Pii: S0925-7721(99)00016-4

LMT-skeleton heuristics for several new classes of optimal triangulations

Given a planar point set, we consider three classes of optimal triangulations: (1) the minimum weight triangulation with angular constraints (constraints on the minimum angle and the maximum angle in a triangulation), (2) the angular balanced triangulation which minimizes the sum of the ratios of the maximum angle to the minimum angle for each triangle and (3) the area balanced triangulation wh...

Regular and non-regular point sets: Properties and reconstruction

In this paper, we address the problem of curve and surface reconstruction from sets of points. We introduce regular interpolants, which are polygonal approximations of curves and surfaces satisfying a new regularity condition. This new condition, which is an extension of the popular notion of r-sampling to the practical case of discrete shapes, seems much more realistic than previously proposed...

Guarding Scenes against Invasive Hypercubes

In recent years realistic input models for geometric algorithms have been studied. The most important models introduced are fatness, low density, unclutteredness, and small simple-cover complexity. These models form a strict hierarchy. Unfortunately, small simple-cover complexity is often too general to enable efficient algorithms. In this paper we introduce a new model based on guarding sets. ...

Pii: S0925-7721(99)00036-x

A (not necessarily convex) object C in the plane is κ-curved for some constant 0 < κ < 1, if it has constant description complexity, and for each pointp on the boundary ofC, one can place a diskB ⊆ C of radius κ ·diam(C) whose boundary passes throughp. We prove that the combinatorial complexity of the boundary of the union of a set C of n κ-curved objects (e.g., fat ellipses or rounded heart-sh...

Minimal Tangent Visibility Graphs