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Efficient and Adaptive Rendering of 2‐D Continuous Scatterplots
Author(s) -
Bachthaler Sven,
Weiskopf Daniel
Publication year - 2009
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2009.01478.x
Subject(s) - computer science , rendering (computer graphics) , interpolation (computer graphics) , octree , domain (mathematical analysis) , algorithm , scalability , multivariate interpolation , computer graphics (images) , artificial intelligence , computer vision , image (mathematics) , mathematics , mathematical analysis , database , bilinear interpolation
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.