Maximizing Ink in Partial Edge Drawings of k-plane Graphs

Hummel, Matthias; Klute, Fabian; Nickel, Soeren; Nöllenburg, Martin

doi:10.1007/978-3-030-35802-0_25

Cited by 6 publications

(4 citation statements)

References 20 publications

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“…As a traditional Chinese art, the tools of Chinese ink painting are mainly brushes, ink, Xuan paper, and ink stone [15]. As an important form of ink painting, ink landscape painting consists of ink lines that first outline the overall trend of the mountain, and then with the rich chapping techniques, the basic process of painting is completed [16,17].…”

Section: Introductionmentioning

confidence: 99%

Morphological Structural Element Optimization for Automatic Line Characterization of Ink Drawings

2022

Security and Communication Networks

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As a traditional Chinese art, the tools of Chinese ink painting are mainly brushes, ink, and rice paper and ink stone. As an important form of ink painting, ink landscape painting consists of ink lines that first outline the overall trend of the mountain and then complete the basic process of painting with rich chapping techniques. The article proposes a process to draw water animation based on Chinese painting style; this method first perceives the position of water form in Chinese painting and enhances it by morphological structural elements used to automatically draw the line feature analysis of ink painting; next, the image rendering technique is used to render the water form, firstly using BF for noise removal processing and then gradienting by Canny edge detection operator to get the gradient amplitude. Next, morphological optimization is applied, and finally the image is visualized. In the process of morphological optimization, the optimal parameters of the structural elements are found through the threshold segmentation number, and the rendering algorithm for ink-based landscape painting is explored in depth, starting from the ink lines. The results reveal that the method is more accurate than typical marker-watershed algorithm segmentation, and that changing different structural elements and their parameters has a bigger impact on the ink painting drawing effect.

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Section: Introductionmentioning

confidence: 99%

Morphological Structural Element Optimization for Automatic Line Characterization of Ink Drawings

2022

Security and Communication Networks

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“…Several approaches have been proposed in the network visualization literature to mitigate this issue, e.g., sophisticated layout algorithms aiming for few crossings [30], edge bundling [39,57], as well as vertex aggregation and interaction techniques [54]. There are also a number of theoretical approaches to deal with drawing non-planar graphs and reducing the visual clutter produced by edge crossings [41,47], ranging from optimizing crossing angles [48] to bundled crossings [3,11,23], confluent drawings [15,19], and partial edge drawings [9,10,31]. Ultimately, one would like to achieve similar readability properties as in crossing-free drawings of planar graphs [46,50,53].…”

Section: Introductionmentioning

confidence: 99%

“…Our reduction is based on a result from Hummel et al [31], who used Planar 3-SAT to prove that finding a symmetrical partial edge drawing of a 3-plane drawing is NP-hard. We will first construct a set S of line segments in the plane based on Γ ϕ and then transform S into a graph G and an integer k, that is a positive instance of Candidate Selection (and of Embedded Splitting Number) if and only if ϕ is satisfiable.…”

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confidence: 99%

Planarizing Graphs and their Drawings by Vertex Splitting

Nickel¹,

Nöllenburg²,

Sorge³

et al. 2022

Preprint

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The splitting number of a graph G = (V, E) is the minimum number of vertex splits required to turn G into a planar graph, where a vertex split removes a vertex v ∈ V , introduces two new vertices v1, v2, and distributes the edges formerly incident to v among its two split copies v1, v2. The splitting number problem is known to be NP-complete. In this paper we shift focus to the splitting number of graph drawings in R 2 , where the new vertices resulting from vertex splits can be re-embedded into the existing drawing of the remaining graph. We first provide a non-uniform fixed-parameter tractable (FPT) algorithm for the splitting number problem (without drawings). Then we show the NP-completeness of the splitting number problem for graph drawings, even for its two subproblems of (1) selecting a minimum subset of vertices to split and (2) for re-embedding a minimum number of copies of a given set of vertices. For the latter problem we present an FPT algorithm parameterized by the number of vertex splits. This algorithm reduces to a bounded outerplanarity case and uses an intricate dynamic program on a sphere-cut decomposition.

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“…For instance, dynamic graphs can be much harder acquire but are still an important object of study in Graph Drawing. To address this issue, many authors have either crafted their own dataset programmatically (examples: [139,2,160]) or modified another one to fit their needs (discussed in the next section).…”

Section: Generatedmentioning

confidence: 99%

Layered graphs and their layouts, evaluations, and applications

Di Bartolomeo

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Graphs are a fundamental data structure, used in many fields of human knowledge work. We read, use, and categorize information through graphs in daily tasks: every time we read a map of public transportation, every time we create a mental map of a concept, every time we send and receive packets through the internet, we are using graphs.Given how widespread graphs are, it is fundamental that we visualize them effectively. Drawings of graphs should strive to respect important readability criteria that were established in previous research. Examples of such criteria include reducing the number of crossings between edges and reducing edge length. Here, graph layout algorithms come into play: each layout algorithm maps nodes and edges in a graph to coordinates in space, allowing us to draw a graph while attempting to respect our previouslymentioned readability criteria. We encounter graphs with a wide variety of features and users with diverse use cases: layout algorithms must take into account this breadth of possible requirements, and specialize accordingly.This thesis focuses on layered graphs-graphs in which each node is assigned to a layer, nodes belonging to the same layer are drawn aligned to a linear axis, and the axes for multiple layers are drawn in parallel.The bulk of the novel contributions of this thesis are found in Stratisfimal Layout, which is an optimal layout algorithm for layered graphs-meaning that its output is one of the best attainable in terms of selected readability criteria. It does so by defining the layout algorithm as a linear programming problem.The other works in this thesis explore heuristic-based approaches to highlight trends and patterns in the underlying data, the application of layout algorithms to hypergraphs, and how the shape of the layout influences the understanding of features in the data.

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Maximizing Ink in Partial Edge Drawings of k-plane Graphs

Cited by 6 publications

References 20 publications

Morphological Structural Element Optimization for Automatic Line Characterization of Ink Drawings

Morphological Structural Element Optimization for Automatic Line Characterization of Ink Drawings

Planarizing Graphs and their Drawings by Vertex Splitting

Layered graphs and their layouts, evaluations, and applications

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