Graph as an indispensable part of mathematics, plays a central role in learning and teaching mathematics. Access to mathematical-graphical description and information, broaden the visually impaired people’s horizon in the discipline, however lack of appropriate tools, either hardware or software, is the main burden. Variety of methods exists for providing tactile images which are discussed e.g. in ,  and  however the following construction techniques are more popular: - Thermoform Graphics in which a sheet of plastic is heated and vacuumed on top of a model which represents the shape to be perceived by touch. This results in the production of high quality tactile drawings, but it is necessary to mould a totally new model when a new drawing has to be produced. Besides being expensive, the resulting graph is rather static, i.e. for enlarging the graph a new mould is required. - Swell-Paper Graphics in which a special paper with a special coating of heat reactive microcapsules is used which enables special printers to shape raised areas. Variable height raised lines and areas can be obtained, but it is a very expensive process. - Embossed Graphics. There are several Braille embossers to produce tactile images by punching dots into paper in such a way as to form graphics. This is the best cost-effective technique. Nonetheless only few embossers (e.g. Tiger embossers) are able to produce high-quality, variable-height tactile drawings . This research pursuing  is to address criteria based on which describing a graph to be fully tactile perceivable, before actually being embossed, would be feasible. As such we can granulate the graphs into three granules namely, fully-perceivable, suspicious-perceivable, non-perceivable. Toward the aim we have used MATHEMATICA which is a powerful tool that provides integrated environment for technical computing and also enable symbolic manipulation. It is important to remind that MATHEMATICA can be used by visually impaired students through a command-line user interface that permits performing all required calculations and symbolic manipulations. Moreover, MATHEMATICA allows for producing quality graphics through its powerful symbolic language, hence visually impaired students can command creating graphics by themselves. Besides MATHEMATICA we have exploit Tiger Graphic Embosser. Regarding the preferred resolution for an image to be tactile perceivable – 25.4 dots/inch - and the density of the graph to be embossed we granulate the graph into aforementioned granules. Moreover and specially for the graphs that are granulated in the suspicious-perceivable granule, based on the mentioned factors and considering the limitations of the embosser, the image will be zoomed. The zooming degree will be calculated to be the minimum, through considering the image density, tactile resolution and the embosser specifications. It is important to notice that perception and interpretation of an image is mainly due to the distribution of entities in the image. If entities in an image have overlapping, their perception will be difficult. That is why indicating a zooming degree while issuing a graph-drawing command in MATHEMATICA, regarding the algorithms applied by MATHEMATICA to draw graphs, will lead to the reduced overlapping. However to keep the size of the graph as small as possible we will find the minimum zooming degree. This is due to the two main features of diagram understanding, namely, easiness to search and immediacy to recognize. Therefore, the following exploration features were taken into account while working on graphs: -The possibility to easily recognize basic components in the diagram (e.g. Braille labels and figures). -The possibility to identify relationships between basic components. -The possibility to easily search for components. -Techniques to hierarchically explore the graphical representation. Be reminded that detailed graphs to be perceivable by blind people must be abstracted to a proper level, however we argue that mathematical graphs are themselves a type of abstraction and thinking of putting them in a different level of abstraction is realizable mainly through a hierarchical structure by introducing some black boxes in higher levels and demonstrating the black boxes in the subsequent levels. This is in accordance with the model presented in . The model shows that the visual image is analyzed hierarchically, from the overall structure down to the fundamental features or elements.
|Titolo:||Improving Tactile Graphics with MATHEMATICA|
BERNAREGGI, CRISTIAN (Primo)
TAHAYORI, HOOMAN (Secondo)
|Data di pubblicazione:||1-dic-2007|
|Tipologia:||Book Part (author)|
|Appare nelle tipologie:||03 - Contributo in volume|