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Abstract:
Virtual prototyping and assembly planning require physically based simulation
techniques. In this setting the relevant objects are mostly mechanical parts,
designed in CAD-programs.
When exported to the prototyping and planning systems, curved parts are
approximated by large polygonal models, thus confronting the simulation
algorithms with high complexity. Algorithms for collision detection in
particular are a bottleneck of efficiency and suffer from accuracy and
robustness problems.
To overcome these problems, our algorithm directly operates on the original
CAD-data. This approach reduces the input complexity and avoids accuracy
problems due to approximation errors.
We present an efficient algorithm for computing the distance between patches of
quadratic surfaces trimmed by quadratic curves. The distance calculation
problem is reduced to the problem of solving univariate polynomials of a degree
of at most 24. Moreover, we will identify an important subclass for which the
degree of the polynomials is bounded by 8.
