Hagrid — Gridify Scatterplots with Hilbert and Gosper Curves

Cutura, Rene; Morariu, Cristina; Cheng, Zhanglin; Wang, Yunhai; Weiskopf, Daniel; Sedlmair, Michael

doi:10.1145/3481549.3481569

Cited by 5 publications

(5 citation statements)

References 19 publications

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“…By design, such algorithms optimize node placements according to a grid size that is directly or indirectly related to the produced screen resolution of the visualization. DGrid [15] and HaGrid [6] are two examples of gridbased overdraw removal algorithms. DGrid [15] recursively splits the VS into subspaces in which nodes cannot overlap.…”

Section: Visual Space Algorithmsmentioning

confidence: 99%

“…DGrid [15] recursively splits the VS into subspaces in which nodes cannot overlap. In HaGrid [6], the node coordinates are assigned using a space-filling curve whose recursion depth is set to produce more or less compact layouts. While these methods have a O(Nlog(N)) time complexity, they produce significant deformation of the initial layout, in particular in dense regions.…”

Section: Visual Space Algorithmsmentioning

confidence: 99%

“…In this quantitative study, GIST is compared with state-of the art Layout Adjustment algorithms. Namely, the selected algorithms are: ScatterplotUnfold (SU) [24], DGrid [15], HaGrid [6], PFS' [14], GTree [30] and PRISM [9], and were presented in Section 2.…”

Section: Quantitative Evaluationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In addition to data point positions, VS methods [6,15,24] also have access to rendering parameters such as screen resolution, opacity or data point screen sizes. In DGrid [15] and HaGrid [6] for instance, a grid (screen) resolution is used to determine candidate positions such that data points do not overlap. In ScatterplotUnfold [24], rendered data point sizes are non-uniformly modified to remove overlaps and enhance the visibility of outliers in sparse regions of the drawing.…”

Section: Introductionmentioning

confidence: 99%

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Section: Visual Space Algorithmsmentioning

confidence: 99%

Section: Visual Space Algorithmsmentioning

confidence: 99%

Section: Quantitative Evaluationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Guaranteed Visibility in Scatterplots with Tolerance

Giovannangeli,

Lalanne,

Giot

et al. 2023

IEEE Trans. Visual. Comput. Graphics

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Hagrid: using Hilbert and Gosper curves to gridify scatterplots

Cutura

Morariu

Cheng

et al. 2022

J Vis

Self Cite

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A common enhancement of scatterplots represents points as small multiples, glyphs, or thumbnail images. As this encoding often results in overlaps, a general strategy is to alter the position of the data points, for instance, to a grid-like structure. Previous approaches rely on solving expensive optimization problems or on dividing the space that alter the global structure of the scatterplot. To find a good balance between efficiency and neighborhood and layout preservation, we propose Hagrid, a technique that uses space-filling curves (SFCs) to “gridify” a scatterplot without employing expensive collision detection and handling mechanisms. Using SFCs ensures that the points are plotted close to their original position, retaining approximately the same global structure. The resulting scatterplot is mapped onto a rectangular or hexagonal grid, using Hilbert and Gosper curves. We discuss and evaluate the theoretic runtime of our approach and quantitatively compare our approach to three state-of-the-art gridifying approaches, DGrid, Small multiples with gaps SMWG, and CorrelatedMultiples CMDS, in an evaluation comprising 339 scatterplots. Here, we compute several quality measures for neighborhood preservation together with an analysis of the actual runtimes. The main results show that, compared to the best other technique, Hagrid is faster by a factor of four, while achieving similar or even better quality of the gridified layout. Due to its computational efficiency, our approach also allows novel applications of gridifying approaches in interactive settings, such as removing local overlap upon hovering over a scatterplot. Graphical abstract

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Dual Space Coupling Model Guided Overlap-Free Scatterplot

Shi

Liu

et al. 2022

IEEE Trans. Visual. Comput. Graphics

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Hagrid — Gridify Scatterplots with Hilbert and Gosper Curves

Cited by 5 publications

References 19 publications

Guaranteed Visibility in Scatterplots with Tolerance

Guaranteed Visibility in Scatterplots with Tolerance

Hagrid: using Hilbert and Gosper curves to gridify scatterplots

Dual Space Coupling Model Guided Overlap-Free Scatterplot

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