Offsetting operations in solid modelling
Computer Aided Geometric Design
Finding the upper envelope of n line segments in O(n log n) time
Information Processing Letters
An algebraic algorithm to compute the exact general sweep boundary of a 2D curved object
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
Monte Carlo simulation of tolerancing in discrete parts manufacturing and assembly
Monte Carlo simulation of tolerancing in discrete parts manufacturing and assembly
Putting the turing into manufacturing: recent developments in algorithmic automation
Proceedings of the twenty-ninth annual symposium on Computational geometry
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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 increasing accuracy. Our experimental results on three realistic examples show that the implemented algorithms produce better results in terms of accuracy and running time than the commonly used Monte Carlo method.