The paper proposes a rational method to derive fairness measures for surfaces. It works in cases where isophotes, reflection lines, planar intersection curves, or other curves are used to judge the fairness of the surface. The surface fairness measure is derived by demanding that all the given curves should be fair with respect to an appropriate curve fairness measure. The method is applied to the field of ship hull design where the curves are plane intersections. The method is extended to the case where one considers, not the fairness of one curve, but the fairness of a one parameter family of curves. Six basic third order invariants by which the fairing measures can be expressed are defined. Furthermore, the geometry of a plane intersection curve is studied, and the variation of the total, the normal, and the geodesic curvature and the geodesic torsion is determined. 相似文献
We consider the following problem: given a set of points in the plane, each with a weight, and capacities of the four quadrants, assign each point to one of the quadrants such that the total weight of points assigned to a quadrant does not exceed its capacity, and the total distance is minimized.
This problem is most important in placement of VLSI circuits and is likely to have other applications. It is NP-hard, but the fractional relaxation always has an optimal solution which is “almost” integral. Hence for large instances, it suffices to solve the fractional relaxation. The main result of this paper is a linear-time algorithm for this relaxation. It is based on a structure theorem describing optimal solutions by so-called “American maps” and makes sophisticated use of binary search techniques and weighted median computations.
This algorithm is a main subroutine of a VLSI placement tool that is used for the design of many of the most complex chips. 相似文献
The formation of silicon oxide precipitates from Czochralski grown silicon depends on the time and temperature of the heat treatment as well as on the initial content of interstitially dissolved oxygen. Samples containing between 5×1017 Oi/cm3 and 13×1017 Oi/cm3 have been heated at 750° C for 96 h. SiO2 precipitates of various shape and size have been obtained and investigated by means of small angle neutron scattering (SANS) in the Q-range 0.05 Å–1<Q<0.2 Å–1. The obtained SANS patterns reveal a typical anisotropy of their intensity distribution, which splits into a central peak at Q<0.1 Å–1 due to the shape of the individual particles and a number of weak intensities for large Q-values, originating from a correlation between defects, possibly between the precipitates. While these correlation peaks in the SANS patterns are seen best for rather low values of about (5–7)×1017 Oi/cm3 oxygen content, the central peak anisotropy is most pronounced for higher values of ca 10×1017 Oi/cm3. The integrated intensity of the central peak increases with increasing initial oxygen content. For comparison, untreated samples of the same initial oxygen content do not reveal any anisotropic SAN scattering or a broadened central peak beam. 相似文献