Offsetting operations in solid modelling
Computer Aided Geometric Design
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
An optimal algorithm for finding segments intersections
Proceedings of the eleventh annual symposium on Computational geometry
Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Shape tolerance in feeding and fixturing
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
On Optimal Tolerancing in Computer-Aided Design
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Point distance and orthogonal range problems with dependent geometric uncertainties
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Uncertain geometry with dependencies
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Technical note: Uncertain lines and circles with dependencies
Computer-Aided Design
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We present a framework for the systematic study of parametric variation in planar mechanical parts and for efficiently computing approximations of their tolerance envelopes. Part features are specified by explicit functions defining their position and shape as a function of parameters whose nominal values vary along tolerance intervals. Their tolerance envelopes model perfect form least and most material conditions (LMC/MMC). Tolerance envelopes are useful in many design tasks such as quantifying functional errors, identifying unexpected part collisions, and determining device assemblability. We derive geometric properties of the tolerance envelopes and describe four efficient algorithms for computing first-order linear approximations with successive accuracy. The results from experiments on 14 realistic part models demonstrate that on average, our algorithms are an order of magnitude faster and more accurate than the commonly used Monte Carlo simulation, and produce better results than the computationally expensive Taguchi method.