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

Bucky Ball data set - continuous scatterplot, tetrahedral approach Bucky Ball data set - discrete scatterplot

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

Blunt fin data set - continuous scatterplot Blunt fin data set - discrete scatterplot

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

Tornado data set - continuous scatterplot Tornado data set - discrete scatterplot

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

Hurricane Isabel data set - continuous scatterplot, low-resolution Hurricane Isabel data set - discrete scatterplot, 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

Hurricane Isabel data set - continuous scatterplot, high-resolution Hurricane Isabel data set - discrete scatterplot, 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

Engine data set - continuous scatterplot, tetrahedral approach Engine data set - discrete scatterplot

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.

Engine data set - continuous scatterplot, subdivision approach Engine data set - continuous scatterplot, hierarchical approach

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.

Engine data set - continuous scatterplot, subdivision approach Engine data set - continuous scatterplot, hierarchical approach

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.