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
We provide a detailed quantum treatment of the spectral characteristics and of the dynamics of nondispersive two-electron
wave packets along the periodically driven, collinear frozen planet configuration of helium. These highly correlated, long-lived
wave packets arise as a quantum manifestation of regular islands in a mixed classical phase space, which are induced by nonlinear
resonances between the external driving and the unperturbed dynamics of the frozen-planet configuration. Particular emphasis
is given to the dependence of the ionization rates of the wave packet states on the driving field parameters and on the quantum
mechanical phase space resolution, preceded by a comparison of 1D and 3D life times of the unperturbed frozen planet. Furthermore,
we study the effect of a superimposed static electric field component, which, on the grounds of classical considerations,
is expected to stabilize the real 3D dynamics against large (and possibly ionizing) deviations from collinearity.
Received 7 November 2002 / Received in final form 2 December 2002 Published online 28 January 2003 相似文献