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Visualization - why ?
The world is full of information. Simulations, experiments and data collections comprise an enormous and permanently increasing accumulation of data. Therefore new ways have to be found to reveal the information hidden in sometimes huge data sets.
Visualization offers a way. It aims at presenting complex information in a comprehensible way - exploiting the sensory apparatus and the highly developed perceptual capabilities of humans. And thereby it supports visual exploration, discovery, and visual communication.
Terminology - citations
"Visualization - 1) formation of mental visual images, 2) the act or process of interpreting in visual terms or of putting into visible form." 
Visualization in its broadest terms represents any technique for creating images to convey information. Thus among other fields computer graphics and animation fall into this category. A more specific task is to obtain visual representations of data, typically by computer graphical means. This is called data visualization.
It is in contrast to visual arts where the emphasis is on visualization of spiritual matters.
Scientific visualization (SciVis) is the formal name given to the field in computer science that encompasses user interface, data representation and processing algorithms, visual representations, and other sensory presentation such as sound or touch.
Historically the US National Science Foundation (NSF) played an important role in the development of Scientific Visualization. In the landmark report on Visualization in Scientific Computing in 1987  it was stated that "ViSC [Visualization in Scientific Computing] is emerging as a major computer-based field" and "as a tool for applying computers to science, it offers a way to see the unseen... [it] promises radical improvements in the human/computer interface." NSF provided funds for visualization at the NSF supercomputing centers from 1990 to 1994. During that time, development and application of visualization techniques spread.
In 2005 the NSF and US National Institutes of Health (NIH) convened the Visualization Research Challenges (VRC) Executive Committee to write a new report, exploring the state of the field, examining the potential impact of visualization, and present findings and recommendations for the future of the growing discipline .
In the last decade a community of researchers separated that is predominantly concerned with the visual representation of abstract data that (typically) have no spatial reference, are often unstructured and/or high-dimensional. They called their discipline Information Visualization (InfoVis) in demarcation to the already existing area of scientific visualization. Information visualization endeavors to visualize abstract information such as hyper-text documents on the World Wide Web, directory/file structures on a computer, or abstract data structures" .
The divide between SciVis and Infovis is unfortunate in several respects: on the one hand information visualization is not unscientific and on the other side scientific visualization depicts information, too. Moreover, there is a broad basis of common methodology - despite subtle differences in goals and approches - and many applications require solutions that comprise methods from both areas. From a practical point of view the shism is counterproductive. And it is not comprehensible for outsiders. The next generation of visualization researchers is called upon to abolish this manifested community divide.
Some people consider information visualization as part of scientific visualization, others (the majority) consider scientific visualization and information visualization as two areas, both doing ... data visualization.
Data visualization - our perspective
Information is given in a symbolic form, e.g. as a mathematical formula, or as a data set. Data sets are built of basic items like numbers or character strings. Usually data sets are structured, i.e. the items are ordered somehow, or there are relations between items.
Most data sets we are concerned with are of mathematical nature. They may contain geometrical objects, time series of scalar values, stationary or time dependent fields (scalar, vector, tensor, ...), graphs with attributes, etc. Though application specific aspects are important, the central goal of scientific visualization is to develop visual representations of mathematical objects.
This encompasses the following activities:
- develop techniques that filter data and extract essential features
- develop techniques for mapping mathematical objects to image synthesis parameters
- develop efficient algorithms to perform such mappings fast
- develop appropriate algorithms for image rendering (this is where computer graphics comes in)
- provides integrated software systems for all steps in data visualization
- solve visualization tasks by professionally applying these techniques.
Data visualization - ingredients
Data visualization requires a solid background in computer graphics, image and geometry processing, applied mathematics and knowledge in at least one application area.
However, all of these disciplines are large and diverse in their own, as, e.g. computer graphics: "Just a few years ago, all one needed to be a competent researcher or practitioner in computer graphics was a solid background in geometry, algebra, calculus, topology, probability, mechanics, electromagnetism, signal processing, image processing, electrical engineering, mechanical engineering, optics, information theory, structured programming, basic algorithms and data structures, complexity theory, computer architecture, human factors, perceptual psychology, colorimetry, graphic design, industrial design, semiotic, and art !
Unfortunately, the list is growing." 
 B.H. McCormick, T.A. DeFanti, and M.D. Brown. Visualization in Scientific Computing., Report to the NSF Advisory Panel on Graphics, Image Processing and Workstations, 1987.
 C.R. Johnson, R. Moorehead, T. Munzner, H. Pfister, P. Rheingans, and T. S. Yoo, (Eds.): NIH-NSF Visualization Research Challenges Report IEEE Press, ISBN 0-7695-2733-7, 2006.
 Merriam-Webster OnLine Dictionary
 W. Schroeder, K. Martin, B. Lorensen, The Visualization Toolkit, Prentice Hall, 1996.
 Joe Marks. Optimization - an emerging tool in computer graphics, Panel discussion; Proceedings of SIGGRAPH 94 (Orlando, Florida, July 25-29, 1994), pp. 483-484.