Rectilinear k-centers of a finite point set P R2 are the centers of at most k congruent axis-parallel squares of minimal size whose union covers P. This paper describes a linear time algorithm based on the prune-and-search paradigm to compute rectilinear 3-centers. The algorithm is elementary in the sense that it does not build on any sophisticated data structures or other algorithms, except fo...

Given a set of terminals in the plane, a rectilinear Steiner minimal tree is a shortest intercon-nection among these terminals using only horizontal and vertical edges. We present an algorithm that constructs a rectilinear Steiner minimal tree for any input terminal set. On a workstation, problems involving 20 input terminals can be solved in a few seconds, and problems involving 30 input termi...

The crossing number cr(G) of a graph G is the minimum number of crossings in a nondegenerate planar drawing of G. The rectilinear crossing number cr(G) of G is the minimum number of crossings in a rectilinear nondegenerate planar drawing (with edges as straight line segments) of G. Zarankiewicz proved in 1952 that cr(Kn1,n2) ≤ Z(n1, n2) := ⌊ n1 2 ⌋ ⌊ n1−1 2 ⌋ ⌊ n2 2 ⌋ ⌊ n2−1 2 ⌋ . We define an ...

Using a scaling approach we consider a 2D comb copolymer brush under bending deformations. We show that the rectilinear brush is locally stable and can be characterized by a persistence length lambda increasing with the molecular weight of grafting side chains as lambda approximately M3. A bending instability due to redistribution of the side chains appears in the non-linear regime where bendin...

Abs t rac t . This paper is devoted to the study of graph embeddings in the grid of non-planar surfaces. We provide an adequate model for those embeddings and we study the complexity of minimizing the number of bends. In particular, we prove that testing whether a graph admits a rectilinear (without bends) embedding essentially equivalent to a given embedding, and that given a graph, testing if...

A distributed cooperative coverage algorithm DCR is presented which is derived from an earlier complete single-robot algorithm, CCR. DCR executes independently on each robot in a team where the individual robots do not know the initial locations of their peers and applies to systems of robots operating in a rectilinear environment that use only intrinsic contact sensing to determine the boundar...

Uniform rectilinear array is commonly used to explain the correspondence relationship between spatial sampling and time sampling, while the characteristics of the spatial sampling is much unfamiliar than rectilinear array for the widely used circular array. In this paper, we pointed out that the circular array sampling sequence has the characteristics of the nonlinear frequency modulation (FM) ...

We present a novel method for hardwareaccelerated texture advection of 3D velocity fields defined on curvilinear grids. For uniform rectilinear grids, texture advection can be efficiently performed within the rasterization unit by existing approaches. In a pre-processing step, the vector field is transformed from the curvilinear grid (P-Space) to a uniform rectilinear grid (C-Space). Hardware a...

This paper introduces interaction mechanisms for conveying temporal characteristics of time-varying volume data based on temporal styles. We demonstrate the flexibility of the new concept through different temporal style transfer function types and we define a set of temporal compositors as operators on them. The data is rendered by a multi-volume GPU raycaster that does not require any grid al...