Layout Of Vertices Research Articles

Evaluation of triangular mesh layout techniques using large mesh simplification

Highly detailed polygonal meshes nowadays were created vastly from a great number of multimedia applications. Insufficient main memory space and inferior locality-of-reference nature of the input mesh sequence incurred frequent page swaps and extremely low runtime efficiency. To address this issue, techniques based on the models of graph layout, matrix bandwidth minimization, and space-filling-curves were reported. However, such models merely considered the optimization of vertex layout on the basis of the graph distance or matrix bandwidths while leave the optimization of face layout either unoptimized or resorted an additional sorting procedure. In this paper, we propose an improved theoretic model suggesting the optimization of index-faced triangular mesh layout on the basis of a jointly consideration on both the vertex and face layout. Unlike previous attempts, we do not need additional efforts in optimizing one layout after the other by sorting, the optimized layouts are generated on the fly with each other with respect to both the vertex or triangle bandwidths. According to the experimental results, our approach outperforms the CM and SFC methods not only at yielding better theoretical results but also at improving the runtime efficiency of large mesh simplification.

Interactive Graph Layout of a Million Nodes

Sensemaking of large graphs, specifically those with millions of nodes, is a crucial task in many fields. Automatic graph layout algorithms, augmented with real-time human-in-the-loop interaction, can potentially support sensemaking of large graphs. However, designing interactive algorithms to achieve this is challenging. In this paper, we tackle the scalability problem of interactive layout of large graphs, and contribute a new GPU-based force-directed layout algorithm that exploits graph topology. This algorithm can interactively layout graphs with millions of nodes, and support real-time interaction to explore alternative graph layouts. Users can directly manipulate the layout of vertices in a force-directed fashion. The complexity of traditional repulsive force computation is reduced by approximating calculations based on the hierarchical structure of multi-level clustered graphs. We evaluate the algorithm performance, and demonstrate human-in-the-loop layout in two sensemaking case studies. Moreover, we summarize lessons learned for designing interactive large graph layout algorithms on the GPU.

Inspired quadrangulation

This paper presents a new approach for the quadrangulation of triangular surfaces. While previous work focused on fully automatic computations or explicitly involved user control for the integration of subjective decisions, we introduce a new example-based quad-meshing paradigm, in order to easily reproduce the subjective decisions made in the design of reference examples found in a corpus. The algorithm enables to reproduce the subjective aspects of the example (extraordinary vertex layout) while minimizing the induced distortion; allowing users to leverage reference meshes considered of quality for fast prototyping. At the core of our technique, we provide the analytic gradient of as-rigid-as-possible 2D transformations. This expression is implemented in a fast solver to automatically register planar unfoldings of the geometries, yielding low-distortion cross maps of the examples onto the input in 3D. In addition, our technique provides interactive feedback for user modifications of the cross maps computed automatically. Our technique supports localized mesh composition and enables to reproduce meshing styles despite intrinsic reflective symmetry, large variation from isometry or even topological variation. Experiments demonstrate the accuracy of the mimicking process as well as its time efficiency.

Minimising the Number of Bends and Volume in 3-Dimensional Orthogonal Graph Drawings with a Diagonal Vertex Layout

A 3-dimensional orthogonal drawing of a graph with maximum degree at most 6, positions the vertices at grid-points in the 3-dimensional orthogonal grid, and routes edges along grid-lines such that edge routes only intersect at common end-vertices. Minimising the number of bends and the volume of 3-dimensional orthogonal drawings are established criteria for measuring the aesthetic quality of a given drawing. In this paper we present two algorithms for producing 3-dimensional orthogonal graph drawings with the vertices positioned along the main diagonal of a cube, so-called diagonal drawings. This vertex-layout strategy was introduced in the 3-BENDS algorithm of Eades et al. [Discrete Applied Math. 103:55–87, 2000]. We show that minimising the number of bends in a diagonal drawing of a given graph is NP-hard. Our first algorithm minimises the total number of bends for a fixed ordering of the vertices along the diagonal in linear time. Using two heuristics for determining this vertex-ordering we obtain upper bounds on the number of bends. Our second algorithm, which is a variation of the above-mentioned 3-BENDS algorithm, produces 3-bend drawings with n3+o(n3) volume, which is the best known upper bound for the volume of 3-dimensional orthogonal graph drawings with at most three bends per edge.