Related papers: Circular-Arc Cartograms
Contours may be viewed as the 2D outline of the image of an object. This type of data arises in medical imaging as well as in computer vision and can be modeled as data on a manifold and can be studied using statistical shape analysis.…
Cartograms depict geographic regions with areas proportional to quantitative data. However, when created using density-equalizing map projections, cartograms may exhibit invalid topologies if boundary polygons are drawn using only a finite…
A map graph is a graph admitting a representation in which vertices are nations on a spherical map and edges are shared curve segments or points between nations. We present an explicit fixed-parameter tractable algorithm for recognizing map…
A circular arc graph is the intersection graph of a collection of connected arcs on the circle. We solve a Tur'an-type problem for circular arc graphs: for n arcs, if m and M are the minimum and maximum number of arcs that contain a common…
The topological organization of several world cities are studied according to respective representations by complex networks. As a first step, the city maps are processed by a recently developed methodology that allows the most significant…
We present an algorithm for creating contiguous cartograms using meshes. We use numerical optimization to minimize cartographic error and distortion by transforming the mesh vertices. The vertices can either be optimized in the plane or…
Circular-arc graphs are the intersection graphs of arcs of a circle. The main result of this work describes the structure of all \emph{normalized intersection models} of circular-arc graphs. Normalized models of a circular-arc graph reflect…
A circular-arc graph is the intersection graph of arcs of a circle. It is a well-studied graph model with numerous natural applications. A certifying algorithm is an algorithm that outputs a certificate, along with its answer (be it…
An algorithm to generate the locus of a circle using the intersection points of straight lines is proposed. The pixels on the circle are plotted independent of one another and the operations involved in finding the locus of the circle from…
Treemaps are a popular technique to visualize hierarchical data. The input is a weighted tree $\tree$ where the weight of each node is the sum of the weights of its children. A treemap for $\tree$ is a hierarchical partition of a rectangle…
Rectangular layouts, subdivisions of an outer rectangle into smaller rectangles, have many applications in visualizing spatial information, for instance in rectangular cartograms in which the rectangles represent geographic or political…
A corner in a map is an edge-vertex-edge triple consisting of two distinct edges incident to the same vertex. A corneration is a set of corners that covers every arc of the map exactly once. Cornerations in a dart-transitive map generalize…
Pattern forming systems allow for a wealth of states, where wavelengths and orientation of patterns varies and defects disrupt patches of monocrystalline regions. Growth of patterns has long been recognized as a strong selection mechanism.…
A plane graph is called a rectangular graph if each of its edges can be oriented either horizontally or vertically, each of its interior regions is a four-sided region and all interior regions can be fitted in a rectangular enclosure. If…
A fractal can be simply understood as a set or pattern in which there are far more small things than large ones, e.g., far more small geographic features than large ones on the earth surface, or far more large-scale maps than small-scale…
A branched covering map of surfaces induces a map in the opposite direction between their arc complexes. We represent a branched covering map combinatorially using what we call a lifting picture, and use this representation to computably…
Scaling of geographic space refers to the fact that for a large geographic area its small constituents or units are much more common than the large ones. This paper develops a novel perspective to the scaling of geographic space using large…
Contour maps are widely used to display estimates of spatial fields. Instead of showing the estimated field, a contour map only shows a fixed number of contour lines for different levels. However, despite the ubiquitous use of these maps,…
In this paper, we introduce a new approach for drawing diagrams that have applications in software visualization. Our approach is to use a technique we call confluent drawing for visualizing non-planar diagrams in a planar way. This…
We introduce the class of circular-arc H-graphs, which generalizes circular-arc graphs, particularly circular-arc bigraphs. We investigate two types of ordering-based characterizations of circular-arc r-graphs. Finally, we provide forbidden…