![]() The topic of this paper is smooth morphing of a DT under such circumstances. A DT with dynamical updates displays visualization artifacts with non-smooth motions when viewed over time. The structure however is well known to undergo significant changes when vertices are inserted or removed. One of the ways to effectively deal with such problems is to employ Delaunay triangulation (DT). For the Delaunay triangulation our main contribution is an analysis of the standard edge-flipping approach we show that the number of flips is O(k2 ∑k2) at each time step.Ī variety of applications nowadays deal with complex dynamical problems where the data sets and interactions change over time. We show how to update the convex hull at each time step in O(k∑k log2 n) amortized time. We analyze our algorithms in terms of ∑k, the so-called k-spread of P. We study the maintenance of the convex hull and the Delaunay triangulation of a planar point set P in the black-box model, under the following assumption on dmax: there is some constant k such that for any point p ∑ P the disk of radius dmax contains at most k points. In this more practical model we receive the position of each object at regular time steps and we have an upper bound on dmax, the maximum displacement of any point in one time step. We study KDSs in the black-box model, which is a hybrid of the KDS model and the traditional time-slicing approach. This assumption severely limits the applicability of KDSs. A fundamental assumption underlying the framework is that the motions of the objects are known in advance. Over the past decade, the kinetic-data-structures framework has become the standard in computational geometry for dealing with moving objects. For the Delaunay triangulation our main contribution is an analysis of the standard edge-flipping approach we show that the number of flips is O(k2Δk2) at each time step. ![]() We show how to update the convex hull at each time step in O(min(n, kΔklog n)log n) amortized time. We analyze our algorithms in terms of Δk, the so-called k-spread of P. In this more practical model we receive the position of each object at regular time steps and we have an upper bound on dmax, the maximum displacement of any point in one time step.We study the maintenance of the convex hull and the Delaunay triangulation of a planar point set P in the black-box model, under the following assumption on dmax: there is some constant k such that for any point p in P the disk of radius dmax contains at most k points. Over the past decade, the kinetic-data-structures framework has become thestandard in computational geometry for dealing with moving objects. ![]()
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