Most methods for computing offsets, bisectors, and medial axes of parametric curves in the plane are based on a local formulation of the distance to a curve. As a consequence, the computed objects may contain spurious parts and components, and have to be trimmed. We approach these problems as global optimization problems, and solve them using interval arithmetic, thus generating robust approxim...

We prove tight bounds on the complexity of bisectors and Voronoi diagrams on so-called realistic terrains, under the geodesic distance. In particular, if n denotes the number of triangles in the terrain, we show the following two results. (i) If the triangles of the terrain have bounded slope and the projection of the set of triangles onto the xy-plane has low density, then the worst-case compl...

The Voronoi diagram is a widely used partition of space which may be implemented in a variety of unconventional computing prototypes, sharing in common the uniform propagation of information via fronts emanating from data point sources. The giant single-celled amoeboid organism Physarum polycephalum constructs minimising transport networks but can also approximate the Voronoi diagram using two ...

The query for retrieving the rank of all neighbors of a moving object at any given time, a continuous rank query, is an important case of continuous nearest neighbor (CNN) queries. An application for ranking queries is given by an ambulance driver who needs to keep track of the closest hospitals at all times. We present a set of incremental algorithms that facilitate efficient rank updates for ...

Spectra have been measured for eleven isotopic forms of imidazole, including single substitutions at each nucleus in turn. A complete restructure is obtained. The ring structure is: N(l)-C(2) = 1.364 A, C(2)-N(3) = 1.314 A, N(3)-C(4) = 1.382 A, C(4)-C(5) = 1.364 A, C(5)-N(l) = 1.377 A, <£N(1)C(2)N(3) = 112.0°, <C(2)N(3)C(4) = 104.9°, <£N(3)C(4)C(5) = 110.7°, <£C(4)C(5)N(1) = 105.5° and <£C(5)N(...

For a given set S of n points in the plane and a fixed point o, we introduce the Voronoi diagram of S anchored at o. It will be defined as an abstract Voronoi diagram that uses as bisectors the following curves. For each pair of points p, q in S, the bisecting curve between p and q is the locus of points x in the plane such that the line segment ox is equidistant to both p and q. We show that t...

Context. So far, red giant oscillations have been studied from radial velocity and/or light curve variations, which reveal frequencies of the oscillation modes. To characterise radial and non-radial oscillations, line profile variations are a valuable diagnostic. Here we present for the first time a line profile analysis of pulsating red giants, taking into account the small line profile variat...