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Haptic exploration adds an additional dimension to working with 3D data: a sense of touch. This is especially useful in areas such as medical simulation, training and pre-surgical planning, as well as in museum display, sculpting, CAD, military applications, assistive technology for blind and visually impaired, entertainment and others. There exist different surface- and voxel-based haptic rendering methods. Unaddressed practical problems for almost all of them are that no guarantees for collision detection could be given and/or that a special topological structure of objects is required. Here we present a novel and robust approach based on employing the ray casting technique to collision detection, which does not have the aforementioned drawbacks while guaranteeing nearly constant time complexity independent of data resolution. This is especially important for such delicate procedures as pre-operation planning. A collision response in the presented prototype system is rigid and operates on voxel data, and no precalculation is needed. Additionally, our collision response uses an implicit surface representation "on the fly", which can be used with dynamically changing objects. [ABSTRACT FROM PUBLISHER]