Overlap of convex polytopes under rigid motion

We present an algorithm to compute a rigid motion that approximately maximizes the volume of the intersection of two convex polytopes P-1 and P-2 in R-3. For all epsilon is an element of (0, 1/2] and for all n >= 1/epsilon, our algorithm runs in O(epsilon(-3) n log(3.5) n) time with probability 1 - n(-O(1)). The volume of the intersection guaranteed by the output rigid motion is a (1 - epsilon)-approximation of the optimum, provided that the optimum is at least lambda . max{vertical bar P-1 vertical bar . vertical bar P-2 vertical bar} for some given constant lambda is an element of (0, 1]. (C) 2013 Elsevier B.V. All rights reserved.X1155Ysciescopu

Methods for computer aided inspection of geometric tolerances

This thesis investigates computational methods for assessing tolerance specifications of geometric features in a context of computer aided inspection. It is concerned with checking the sampled features for containment within tolerance zones specified at the design stage, not with explicit shape measurement. The significance of this difference is highlighted when two or more features are to be inspected in combination. The approach adopted is to express the tolerance information as a set of inequality constraints and then to seek efficient methods for determining the feasibility of the set, that is whether all the constraints can be simultaneously satisfied. Roundness inspection is used to introduce all the concepts of the new formulations. By linearisation of the constraints, a standard approximation in roundness measurement, a new algorithm is implemented which provides a “GO-NOGO” result of inspection by checking for feasibility in a highly efficient way. This algorithmic approach is then extended to other inspection situations where naturally linear constraints or valid linearisation occur. Since there are many inspection cases where linearisation is not appropriate, non-linear optimisation techniques are then investigated for their effectiveness in feasibility testing. The inspection of arrays of circular features is used here as a typical test case. Genetic search methods are explored as a possible alternative to formal non-linear programming and guidelines for their efficient use for this problem are proposed. These methods are then compared and contrasted with formal methods, particularly generalised reduced gradient (GRG) and sequential quadratic programming (SQP). The linear algorithm is shown to be the most efficient when it can be used, although all techniques were fast enough for on-line use with modest sized data sets. Currently all the non-linear methods are too expensive for routine use on large data sets. GRG is recommended as having the most favourable combination of good and bad features, but there is some evidence that genetic search might be relatively more efficient for more complex inspection problems

Inscribing an axially symmetric polygon and other approximation algorithms for planar convex sets

10.1016/j.comgeo.2005.06.001Computational Geometry: Theory and Applications333152-164CGOM

Inscribing an axially symmetric polygon and other approximation algorithms for planar convex sets

Given a planar convex set C, we give sublinear approximation algorithms to determine approximations of the largest axially symmetric convex set S contained in P, and the smallest such set S ′ that contains P. More precisely, for any ε> 0, we find an axially symmetric convex polygon Q ⊂ C with area |Q |> (1 − ε)|S | and we find an axially symmetric convex polygon Q ′ containing C with area |Q ′ | < (1 + ε)|S ′ |. We assume that C is given in a data structure that allows to answer the following two types of query in time TC: given a direction u, find an extreme point of C in direction u, and given a line ℓ, find C ∩ ℓ. For instance, if C is a convex n-gon and its vertices are given in a sorted array, then TC = O(log n). Then we can find Q in time O(TCε −1/2 + ε −3/2) and we can find Q ′ in time O(TCε −1/2 + ε −3/2 log(ε −1)). Using these techniques, we can also find approximations to the perimeter, area, diameter, width, smallest enclosing restangle and smallest enclosing circle of C in time O(TCε −1/2).

Modeling the fundamental characteristics and processes of the spacecraft functioning

The fundamental aspects of modeling of spacecraft characteristics by using computing means are considered. Particular attention is devoted to the design studies, the description of physical appearance of the spacecraft, and simulated modeling of spacecraft systems. The fundamental questions of organizing the on-the-ground spacecraft testing and the methods of mathematical modeling were presented

Cumulative index to NASA Tech Briefs, 1986-1990, volumes 10-14

Tech Briefs are short announcements of new technology derived from the R&D activities of the National Aeronautics and Space Administration. These briefs emphasize information considered likely to be transferrable across industrial, regional, or disciplinary lines and are issued to encourage commercial application. This cumulative index of Tech Briefs contains abstracts and four indexes (subject, personal author, originating center, and Tech Brief number) and covers the period 1986 to 1990. The abstract section is organized by the following subject categories: electronic components and circuits, electronic systems, physical sciences, materials, computer programs, life sciences, mechanics, machinery, fabrication technology, and mathematics and information sciences