Scatterplots are well established means of visualizing discrete data
values with two data variables as a collection of discrete points.
We aim at generalizing the concept of scatterplots to the visualization
of spatially continuous input data by a continuous and dense plot.
An example of a continuous input field is data defined on an n-D
spatial grid with respective interpolation or reconstruction of in-between
values. We propose a rigorous, accurate, and generic mathematical
model of continuous scatterplots that considers an arbitrary density
defined on an input field on an n-D domain and that maps this density
to m-D scatterplots. Special cases are derived from this generic
model and discussed in detail: scatterplots where the n-D spatial
domain and the m-D data attribute domain have identical dimension,
1-D scatterplots as a way to define continuous histograms, and 2-D
scatterplots of data on 3-D spatial grids. We show how continuous
histograms are related to traditional discrete histograms and to
the histograms of isosurface statistics. Based on the mathematical
model of continuous scatterplots, respective visualization algorithms
are derived, in particular for 2-D scatterplots of data from 3-D
tetrahedral grids. For several visualization tasks, we show the applicability
of continuous scatterplots. Since continuous scatterplots do not
only sample data at grid points but interpolate data values within
cells, a dense and complete visualization of the data set is achieved
that scales well with increasing data set size. Especially for irregular
grids with varying cell size, improved results are obtained when
compared to conventional scatterplots. Therefore, continuous scatterplots
are a suitable extension of a statistics visualization technique
to be applied to typical data from scientific computation.
%0 Journal Article
%1 Bachthaler2008
%A Bachthaler, S.
%A Weiskopf, D.
%D 2008
%J Visualization and Computer Graphics, IEEE Transactions on
%K 3D analysis; attribute data domain;computational domain;data geometry;data grid grid;continuous histogram;continuous histogram;spatial mathematical model;interpolation;isosurface plot;discrete point;generic scatterplot;data statistical tetrahedral value variable;dense visualisation;interpolation;statistical visualization;discrete
%N 6
%P 1428 -1435
%R 10.1109/TVCG.2008.119
%T Continuous Scatterplots
%V 14
%X Scatterplots are well established means of visualizing discrete data
values with two data variables as a collection of discrete points.
We aim at generalizing the concept of scatterplots to the visualization
of spatially continuous input data by a continuous and dense plot.
An example of a continuous input field is data defined on an n-D
spatial grid with respective interpolation or reconstruction of in-between
values. We propose a rigorous, accurate, and generic mathematical
model of continuous scatterplots that considers an arbitrary density
defined on an input field on an n-D domain and that maps this density
to m-D scatterplots. Special cases are derived from this generic
model and discussed in detail: scatterplots where the n-D spatial
domain and the m-D data attribute domain have identical dimension,
1-D scatterplots as a way to define continuous histograms, and 2-D
scatterplots of data on 3-D spatial grids. We show how continuous
histograms are related to traditional discrete histograms and to
the histograms of isosurface statistics. Based on the mathematical
model of continuous scatterplots, respective visualization algorithms
are derived, in particular for 2-D scatterplots of data from 3-D
tetrahedral grids. For several visualization tasks, we show the applicability
of continuous scatterplots. Since continuous scatterplots do not
only sample data at grid points but interpolate data values within
cells, a dense and complete visualization of the data set is achieved
that scales well with increasing data set size. Especially for irregular
grids with varying cell size, improved results are obtained when
compared to conventional scatterplots. Therefore, continuous scatterplots
are a suitable extension of a statistics visualization technique
to be applied to typical data from scientific computation.
@article{Bachthaler2008,
abstract = {Scatterplots are well established means of visualizing discrete data
values with two data variables as a collection of discrete points.
We aim at generalizing the concept of scatterplots to the visualization
of spatially continuous input data by a continuous and dense plot.
An example of a continuous input field is data defined on an n-D
spatial grid with respective interpolation or reconstruction of in-between
values. We propose a rigorous, accurate, and generic mathematical
model of continuous scatterplots that considers an arbitrary density
defined on an input field on an n-D domain and that maps this density
to m-D scatterplots. Special cases are derived from this generic
model and discussed in detail: scatterplots where the n-D spatial
domain and the m-D data attribute domain have identical dimension,
1-D scatterplots as a way to define continuous histograms, and 2-D
scatterplots of data on 3-D spatial grids. We show how continuous
histograms are related to traditional discrete histograms and to
the histograms of isosurface statistics. Based on the mathematical
model of continuous scatterplots, respective visualization algorithms
are derived, in particular for 2-D scatterplots of data from 3-D
tetrahedral grids. For several visualization tasks, we show the applicability
of continuous scatterplots. Since continuous scatterplots do not
only sample data at grid points but interpolate data values within
cells, a dense and complete visualization of the data set is achieved
that scales well with increasing data set size. Especially for irregular
grids with varying cell size, improved results are obtained when
compared to conventional scatterplots. Therefore, continuous scatterplots
are a suitable extension of a statistics visualization technique
to be applied to typical data from scientific computation.},
added-at = {2010-06-23T08:39:21.000+0200},
author = {Bachthaler, S. and Weiskopf, D.},
biburl = {https://www.bibsonomy.org/bibtex/20236ab9dc0265c54341901cf3592f2dc/joelotz},
doi = {10.1109/TVCG.2008.119},
interhash = {e295d30e009c897a44cdb24c629dcffe},
intrahash = {0236ab9dc0265c54341901cf3592f2dc},
issn = {1077-2626},
journal = {Visualization and Computer Graphics, IEEE Transactions on},
keywords = {3D analysis; attribute data domain;computational domain;data geometry;data grid grid;continuous histogram;continuous histogram;spatial mathematical model;interpolation;isosurface plot;discrete point;generic scatterplot;data statistical tetrahedral value variable;dense visualisation;interpolation;statistical visualization;discrete},
month = {nov.-dec. },
number = 6,
owner = {joe},
pages = {1428 -1435},
timestamp = {2010-06-23T08:39:21.000+0200},
title = {Continuous Scatterplots},
volume = 14,
year = 2008
}