Date of Completion


Embargo Period



Thomas J. Peters and Chun-Hsi (Vincent) Huang

Field of Study

Computer Science and Engineering


Master of Science

Open Access

Open Access


Haptic-assisted virtual assembly and prototyping has seen significant attention over the past two decades. However, in spite of the appealing prospects, the adoption has been slower than expected. Putting hardware limitations aside, the main roadblocks faced in software development can be traced to the lack of effective and efficient computational models. Such models must 1) accommodate the inherent geometric complexities faced when assembling objects of arbitrary shape; and 2) conform to the computation time limitation imposed by the frame rate requirements---namely, 1 kHz for haptic feedback compared to the more manageable 30-60 Hz for graphic rendering. The fulfillment of these competing objectives is far from trivial.

In this thesis, I propose the concept of a generic `geometric energy' field to obtain the guidance forces and torques that effectively assist the user in the exploration of the virtual environment (VE), from repulsing collisions to attracting proper contact. The energy function is formulated as a cross-correlation of shape descriptors called skeletal density functions (SDF), which applies to arbitrary geometry. I show that this approach unifies the two phases of free motion (based on collision detection) and fine insertion (based on geometric constraints) widely popular in the recent implementations. The formulation can thus be regarded as a generalization of the manually specified `virtual fixtures' or heuristically identified `mating constraints' proposed in the literature. % Although such a generalization comes at the expense of computational intensity in its original form, the computations can be streamlined by leveraging Fourier transforms. % Particularly, the real-time algorithm admits an efficient implementation using fast Fourier transforms (FFT) accelerated via graphics processing units (GPU). I show that the proposed method is effective for assembling objects of arbitrary topological, geometric, and syntactic complexity, providing a meaningful trade-off between the desired fidelity and computational efficiency.

The results suggest that the proposed approach is a powerful unifying alternative to the existing myriad of ad hoc techniques, thus opens up new promising theoretical and computational directions for haptics researchers and developers.

Major Advisor

Horea T. Ilies