency of sensory feedback as well as the limited degrees-of-freedom of input motion still hinders precise and elaborate manipulation in virtual reality. Aiming at more precise 3D manipulation, we present a new method of extending the user's spatial perception ability with the 'virtual mirrors', which expose the hidden spatial information of given virtual scenes to the user. The movement of a virtual mirror is automatically controlled by solving an optimization problem iteratively, in which the objective function prefers the placement of the mirror that can highlight the spatial relationship between the manipulated object and the object nearest to it. The optimization process is handled efficiently for each time step based on our method for finding the closest gap between any two objects based on the OBB (oriented bounding box) trees and our samplingbased approximate approach to the optimization problem. The usefulness of our method is demonstrated by several pilot applications under various usage scenarios, such as assembling construction toys and solving 3D dissection puzzles. The quantitative results of our user study show that the virtual mirror is very helpful in increasing the precision in 3D manipulation tasks in virtual reality.