  An important application of haptic technology to digital product development
is in virtual prototyping (VP), part of which deals with interactive planning,
simulation, and verification of assembly-related activities, collectively
called virtual assembly (VA). In spite of numerous research and development
efforts over the last two decades, the industrial adoption of haptic-assisted
VP/VA 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 of haptic feedback. 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 notorious frame rate requirements---namely, 1 kHz for haptic
feedback compared to the more manageable 30-60 Hz for graphic rendering. The
simultaneous fulfillment of these competing objectives is far from trivial.
  This survey presents some of the conceptual and computational challenges and
opportunities as well as promising future directions in haptic-assisted VP/VA,
with a focus on haptic assembly from a geometric modeling and spatial reasoning
perspective. The main focus is on revisiting definitions and classifications of
different methods used to handle the constrained multibody simulation in
real-time, ranging from physics-based and geometry-based to hybrid and unified
approaches using a variety of auxiliary computational devices to specify,
impose, and solve assembly constraints. Particular attention is given to the
newly developed 'analytic methods' inherited from motion planning and protein
docking that have shown great promise as an alternative paradigm to the more
popular combinatorial methods.
