Humans use tactile and force cues to explore the environment around them and to identify and manipulate objects. An ideal human-machine interface for virtual environments should empower the user to feel and orient objects by providing force feedback. The synthesis of force and torque feedback arising from object-object interaction, commonly referred to as six-degree-of-freedom (6-DoF) haptic rendering, can greatly benefit many applications involving dexterous manipulation and complex maneuvering of virtual objects. Examples of such applications include assembly and disassembly operations in rapid prototyping, endoscopic surgical training, and virtual exploration with limited visual feedback. However, existing techniques for 6-DoF haptic rendering are applicable only to relatively simple contact configurations or low-complexity models.; In this dissertation, I propose a novel approach for 6-DoF haptic rendering that combines multiresolution representations, hierarchical collision detection algorithms, and perception-based force models. This approach enables 6-DoF haptic rendering of interaction between two polygonal models of high combinatorial complexity. I introduce contact levels of detail, a collision detection algorithm based on multiresolution hierarchies for performing contact queries between complex models at force update rates, by adaptively selecting the appropriate contact resolutions. I also present a new algorithm for 6-DoF haptic rendering of intricate interaction between textured surfaces, based on a perceptually inspired force model and the representation of the objects as low-resolution models with haptic textures. Finally, I derive a novel implicit formulation for computing rigid body dynamics with haptic interaction, and I integrate all these techniques together, thereby achieving stable and responsive 6-DoF haptic rendering.
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