TRIANGLE: A Tri-modal Access Program for Reading, Writing, and Doing Math
TRIANGLE is a DOS and Windows 95 computer program intended for print-impaired students and professionals in math, science, and engineering. It includes:
- a math/science word processor
- a graphing calculator
- a viewer for y versus x plots
- a table viewer
- the Touch-and-Tell Program for audio and/or braille-assisted reading of tactile figures on an external digitizing pad.
The keyboard or any assistive device/software that emulates a keyboard may be used for input. TRIANGLE output may be viewed visually, audibly, and/or by braille.
DOS TRIANGLE has an on-line help file describing all editing, calculating, graph-viewing, table-browsing, and figure-reading commands. Several tutorials are also included with the distribution files. DOS TRIANGLE is available to anyone interested in trying it. The expanded symbol set used with the mathematical word processor can be accessed with DOS screen readers only if the appropriate character tables are installed. Support is included for Vocal-Eyes speech screen reader and TSI braille displays. Instructions are included for use with other screen readers, but some expertise and effort on the part of the user is required. TRIANGLE menus and help files are in English, but the program should work with most languages using the roman alphabet. The new Windows 95 TRIANGLE (beta release expected in summer 1998) has all the features of DOS TRIANGLE but is self-voicing through any MS SAPI-compliant speech engine and will also be accessible in braille through any on-line screen display that supports the new MS Braille API. This version of the TRIANGLE program will be demonstrated during the presentation.
2. Windows TRIANGLE mathematical word processor
The Windows TRIANGLE word processor is an RTF (rich text format) word processor whose character set includes typographic and foreign characters and the math symbol fonts of math editors bundled with MS Word or Word Perfect. TRIANGLE also utilizes special math and markup symbols to permit all scientific expressions (including fractions, superscripts, subscripts, and tabular arrays) to be written in a linear form. These characters may be entered through a Windows menu, with several of the most common characters having single-stroke short cuts. This is a particularly convenient format for blind users.
Expressions may be entered and manipulated with the usual kinds of editing capabilities found in any text processor, such as the Windows clipboard for cutting and pasting. In addition TRIANGLE has a number of special editing and browsing capabilities that make it particularly convenient for reading and writing math and scientific expressions. For example, there are ten specially-addressable clipboards that allow a user to cut and paste several text selections without losing the last one every time a new item is saved. This facility provides significantly increased flexibility that is handy when manipulating math, solving algebraic equations, etc.
There are several browsing features designed for ease of reading equations. These include "read enclosed expression" commands that jump to the beginning of the next or previous enclosure and read aloud either the entire expression or the portion of that expression to the next enclosure. Enclosures include standard items such as parentheses, brackets, and braces, as well as markup characters defining numerator and denominator of fractions, complex superscripts, subscripts, or radicals. The user has a number of audio templates for representing math symbols and can custom- design them to personal preferences.
Braille access poses a difficult problem, since there is no "accepted" braille representation for anything except letters. We have adopted the GS braille representation used in DOS TRIANGLE. Although DOS TRIANGLE is restricted to 8-dot GS, Windows TRIANGLE can use either 8-dot or 6-dot GS codes.
GS is a dual 6/8-dot braille representation developed by John Gardner and Norberto Salinas (Prof. of Mathematics, Univ. of Kansas). GS was inspired by the current on-going unified braille code (UBC) development effort by the International Committee on English Braille. GS adopts the UBC philosophy of retaining as much as possible of current literary braille. TRIANGLE includes a GS tutorial for braille users.
Users have a number of options for printing from the TRIANGLE editor. An ink copy for sighted people can be printed on any standard printer. The sighted reader must learn the GS markup symbols for such things as subscript, superscript, fractions, and arrays, but the representations are straightforward and the authors believe that such copy should be acceptable for almost any academic purpose.
There are a number of options for making tactile hard copies. A GS6 braille copy may be made on any braille embosser. A GS8 copy may be made on any braille embosser that has the ability to load the GS8 font set. Copies printed in DotsPlus, GS6, or GS8 may also be printed using the new TIGER printer. Another output option is to make a font change to an on-screen braille dot pattern and print using swell paper or with the Tektronix Phasor wax jet printer.
3. The Windows TRIANGLE graphing calculator
TRIANGLE includes the equivalent of a scientific graphing calculator. The calculator allows the user to input or define constants and expressions for convenience and accepts several types of notation for operations - e.g. one can use a GS multiply symbol or the * which is commonly used to indicate multiplication on computers. The result of the computation is displayed in a calculator window. Results may then be copied and pasted into an editor window.
TRIANGLE also has a graphing calculator that computes and displays a y vs. x function (or several functions simultaneously) on the screen. A number of screen display choices are available. The graph may be printed for sighted people on any standard printer. TIGER can print a tactile copy directly, or indirectly with swell paper or the Phasor. A graphics braille embosser can be used to make a low resolution copy of the graph (without any text or labels of course). However the graph may also be viewed on-line with the x-y graph viewer.
4. The DOS and WINDOWS TRIANGLE x-y graph viewer
A graphed function is scaled so that it can be displayed as a convenient size picture on the screen. It is "viewed" audibly by a blind user through the use of a tone plot. The user may move a pointer along the independent variable axis, and the value of the function is indi-cated by the pitch of a tone. The function is scaled so that the full range from the minimum and maximum of the function corresponds to a pitch well within the normal range of human hearing. The function is also displayed with a moving icon on the bottom line of the screen. As the pointer is moved along the independ-ent-variable axis, the icon moves to the right as the function becomes larger and to the left as it becomes smaller. This icon is primarily intended for deaf blind users who would view it with an on-line braille display.
The graph's pointer may be moved one point at a time or allowed to scan automatically from left to right, or from right to left. In addition to the tone indicating the function, the values of the independent variable and the function are displayed on the screen, and may be read aloud if desired. The viewer functions include the ability to find both relative and absolute maxima and minima, zeros, etc. The simple tone reader gives a reasonable qualitative overview, and a user may look individually at various points for quantitative information.
5. The DOS and Windows TRIANGLE table viewer
Tables may be included as part of a text file or saved as table files with a defined file extension. In either case, they should be marked up with the GS markup indicators that tell where the table begins and ends and where each element and line ends.
The table view has two modes. A formatted mode is intended primarily for small tables being read using an on-line braille display. In this mode, tables are displayed on the screen much as they would be if formatted for sighted readers.
The formatted table mode is clumsy if the table is large or if the user (of DOS TRIANGLE) is reading with a speech synthesizer. The cell-by-cell mode is intended for such cases. The reader views one cell at a time and can navigate right and left, up and down from cell to cell in the table. The screen also shows the title and the cell row and column number. Optional information such as the row or column labels may also be displayed. This mode permits blind readers to read extremely large or complex tables.
The table viewer may be entered at will, and a table remains in the viewer until it is replaced by another one. Tables appearing in the text may be captured into the reader by placing the cursor anywhere within the table and pressing a "capture table" short cut key.
6. The DOS and Windows TRIANGLE Touch-and-Tell figure viewer
This feature requires use of an external digitizing tablet on which a tactile figure is mounted. A computer "map" file is required, so that whenever a user identifies an object on the figure, the computer can display information about that object. The information is read by speech and/or braille and may be arbitrarily large. The map files are produced by a sighted user to create the annotated pictures. Once the files are created, they can be read by the TRIANGLE program and printed to a graphics embosser.
The figure viewer can be entered at will, and once a map file is read in, the figure is scaled by indicating marks at the top right and bottom left of the figure. This information remains until a new figure is mounted and a new map file read into the table viewer.
7. Preparing materials for TRIANGLE
Both sighted and blind users can create scientific documents in the word processor, save expressions to be computed and graphed, and create tables in the table viewer. It is possible in principle to translate TRIANGLE files to and from other formats that typeset information in standard two-dimensional notation for sighted people. The authors expect to support the new XML world wide web language for this purpose.
A sighted person can create tactile figures and the accompanying computer map files with our Objectif program. Objectif runs under Microsoft Windows and permits a sighted person easily to edit and simplify a bit mapped image file to be printed on a braille graphics embosser or one of the new direct technologies.[5-7]
The map file is created by selecting objects on the computer screen and entering labels or any desired text information to be displayed when the blind user selects that object. At present there is no way for a blind user to create TRIANGLE figures and map files.
This research was supported by National Science Foundation grant HRD-9452881.
 Hadi Bargi Rangin, Steve Sahyun, Randy Lundquist, and John Gardner, "TRIANGLE: TRI-MODAL ACCESS TO TEXT, TABLES, EQUATIONS, GRAPHS, CALCULATIONS, AND FIGURES", Proceedings of the 1997 CSUN International Conference on Technology and Persons with Disabilities, Los Angeles, March 1997.
 Up-to-date information about DOS TRIANGLE and Objectif is maintained on the Science Access Project web site http://dots.physics.orst.edu
 The Unified Braille Code project is described at: http://world.std.com/~duxbury/ubc.html.
 DotsPlus is a tactile font set developed by this research group and described in another presentation at this conference. See http://dots.physics.orst.edu/dotsplus.html.
 The TIGER (TactIle Graphics EmbosseR) is a Windows 95 tactile printer capable of printing from standard Windows 95 applications. Text can be printed in 6- or 8-dot DotsPlus or any braille font including American, DIN, or British computer braille or either GS6 or GS8. TIGER was invented and developed in this research group and has been licensed to ViewPlus Technologies, Inc. That company has a booth at this conference. TIGER will be available commercially in summer 1998 at $6,000. For more information, see http://www.viewplustech.com
 Swell paper is the currently most common technique for making tactile printouts of arbitrary line and block graphics. See http://www.repro-tronics.com.
 Tektronix Inc. is marketing a version of their Phasor wax jetcolor printer that allows extra wax to be deposited in order to make a tactile image. Cost for the lowest priced model is $14,000.