An efficient parallel algorithm for planarity

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1986.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERINGBibliography: leaves 56-57.by Philip Nathan Klein.M.S

An efficient parallel algorithm for planarity

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1986.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERINGBibliography: leaves 56-57.by Philip Nathan Klein.M.S

Applications of Graph Embedding in Mesh Untangling

The subject of this thesis is mesh untangling through graph embedding, a method of laying out graphs on a planar surface, using an algorithm based on the work of Fruchterman and Reingold[1]. Meshes are a variety of graph used to represent surfaces with a wide number of applications, particularly in simulation and modelling. In the process of simulation, simulated forces can tangle the mesh through deformation and stress. The goal of this thesis was to create a tool to untangle structured meshes of complicated shapes and surfaces, including meshes with holes or concave sides. The goals of graph embedding, such as minimizing edge crossings align very well with the objectives of mesh untangling. I have designed and tested a tool which I named MUT (Mesh Untangling Tool) on meshes of various types including triangular, polygonal, and hybrid meshes. Previous methods of mesh untangling have largely been numeric or optimizationbased. Additionally, most untangling methods produce low quality graphs which must be smoothed separately to produce good meshes. Currently graph embedding techniques have only been used for smoothing of untangled meshes. I have developed a tool based on the Fruchterman-Reingold algorithm for force-directed layout[1] that effectively untangles and smooths meshes simultaneously using graph embedding techniques. It can untangle complicated meshes with irregular polygonal frames, internal holes, and other complications that previous methods struggle with. The MUT does this by using several different approaches: untangling the mesh in stages from the frame in and anchoring the mesh at corner points to stabilize the untangling

A control for graph representation and interaction

Estágio realizado na ParadigmaXis e orientado pelo Eng.º Filipe CorreiaTese de mestrado integrado. Engenharia Informátca e Computação. Faculdade de Engenharia. Universidade do Porto. 200

MetroSets: Visualizing Sets as Metro Maps

We propose MetroSets, a new, flexible online tool for visualizing set systems using the metro map metaphor. We model a given set system as a hypergraph $\mathcal{H} = (V, \mathcal{S})$, consisting of a set $V$ of vertices and a set $\mathcal{S}$, which contains subsets of $V$ called hyperedges. Our system then computes a metro map representation of $\mathcal{H}$, where each hyperedge $E$ in $\mathcal{S}$ corresponds to a metro line and each vertex corresponds to a metro station. Vertices that appear in two or more hyperedges are drawn as interchanges in the metro map, connecting the different sets. MetroSets is based on a modular 4-step pipeline which constructs and optimizes a path-based hypergraph support, which is then drawn and schematized using metro map layout algorithms. We propose and implement multiple algorithms for each step of the MetroSet pipeline and provide a functional prototype with \new{easy-to-use preset configurations.} % many real-world datasets. Furthermore, \new{using several real-world datasets}, we perform an extensive quantitative evaluation of the impact of different pipeline stages on desirable properties of the generated maps, such as octolinearity, monotonicity, and edge uniformity.Comment: 19 pages; accepted for IEEE INFOVIS 2020; for associated live system, see http://metrosets.ac.tuwien.ac.a

Bio-inspired adaptive wingtip devices for low Reynolds number operation

Birds are highly capable and maneuverable fliers, traits not currently shared with current unmanned aerial vehicles. They are able to achieve these flight capabilities by adapting the shape of their wings during flight in a variety of complex manners. One feature of bird wings, the primary feathers, separate to form wingtip gaps at the distal end of the wing. This research presents bio-inspired wingtip devices with varying wingtip gap sizes, defined as the chordwise distance between wingtip devices, for operation in low Reynolds number conditions of Re = 100,000, similar to conditions experienced by many species of birds. Lift and drag data was measured for planar and nonplanar wingtip devices with the total wingtip gap size ranging from 0% to 40%. For a planar wing with a gap size of 20%, the mean coefficient of lift in the pre-stall region is increased by 7.25%, and the maximum coefficient of lift is increased by 5.6% compared to a configuration with no gaps. The nonplanar wingtip device was shown to reduce the induced drag. The effect of wingtip gap sizes is shown to be independent of the planarity/nonplanarity of the wingtip device, thereby allowing designers to decouple the wingtip parameters to tune the desired lift and drag produced. A light weight morphing mechanism design process is proposed, thereby enabling designers to build an adaptive wing that takes advantage of high lift benefits of having 20% wingtip gaps, useful for high payload conditions, as well as low drag benefits of having no gaps, useful for cruise conditions