and Applied Analysis 3

We propose a novel algorithm for placement of streamlines from two-dimensional steady vector or direction fields. Our method consists of placing one streamline at a time by numerical integration started the furthest away from all previously placed streamlines. Such a farthest point seeding strategy leads to high quality placements by favoring long streamlines, while retaining uniformity with th...

We study the farthest point mapping in a p-normed space X in virtue of subdifferential of rx sup{{x − z p : z ∈ M}, where M is a weakly sequentially compact subset of X. We show that the set of all points in X which have farthest point in M contains a dense G δ subset of X.

We present an algorithm to compute the geodesic $$L_1$$ farthest-point Voronoi diagram of m point sites in presence n rectangular obstacles plane. It takes $$O(nm+n \log + m\log m)$$ construction time using O(nm) space. This is first optimal for constructing obstacles. can construct a data structure same and space that answers farthest-neighbor query $$O(\log (n+m))$$ time.

Given a set of sites in a simple polygon, a geodesic Voronoi diagram partitions the polygon into regions based on distances to sites under the geodesic metric. We present algorithms for computing the geodesic nearest-point, higher-order and farthest-point Voronoi diagrams of m point sites in a simple n-gon, which improve the best known ones form ≤ n/polylogn. Moreover, the algorithms for the ne...

A digital edge is a digitization of a straight segment joining two points of integer coordinates. Such a digital set may be analytically defined by the rational slope of the straight segment. We show in this paper that the convex hull, the Euclidean farthest-point Voronoi diagram as well as the dual farthest-point Delaunay triangulation of a digital edge can be fully described by the continued ...