Continuous Scatterplots
This website presents high-resolution images for the paper "Continous Scatterplots" and "Effective and Adaptive Rendering of 2-D Continuous Scatterplots".
The images are captured from the software that was implemented for these papers. The software is open-source and is available for download. The software was created in Visual Studio 2008 and is implemented with GLUT and OpenGL.
Bucky Ball
These two images show a continuous and a discrete scatterplot of the bucky ball
data set. The continuous version was created with the tetrahedral approach as
described in the paper "Continuous Scatterplots".
The scatterplot axes represent the scalar
value and the gradient magnitude of the scalar field, respectively. As
discussed by Kniss et al.*, material boundaries lead to
pronounced arc-like structures in such scatterplots. In a brushing-and-linking
approach, those arc-like structures are selected by the user and the
corresponding regions of the 3D scalar field are highlighted in the
volume visualization within the spatial domain. For this and all following examples,
we use a logarithmic color table to encode density values. Low density is
mapped to black/dark blue, mid-density values are shown in red, and high
density values are yellow/white.
* J. Kniss, G. Kindlmann, and C. Hansen: Multi-dimensional transfer functions
for interactive volume rendering. IEEE Transactions on Visualization
and Computer Graphics.
Blunt fin data set
These two images show a continuous and a discrete scatterplot of the blunt fin
data set. The continuous version was created with the tetrahedral approach as
described in the paper "Continuous Scatterplots".
This data set is given on an unstructured grid derived from a curvilinear grid of
resolution 40 x 32 x 32. The discrete scatterplot just uses the
data at the grid points and ignores the underlying grid structure. In contrast,
the continuous scatterplot takes into account the varying size and shape of
grid cells by computing gradients within cells. Therefore, differences between
discrete and continuous scatterplots are typically more pronounced for
unstructured or curvilinear grids than for uniform grids.
Tornado data set
These two images show a continuous and a discrete scatterplot of the tornado
data set. The continuous version was created with the tetrahedral approach as
described in the paper "Continuous Scatterplots".
This data set has a size of 128^3. We map the magnitude of the velocity to
the horizontal axis and the velocity in z-direction to the vertical axis. In this
way, different features of the “tornado” are distinguishable and therefore they are
easy to extract by brushing-and-linking.
Hurricane Isabel data set, low-resolution
These two images show a continuous and a discrete scatterplot of the hurricane Isabel
data set. The continuous version was created with the tetrahedral approach as
described in the paper "Continuous Scatterplots".
This data set is the downsampled version with a size of 128 x 128 x 30. In the discrete scatterplot,
near-vertically aligned clusters of points are visible. Those clusters are misleading, since they originate
solely from the low sampling density in the z-dimension. (See next example for a high-resolution version
of this data set.)
Hurricane Isabel data set, high-resolution
These two images show a continuous and a discrete scatterplot of the original hurricane Isabel
data set. The continuous version was created with the tetrahedral approach as
described in the paper "Continuous Scatterplots".
This data set has a size of 500x500x100. The vertical clusters are less prominent now,
since the resolution in the z-dimension is much higher. Please note the similarity of the continuous scatterplot
to its low-resolution counterpart of the previous example.
Engine data set
These two images show a continuous and a discrete scatterplot of the engine
data set. The scatterplot axes represent the scalar
value and the gradient magnitude of the scalar field, respectively.
The continuous version was created with the tetrahedral approach as
described in the paper "Continuous Scatterplots".
This data set has a size of 256x256x110.
The pictures show additional continuous scatterplots, which are created with the techniques described in
"Effective and Adaptive Rendering of 2-D Continuous Scatterplots".
The image on the left shows the continuous version created with the subdivision approach that uses the convex hull to
estimate the size of phi in scatterplot space. The threshold for this image was set to 50.
The image on the right shows the continuous version created with the hierarchical approach that uses an octree to speed up
the computation. Here, simple axis-aligned bounding rectangles were used to estimate phi. The threshold was set to 50 as well.
In order to reduce computation time greatly, the user can modify the threshold to allow for larger approximation
errors for the estimation of phi in scatterplot space. This reduces the time to compute the continuous scatterplot
significantly and the user gets a rough impression of how the continous scatterplot will look like. For these two
images, the same technique as in the above example is used, however, this time the threshold is set to 200.
(c) 2009, Sven Bachthaler and Daniel Weiskopf.
