A representation of 2-dimensional data: an x-y plot.
Bradley Matson
Whether computed via analytical functions or derived from measurements, the data from computational problems must eventually interpreted by a human. The final job of the computational modeler is to intepret and then present their hard work to their peers. This job is by no means easiest, since, as humans we have rather limited senses. Searching though a complicated data set can be tedious and invariablily provides the researcher with some amount of pain. Once the researcher has some understanding of the data, its final presentation for the benefit of others often must strike a balance between complete comprehension that can overwhelm and oversimplification.
Rarely, at the end of a complicated computational modeling effort, is a single number obtained. Such data we would call a one-dimensional datum. More frequently, the resulting data is multi-dimensional. As a college student, you are familiar with two-dimensional data, for you have made countless x-y plots. Two-dimensional data have values of a dependent variable, y, for values of an independent variable x. An obvious example is shown below, where y = x2.
A representation of 2-dimensional data: an x-y plot.
Since two-dimensional plotting is relatively simple, the concentration here will be on three- and four-dimensional data sets. Unfortunately, humans live in a three-dimensional world and our peers, unless are uniquely gifted, cannot imagine stuctures in four or higher dimensions. (Certainly some our peers are less adapt at imagining three dimensions and some have enough trouble with two!) Thus, there is a challenge in presenting complex data in a way that is easy to visualize, meaningful to the person interpreting it, and representative of the data.
A colleague once remarked, "the data analysis is a piece of cake, the real work comes in showing it off." Creating the final presentation of the data can be frustrating and time consuming. Much trial-and-error experimentation with different visualization techniques is usually required. Often, the final product combines different techniques. One must also consider the audience to whihc the data is to be presented. An seasoned computational researcher may have no difficulty viewing a MRI scan of a brain from a raw data file, however a medial professional may not have that experience.
Although presentation of data may be directed at one or several of the human senses, this exercise will investigate only the visual presentation of data. Rubin, here's a good place to reference other presentation types such as tactile or sound for the sight impared.
Upon completion of this exercise, one should be familiar with the several of the data file standards and common visual techniques for three- and four-dimensional data presentation. Although there are a number of different software packages available each with tools that can unleash these techniques, many are similar. Hence, one can concentrate on the techniques and not the software packages or exact tools they provide. Some discussion will be given on how to choose the best software packages for the task.
Consider a whole computational project: A model of a physical system is agreed upon, the model is programmed, the code is tested and its limits are established, the code is used to analyse how the physical system behaves while saving the results or 'data'. Next is the interpretation and dissemination phase.
How can your get your peers to believe your intepretation? How can you present the data such that your peers might make their own intepretations of your data? The first thing you can do is provide them with the code and the data saved in a data file they can read. There several common ways to save data into data files. Should the programmer wish to make the data files available to the widest audience of researchers, a file standard ought to be considered. For large data sets, it is best to consider a well-established standard. Provide them with adaquate documentation concerning the standard. Of course, you need to provide the range of applibility of the code -- when does the model fail? These details and proof that the range you have worked in needs to be availible. The power of web technology with integrated download capabilities is perhaps ideal as a avenue for dissemination. Even if the primary medium of dissemination is paper, references to web pages are now widely accepted and appriciated.
Only those peers who are not frightened at using complicated visualization software packages will be willing to read in your data files and try their own hand with visualization techniques on it. This may take many hours of experimentation. Your peers will not have the luxury of hours of experimenting with presenting the data. Thus, the second step of the interpretation and dissemination phase is to provide a presentation of the data that can be used for easy interpretation by others. (Since visual presentations are emphasised here, this means you suppy still or animated images.) Such a presentation does not require reading data files or use of difficult-to-use software. It is incumbent on the researcher to obatin the best visualization technique or combination techniques which strike that balance between oversimplification and overwhelming detail. Also, you should provide a written description of how you explored the data, your interpreation and impressions, and adaquete evidence that supports your these statements. If software packages are emplyed to created the presentation images, viewing or programming code files should be provided.
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Idea/to do list:
These also avail. not zipped on the FTP site (just ftp to www.hokaar.org/computational_physics/cp_2slit.hdf)
These also avail. not zipped on the FTP site (just ftp to www.hokaar.org/computational_physics/gauss.hdf)
These also avail. not zipped on the FTP site (just ftp to www.hokaar.org/computational_physics/cp_bigt.hdf)
These also avail. not zipped on the FTP site (just ftp to www.hokaar.org/computational_physics/unknown_dem.hdf)
These also avail. not zipped on the FTP site (just ftp to www.hokaar.org/computational_physics/h_atom_310.hdf)
These also avail. not zipped on the FTP site (just ftp to www.hokaar.org/computational_physics/h_atom_321.hdf)
For those with (Noyesys) 3DTransform a colour table for further experimentation. download here
Not for students, but for instructor's as a guide of what I think is a fairly good visualization og the atom: download here
These also avail. not zipped on the FTP site (just ftp to www.hokaar.org/computational_physics/jord34.hdf)
These also avail. not zipped on the FTP site (just ftp to www.hokaar.org/computational_physics/jord48a.hdf)
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Three-dimensional data visualization is sometimes called surface visualization. A common example of a three-dimensional data sets is a surface plot. Here a function f (the dependent variable) has two dependent variables x and y. That is, f = f(x,y). It is easy to imagine the walking over a surface From a programmer's view, the number of dimensions of a data set is equal to the number of dimensions an array must be in order to store that data. In this exercise,
Contour Plots, False-colour surface plots, 3-D surface plots, vector plots (wait is this 5-D?)
Four-dimensional data visualization is also referred to as volume visualization
Slices, Isosurfaces, Volume Rendering: Transparency (Alpha + RGB channels), lighting and shadowing. Animations.
As will be seen, sometimes learning the software packages is challenging enough.
Since in this exercise, visual presentations are emphasised, this means you must supply pictures. Often many different pictures are needed to
Another tool which can be employed is the animation of .... Many of the tools are available in and four-dimensional data sets are a