SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Journal of Computer Science and Technology - Special issue on computer graphics and computer-aided design
Efficient collision detection for moving ellipsoids using separating planes
Computing - Geometric modelling dagstuhl 2002
Computing minimum distance between two implicit algebraic surfaces
Computer-Aided Design
Oriented bounding surfaces with at most six common normals
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
A reliable extended octree representation of CSG objects with an adaptive subdivision depth
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
Precise Hausdorff distance computation between polygonal meshes
Computer Aided Geometric Design
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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.