Efficient and Adaptive Rendering of 2-D Continuous Scatterplots

We extend the rendering technique for continuous scatterplots to allow for a broad class of interpolation methods within the spatial grid instead of only linear interpolation. To do this, we propose an approach that projects the image of a cell from the spatial domain to the scatterplot domain. We a...

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Veröffentlicht in:Computer graphics forum Jg. 28; H. 3; S. 743 - 750
Hauptverfasser: Bachthaler, Sven, Weiskopf, Daniel
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford, UK Blackwell Publishing Ltd 01.06.2009
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ISSN:0167-7055, 1467-8659
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Abstract We extend the rendering technique for continuous scatterplots to allow for a broad class of interpolation methods within the spatial grid instead of only linear interpolation. To do this, we propose an approach that projects the image of a cell from the spatial domain to the scatterplot domain. We approximate this image using either the convex hull or an axis‐aligned rectangle that forms a tight fit of the projected points. In both cases, the approach relies on subdivision in the spatial domain to control the approximation error introduced in the scatterplot domain. Acceleration of this algorithm in homogeneous regions of the spatial domain is achieved using an octree hierarchy. The algorithm is scalable and adaptive since it allows us to balance computation time and scatterplot quality. We evaluate and discuss the results with respect to accuracy and computational speed. Our methods are applied to examples of 2‐D transfer function design.
AbstractList We extend the rendering technique for continuous scatterplots to allow for a broad class of interpolation methods within the spatial grid instead of only linear interpolation. To do this, we propose an approach that projects the image of a cell from the spatial domain to the scatterplot domain. We approximate this image using either the convex hull or an axis-aligned rectangle that forms a tight fit of the projected points. In both cases, the approach relies on subdivision in the spatial domain to control the approximation error introduced in the scatterplot domain. Acceleration of this algorithm in homogeneous regions of the spatial domain is achieved using an octree hierarchy. The algorithm is scalable and adaptive since it allows us to balance computation time and scatterplot quality. We evaluate and discuss the results with respect to accuracy and computational speed. Our methods are applied to examples of 2-D transfer function design.
We extend the rendering technique for continuous scatterplots to allow for a broad class of interpolation methods within the spatial grid instead of only linear interpolation. To do this, we propose an approach that projects the image of a cell from the spatial domain to the scatterplot domain. We approximate this image using either the convex hull or an axis-aligned rectangle that forms a tight fit of the projected points. In both cases, the approach relies on subdivision in the spatial domain to control the approximation error introduced in the scatterplot domain. Acceleration of this algorithm in homogeneous regions of the spatial domain is achieved using an octree hierarchy. The algorithm is scalable and adaptive since it allows us to balance computation time and scatterplot quality. We evaluate and discuss the results with respect to accuracy and computational speed. Our methods are applied to examples of 2-D transfer function design. [PUBLICATION ABSTRACT]
Author Weiskopf, Daniel
Bachthaler, Sven
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Cites_doi 10.1109/TVCG.2008.119
10.1016/0020-0190(73)90020-3
10.1145/99308.99322
10.1109/TVCG.2008.160
10.1145/130881.130882
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SubjectTerms Algorithms
Approximation
Computer graphics
Computer Graphics [I.3.3]: Picture/Image Generation - Display algorithms
Computer science
Image coding
Studies
Title Efficient and Adaptive Rendering of 2-D Continuous Scatterplots
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