Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 46, no. 1, 2013]]>

Journal: Computational Geometry: Theory and Applications - COMGEO, 2012]]>

Journal: Computational Geometry: Theory and Applications - COMGEO, pp. 38-53, 2012]]>

This paper examines how residents of neotraditional neighbourhoods in the Netherlands socially construct a ‘classed’ place identity and what role the historicised architecture plays within that process. Given that place identity is constructed through social and cultural practices, the paper argues that residents' consumption of historicised environment is bound up with drawing symbolic boundaries that have been explored here by ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. ahead-of-p, no. ahead-of-p, pp. 1-19, 2012]]>Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 27, no. 5, pp. 296-314, 2012]]>

Eén op de drie Nederlanders heeft ten minste één chronische aandoening. Sarah Detaille onderzocht knelpunten die zij op het werk tegenkomen, en evalueerde een zelfmanagementtraining bedoeld om hen te ondersteunen. Die training bestaat uit zes groepsbijeenkomsten waarin deelnemers advies krijgen over leefstijl, arbeid en belastbaarheid, communicatietechnieken en de omgang met symptomen van de aandoening. Daarnaast moeten zij thuis of ...

Journal: Computational Geometry: Theory and Applications - COMGEO, 2012]]>Journal: Computational Geometry: Theory and Applications - COMGEO, 2012]]>

Journal: Computational Geometry: Theory and Applications - COMGEO, pp. 219-226, 2012]]>

â–º We develop a model predicting innovative behavior of agents. â–º Environmental change is the independent variable; recent experience and economic status are moderators. â–º Our model is largely confirmed in a laboratory experiment and a stated discrete choice experiment. â–º Economic status is related through an inverted U-shape to innovation in stable environments. ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 41, no. 5, pp. 833-847, 2012]]>Journal: Computational Geometry: Theory and Applications - COMGEO, 2012]]>

Journal: Computational Geometry: Theory and Applications - COMGEO, 2012]]>

Inspired by air-traffic control and other applications where moving objects have to be labeled, we consider the following (static) point-labeling problem: given a set P of n points in the plane and labels that are unit squares, place a label with each point in P in such a way that the number of free labels (labels not intersecting ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 45, no. 4, 2012]]>Knoben J. and Oerlemans L. A. G. Configurations of inter-organizational knowledge links: does spatial embeddedness still matter?, Regional Studies. The actor composition of inter-organizational ego-networks is largely ignored in research on territorial innovation models. To fill this gap, this paper explores with which sets of external actors (that is, configurations) firms maintain inter-organizational knowledge links. Subsequently, ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 46, no. 8, pp. 1005-1021, 2012]]>We prove that every set of squares with total area 1 can be packed into a rectangle of area at most 2867/2048=1.399… . This improves on the previous best bound of 1.53. Also, our proof yields a linear time algorithm for finding such a packing.

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 8, pp. 456-463, 2011]]>Euler diagrams are an accessible and effective visualisation of data involving simple set-theoretic relationships. Sets are represented by closed curves in the plane and often have wellformedness conditions placed on them in order to enhance comprehensibility. The theoretical underpinning for tool support has usually focussed on the problem of generating an Euler diagram from an abstract model. However, the ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 1, pp. 52-68, 2011]]>Proximity graphs are used in several areas in which a neighborliness relationship for input data sets is a useful tool in their analysis, and have also received substantial attention from the graph drawing community, as they are a natural way of implicitly representing graphs. However, as a tool for graph representation, proximity graphs have some limitations that may be overcome ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 6-7, pp. 329-344, 2011]]>Journal: Computational Geometry: Theory and Applications - COMGEO, pp. 1-4, 2011]]>

We present an algorithm capable of reconstructing a non-manifold surface embedded as a point cloud in a high-dimensional space. Our algorithm extends a previously developed incremental method and produces a non-optimal triangulation, but will work for non-orientable surfaces, and for surfaces with certain types of self-intersection. The self-intersections must be ordinary double curves and ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 8, pp. 427-441, 2011]]>Let S be a finite set of points in the Euclidean plane. Let G be a geometric graph in the plane whose point set is S. The stretch factor of G is the maximum ratio, among all points p and q in S, of the length of the shortest path from p to q in G over the Euclidean distance |...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 2, pp. 104-109, 2011]]>Let P be a set of n points that lie on an n×n grid. The well-known orthogonal range reporting problem is to preprocess P so that for any query rectangle R, we can report all points in P∩R efficiently. In many applications driven by the information retrieval or the bioinformatics communities, we do not need all the points in ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 3, pp. 148-159, 2011]]>For a set of n points in the plane, we consider the axis-aligned (p,k)-Box Covering problem: Find p axis-aligned, pairwise-disjoint boxes that together contain at least n−k points. In this paper, we consider the boxes to be either squares or rectangles, and we want to minimize the area of the largest box. For general p ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 3, pp. 178-190, 2011]]>In this note, we show that the size of the perimeter of (; )-covered objects is a linear function of the diameter. Specifically, for an (; )-covered object O, per(O) c diam(O) sin2 , for a positive constant c. One easy consequence of the result is that every point on the boundary of such an object sees a constant fraction of ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 1, pp. 1-8, 2011]]>Osteopontin (OPN) is a glycophosphoprotein with multiple intracellular and extracellular functions. In vitro, OPN enhances migration of mouse neutrophils and macrophages. In cancer, extracellular OPN facilitates migration of cancer cells via its RGD sequence. The present study was designed to investigate whether osteopontin is responsible for neutrophil and macrophage infiltration in human cancer and in particular in glioblastoma. We found ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 132, no. 1, pp. 39-48, 2011]]>Context: Gaucher disease (GD) is a lysosomal storage disorder characterized by abundant presence of macrophages. Bone complications and low bone density are believed to arise from enhanced bone resorption mediated through macrophage-derived factors. Objective: The objective of the study was to investigate the relationship between bone turnover and bone complications in GD. Design: This was a retrospective cohort study ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 96, no. 7, pp. 2194-2205, 2011]]>Journal: Computational Geometry: Theory and Applications - COMGEO, 2011]]>

In lung fibrosis tissue architecture and function is severely hampered by myofibroblasts due to excessive deposition of extracellular matrix and tissue contraction. Myofibroblasts differentiate from fibroblasts under the influence of transforming growth factor (TGF) β1 but this process is also controlled mechanically by cytoskeletal tension. In healthy lungs, the cytoskeleton of fibroblasts is mechanically strained during breathing. In stiffer fibrotic ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 404, no. 1, pp. 23-27, 2011]]>Increasing evidence suggests the existence of osteoclast diversity. Here we investigated whether precursors obtained from marrow of the mandibula or long bone could give rise to phenotypically different osteoclasts. Formation of multinucleated cells was assessed after culturing mouse marrow cells of the two bone types with macrophage colony stimulating factor (M-CSF) and receptor activator of NFκB ligand (RANKL) for ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 409, no. 2, pp. 205-210, 2011]]>The balance between bone formation and bone resorption in inflammatory diseases is often disturbed. Periodontitis, a chronic inflammation of the tooth gums, leads to unwanted bone loss as a response to inflammatory compounds such as interleukin-1β (IL-1β). This excessive bone loss reflects an increased osteoclast formation and activity. Osteoclast formation is a multistep process driven by osteoclastogenesis supporting ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 112, no. 7, pp. 1890-1897, 2011]]>Osteoclasts have traditionally been associated exclusively with catabolic functions that are a prerequisite for bone resorption. However, emerging data suggest that osteoclasts also carry out functions that are important for optimal bone formation and bone quality. Moreover, recent findings indicate that osteoclasts have different subtypes depending on their location, genotype, and possibly in response to drug intervention. The aim of ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 32, no. 1, pp. 31-63, 2011]]>Given a family of k disjoint connected polygonal sites in general position and of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(nlog3n) time algorithm ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 4, pp. 234-247, 2011]]>An n-town, n∈N, is a group of n buildings, each occupying a distinct position on a 2-dimensional integer grid. If we measure the distance between two buildings along the axis-parallel street grid, then an n-town has optimal shape if the sum of all pairwise Manhattan distances is minimized. This problem has been studied for cities, i....

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 2, pp. 82-94, 2011]]>We introduce the snowblower problem (SBP), a new optimization problem that is closely related to milling problems and to some material-handling problems. The objective in the SBP is to compute a short tour for the snowblower to follow to remove all the snow from a domain (driveway, sidewalk, etc.). When a snowblower passes over each region along the tour, ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 8, pp. 370-384, 2011]]>Journal: Computational Geometry: Theory and Applications - COMGEO, 2011]]>

We present a simple randomized scheme for triangulating a set P of n points in the plane, and construct a kinetic data structure which maintains the triangulation as the points of P move continuously along piecewise algebraic trajectories of constant description complexity. Our triangulation scheme experiences an expected number of O(n2βs+2(n)log2n) discrete changes, and handles them in ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 4, pp. 191-205, 2011]]>Let P be a set of n points in the plane. A geometric proximity graph on P is a graph where two points are connected by a straight-line segment if they satisfy some prescribed proximity rule. We consider four classes of higher order proximity graphs, namely, the k-nearest neighbor graph, the k-relative neighborhood graph, the k-Gabriel ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 4, pp. 216-233, 2011]]>Controlled Perturbation (CP, for short) is an approach to obtaining efficient and robust implementations of a large class of geometric algorithms using the computational speed of multiple precision floating point arithmetic (compared to exact arithmetic), while bypassing the precision problems by perturbation. It also allows algorithms to be written without consideration of degenerate cases. CP replaces the input objects by ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 9, pp. 507-528, 2011]]>Consider the Delaunay triangulation T of a set P of points in the plane as a Euclidean graph, in which the weight of every edge is its length. It has long been conjectured that the stretch factor in T of any pair p,p′∈P, which is the ratio of the length of the shortest path from p to p′ in ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 2, pp. 121-127, 2011]]>Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 2, pp. 69-69, 2011]]>

In this paper we consider the problem of adding the smallest number of additional (relay) nodes to a network of static nodes with limited communication range so that the induced communication graph is 2-connected (we consider both edge and vertex connectivity). The problem is NP-hard. We develop algorithms that find close to optimal solutions for both edge and ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 4, pp. 206-215, 2011]]>We introduce a family of directed geometric graphs, whose vertices are points in Rd. The graphs Gλθ in this family depend on two real parameters λ and θ. For 12λ1 and π3θπ2, the graph Gλθ is a strong t-spanner for t=1(1−λ)cosθ. That is, for any two vertices p and q, Gλθ contains a path from p ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 6-7, pp. 319-328, 2011]]>We consider the Minimum Vertex Cover problem in intersection graphs of axis-parallel rectangles on the plane. We present two algorithms: The first is an EPTAS for non-crossing rectangle families, rectangle families R where R1∖R2 is connected for every pair of rectangles R1,R2∈R. This algorithm extends to intersection graphs of pseudo-disks. The second algorithm achieves a factor ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 6, pp. 356-364, 2011]]>Journal: Computational Geometry: Theory and Applications - COMGEO, 2011]]>

Journal: Computational Geometry: Theory and Applications - COMGEO, 2011]]>

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 38, no. 1, pp. 93-97, 2011]]>

In this paper, we introduce a new generalization of the well-known Fréchet distance between two polygonal curves, and provide an efficient algorithm for computing it. The classical Fréchet distance between two polygonal curves corresponds to the maximum distance between two point objects that traverse the curves with arbitrary non-negative speeds. Here, we consider a problem instance in whic...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 2, pp. 110-120, 2011]]>Motivated by the gateway placement problem in wireless networks, we consider the geometric k-centre problem on unit disc graphs: given a set of points P in the plane, find a set F of k points in the plane that minimizes the maximum graph distance from any vertex in P to the nearest vertex in F in the unit disc ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 5, pp. 286-302, 2011]]>A natural time-dependent similarity measure for two trajectories is their average distance at corresponding times. We give algorithms for computing the most similar subtrajectories under this measure, assuming the two trajectories are given as two polygonal, possibly self-intersecting lines with time stamps. For the case when a minimum duration of the subtrajectories is specified and the subtrajectories must ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 9, pp. 465-476, 2011]]>The problem of computing a representation of the stabbing lines of a set S of segments in the plane was solved by Edelsbrunner et al. We provide efficient algorithms for the following problems: computing the stabbing wedges for S, finding a stabbing wedge for a set of parallel segments with equal length, and computing other stabbers for S such as ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 5, pp. 303-318, 2011]]>We study a combinatorial geometric problem related to the design of wireless networks with directional antennas. Specifically, we are interested in necessary and sufficient conditions on such antennas that enable one to build a connected communication network, and in efficient algorithms for building such networks when possible.We formulate the problem by a set P of n points in the ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 9, pp. 477-485, 2011]]>A set of planar graphs {G1(V,E1),…,Gk(V,Ek)} admits a simultaneous embedding if they can be drawn on the same pointset P of order n in the Euclidean plane such that each point in P corresponds one-to-one to a vertex in V and each edge in Ei does not cross any other edge in ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 8, pp. 385-398, 2011]]>We study the problem of fitting a two-joint orthogonal polygonal chain to a set S of n points in the plane, where the objective function is to minimize the maximum orthogonal distance from S to the chain. We show that this problem can be solved in Θ(n) time if the orientation of the chain is fixed, and in ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 3, pp. 135-147, 2011]]>Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 14, no. 4, pp. 18-21, 2011]]>

We prove that n cops can capture (that is, some cop can get less than unit distance from) a robber in a continuous square region with side length less than 5n and hence that ⌊n/5⌋+1 cops can capture a robber in a square with side length n. We extend these results to three dimensions, proving that 0.34869…n2+O(n) ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 8, pp. 365-369, 2011]]>Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 5, no. 2, pp. 235-255, 2011]]>

This survey gives a brief overview of theoretically and practically relevant algorithms to compute geodesic paths and distances on three-dimensional surfaces. The survey focuses on three-dimensional polyhedral surfaces. The goal of this survey is to identify the most relevant open problems, both theoretical and practical.

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 9, pp. 486-498, 2011]]>In this paper, we address the problem of covering points with orthogonally convex polygons. In particular, given a point set of size n on the plane, we aim at finding if there exists an orthogonally convex polygon such that each edge of the polygon covers exactly one point and each point is covered by exactly one edge. We show that ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 5, pp. 249-264, 2011]]>Silhouettes of polyhedra are an important primitive in application areas such as machine vision and computer graphics. In this paper, we study how to select view points of convex polyhedra such that the silhouette satisfies certain properties. Specifically, we give algorithms to find all projections of a convex polyhedron such that a given set of edges, faces and/or vertices ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 8, pp. 399-408, 2011]]>We study the problem of reconstructing a simple polygon from angles measured at the vertices of the polygon. We assume that at each vertex v a sensing device returns a list of angles α1,α2,…, where αi is the angle between the i-th and the (i+1)-th vertices visible to v in counterclockwise (ccw) order starting with the ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 8, pp. 418-426, 2011]]>The Delaunay triangulation and the weighted Delaunay triangulation are not uniquely defined when the input set is degenerate. We present a new symbolic perturbation that allows to always define these triangulations in a unique way, as soon as the points are not all coplanar. No flat tetrahedron exists in the defined triangulation. The perturbation scheme is easy to code. It ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 3, pp. 160-168, 2011]]>We introduce a local operation for polygons and subdivisions called an edge-move. Edge-moves do not change the edge orientations present in the input and are thus suitable for iterative simplification or even schematization. Based on edge-moves we present a new efficient method for area- and topology-preserving subdivision simplification. We show how to tailor this generic method ...

Journal: Computational Geometry: Theory and Applications - COMGEO, pp. 261-270, 2011]]>A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum number of edges that a thrackle of n vertices can have. According to a 40 years old conjecture of Conway, t(n)=n for ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 6, pp. 345-355, 2011]]>We give a short proof of the following geometric inequality: for any two triangular meshes A and B of the same polygon C, if the number of vertices in A is at most the number of vertices in B, then the maximum length of an edge in A is at least the minimum distance between two vertices in B. Here ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 2, pp. 100-103, 2011]]>Clarkson's algorithm is a three-staged randomized algorithm for solving linear programs. This algorithm has been simplified and adapted to fit the framework of LP-type problems. In this framework we can tackle a number of non-linear problems such as computing the smallest enclosing ball of a set of points in Rd. In 2006, it has been shown ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 2, pp. 70-81, 2011]]>A (weak) closed rectangle-of-influence (RI for short) drawing is a straight-line planar grid drawing in which there is no other vertex inside or on the boundary of the axis parallel rectangle defined by the two end vertices of any edge. Biedl et al. (1999) [1] showed that a plane graph G has a closed RI drawing, if ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 1, pp. 9-19, 2011]]>In their seminal paper on geometric minimum spanning trees, Monma and Suri (1992) [31] showed how to embed any tree of maximum degree 5 as a minimum spanning tree in the Euclidean plane. The embeddings provided by their algorithm require area O(2n2)×O(2n2) and the authors conjectured that an improvement below cn×cn is not possible, for some constant ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 9, pp. 529-543, 2011]]>Given a set of polyhedral cones C1,…,Ck⊂Rd, and a convex set D, does the union of these cones cover the set D? In this paper we consider the computational complexity of this problem for various cases such as whether the cones are defined by extreme rays or facets, and whether D is the entire Rd or a given ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 3, pp. 129-134, 2011]]>Journal: Computational Geometry: Theory and Applications - COMGEO, pp. 2-7, 2011]]>

This paper describes algorithms to compute Voronoi diagrams, shortest path maps, the Hausdorff distance, and the Fréchet distance in the plane with polygonal obstacles. The underlying distance measures for these algorithms are either shortest path distances or link distances. The link distance between a pair of points is the minimum number of edges needed to connect the two points with...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 8, pp. 442-455, 2011]]>Controlled Perturbation is a framework for perturbing geometric sets to make the processes that use them more robust for fixed-precision manipulation. We present a Controlled Perturbation scheme for sets of line segments in R2 (CPLS, for short). CPLS iteratively perturbs the endpoints of the line segments to eliminate potential degeneracies that may cause round-off errors when using fixed-...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 5, pp. 265-285, 2011]]>Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 5, pp. 265-285, 2011]]>

When a graph is drawn in a classical manner, its vertices are shown as small disks and its edges with a positive width; zero-width edges and zero-size vertices exist only in theory. Let r denote the radius of the disks that show vertices and w the width of edges. We give a list of conditions that make such ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 9, pp. 499-506, 2011]]>Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 14, no. 3, pp. 13-14, 2011]]>

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 14, no. 3, pp. 13-14, 2011]]>

The theoretical complexity of vertex removal in a Delaunay triangulation is often given in terms of the degree d of the removed point, with usual results O(d), O(dlogd), or O(d2). In fact, the asymptotic complexity is of poor interest since d is usually quite small. In this paper we carefully design code for small degrees 3⩽d⩽7, it ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 3, pp. 169-177, 2011]]>Journal: Computational Geometry: Theory and Applications - COMGEO, 2011]]>

Journal: Computational Geometry: Theory and Applications - COMGEO, 2011]]>

We investigate the relationship between geometric thickness, thickness, outerthickness, and arboricity of graphs. In particular, we prove that all graphs with arboricity two or outerthickness two have geometric thickness O(logn). The technique used can be extended to other classes of graphs so long as a separator theorem exists. For example, we can apply it to show the known bound ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 44, no. 2, pp. 95-99, 2011]]>We use Bernstein's Theorem (1) to obtain combinato- rial bounds for the number of embeddings of Laman graph frameworks modulo rigid motions. For this, we study the mixed volume of suitable systems of poly- nomial equations obtained from the edge length con- straints. The bounds can easily be computed and for some classes of graphs, the bounds are tight.

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 2, pp. 84-93, 2010]]>Map labeling encounters unique issues in the context of dynamic maps with continuous zooming and panning—an application with increasing practical importance. In consistent dynamic map labeling, distracting behavior such as popping and jumping is avoided. We use a model for consistent dynamic labeling in which a label is represented by a 3d-solid, with scale as the third dimension. ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 3, pp. 312-328, 2010]]>Let G=(V,E) be an undirected graph with n vertices embedded in a metric space. We consider the problem of adding a shortcut edge in G that minimizes the dilation of the resulting graph. The fastest algorithm to date for this problem has O(n4) running time and uses O(n2) space. We show how to improve the running ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 2, pp. 68-72, 2010]]>With the advent of autonomous robots with two- and three-dimensional scanning capabilities, classical visibility-based exploration methods from computational geometry have gained in practical importance. However, real-life laser scanning of useful accuracy does not allow the robot to scan continuously while in motion; instead, it has to stop each time it surveys its environment. This requirement was studied ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 2, pp. 148-168, 2010]]>We develop a method for measuring homology classes. This involves two problems. First, we define the size of a homology class, using ideas from relative homology. Second, we define an optimal basis of a homology group to be the basis whose elements' size have the minimal sum. We provide a greedy algorithm to compute the optimal basis and measure classes ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 2, pp. 169-181, 2010]]>The Fréchet distance between two curves in the plane is the minimum length of a leash that allows a dog and its owner to walk along their respective curves, from one end to the other, without backtracking. We propose a natural extension of Fréchet distance to more general metric spaces, which requires the leash itself to move continuously over time...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 3, pp. 295-311, 2010]]>In this paper we study the problem of computing an upward straight-line embedding of a planar DAG (directed acyclic graph) G into a point set S, i.e. a planar drawing of G such that each vertex is mapped to a point of S, each edge is drawn as a straight-line segment, and all the edges are oriented ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 2, pp. 219-232, 2010]]>An assumption of nearly all algorithms in computational geometry is that the input points are given precisely, so it is interesting to ask what is the value of imprecise information about points. We show how to preprocess a set of n disjoint unit disks in the plane in O(nlogn) time so that if one point per disk is specified ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 3, pp. 234-242, 2010]]>This paper discusses optimization of quality measures over first order Delaunay triangulations. Unlike most previous work, our measures relate to edge-adjacent or vertex-adjacent triangles instead of only to single triangles. We give efficient algorithms to optimize certain measures, including measures related to the area ratio of adjacent triangles, angle between outward normals of adjacent triangles (for polyhedral terrains), ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 4, pp. 377-394, 2010]]>We present a method to compute the exact topology of a real algebraic surface S, implicitly given by a polynomial f∈Q[x,y,z] of arbitrary total degree N. Additionally, our analysis provides geometric information as it supports the computation of arbitrary precise samples of S including critical points. We compute a stratification ΩS of S into O(N5) non-...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 3, pp. 257-278, 2010]]>We consider the problem of finding a large number of disjoint paths for unit disks moving amidst static or dynamic obstacles. The problem is motivated by the capacity estimation problem in air traffic management, in which one must determine how many aircraft can safely move through a domain while avoiding each other and avoiding “no-fly zones” and predicted weather ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 3, pp. 279-294, 2010]]>Imprecision of input data is one of the main obstacles that prevent geometric algorithms from being used in practice. We model an imprecise point by a region in which the point must lie. Given a set of imprecise points, we study computing the largest and smallest possible values of various basic geometric measures on point sets, such as the diameter, ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 4, pp. 419-433, 2010]]>Given n axis-parallel boxes in a fixed dimension d⩾3, how efficiently can we compute the volume of the union? This standard problem in computational geometry, commonly referred to as Klee's measure problem, can be solved in time O(nd/2logn) by an algorithm of Overmars and Yap (FOCS 1988). We give the first (albeit small) improvement: our new ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 3, pp. 243-250, 2010]]>Range searching is a well known problem in the area of geometric data structures. We consider this problem in the context of approximation, where an approximation parameter ε>0 is provided. Most prior work on this problem has focused on the case of relative errors, where each range shape R is bounded, and points within distance ε⋅diam(R) of ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 4, pp. 434-444, 2010]]>We consider a generalization of the Gabriel graph, the witness Gabriel graph. Given a set of vertices P and a set of witnesses W in the plane, there is an edge ab between two points of P in the witness Gabriel graph GG-(P,W) if and only if the closed disk with diameter ab does not contain any witness ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. abs/1008.1, 2010]]>The article is devoted to mathematical models and practical algorithms for solving the cutting and packing (C&P) problem. We review and further enhance the main tool of our studies – phi-functions. Those are constructed here for 2D and 3D objects (unlike other standard tools, such as No-Fit Polygons, which are restricted to the 2D geometry). We also ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 5, pp. 535-553, 2010]]>We prove that the robber can evade (that is, stay at least unit distance from) at least ⌊n/5.889⌋ cops patroling an n×n continuous square region, that a robber can always evade a single cop patroling a square with side length 4 or larger, and that a single cop on patrol can always capture the robber in a square ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 9, pp. 749-766, 2010]]>For n disjoint line segments in the plane we construct in optimal O(n log n) time and linear space an encompassing tree of maximum degree three such that at every vertex all incident edges lie in a halfplane dened by the incident input segment. In particular, this tree is pointed since every vertex has an incident angle greater than . ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 1, 2010]]>The contour tree is an abstraction of a scalar field that encodes the nesting relationships of isosurfaces. We show how to use the contour tree to represent individual contours of a scalar field, how to simplify both the contour tree and the topology of the scalar field, how to compute and store geometric properties for all possible contours in the ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 1, pp. 42-58, 2010]]>We show how to divide the edge graph of a Voronoi diagram into a tree that corresponds to the medial axis of an (augmented) planar domain. Division into base cases is then possible, which, in the bottom-up phase, can be merged by trivial concatenation. The resulting construction algorithm—similar to Delaunay triangulation methods—is not bisector-based and merely ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 8, pp. 688-699, 2010]]>Many problems concerning the theory and technology of rhythm, melody, and voice-leading are fundamentally geometric in nature. It is therefore not surprising that the field of computa- tional geometry can contribute greatly to these problems. The interaction between computational geometry and music yields new insights into the theories of rhythm, melody, and voice-leading, as well as new problems ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 1, pp. 2-22, 2010]]>Thefloodlight illumination problem asks whether there exists a one-to-one placement ofnfloodlights illuminating infinite wedges of angles 1,..., n at n sites p1,...,pn in a plane such that a given infinite wedge W of angle located at point q is completely illuminated by the floodlights. We prove that this problem is NP-hard, closing an open problem from ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 1, pp. 23-34, 2010]]>Computers with multiple processor cores using shared memory are now ubiquitous. In this paper, we present several parallel geometric algorithms that specifically target this environment, with the goal of exploiting the additional computing power. The algorithms we describe are (a) 2-/3-dimensional spatial sorting of points, as is typically used for preprocessing before using incremental algorithms, (b) d-dimensional ...

Journal: Computational Geometry: Theory and Applications - COMGEO, vol. 43, no. 8, pp. 663-677, 2010]]>