[Blindmath] Software to produce tactile diagrams for Geometry?

[Bernard M Diaz]

Hi,

I'm sighted, thus not possibly the best to advise ... however.

1. there is software (of various kinds) that allow you you type/voice
    instructions in a general sort of way. For example in "pic", one
    could say:
    .PS           # picture start directive
      .ps 10      # sets pointsize (for text) to 10 points
      .vs 12      # sets vertical separation (of text lines to
                  # 12 points, each 1/72 of an inch
      boxht = 1.2; boxwid = 1.2; movewid = 1.4; # in inches
      B1: box "2" # a box at top, left margin with label "2" in it
          move    # assumes to the right
      B2: box "3" # a box 1.4 inches from the first labelled "3"
          down    # moves down 1.4 inches, under box 3
      B3: box "5" # another box
          arrow from B1.bottomleft to B3.topmiddle
          arrow from B3.topright to B2.bottommiddle
    .PE           # picture end directive
    (My visual layout above, may be garbalised by email viewers, for
    which I apologise - it may be best to skip this response ...)
    And this is the specification of 3 boxes with arrows, which could
    be stored in a file and embedded into other documents, etc.
    However, the problem is what happens next.  Typically, this is
    either "rendered" into image form, essentially n by m pixels each
    pixel coded using some 3 integers (colour); or single integer
    (grayscale);
    or converted into "Scaleable Vector Graphics" (point based
    specifications, that use constructs such "dotted line" to join
    the dots specified by the points), or some such.
    (It may be that you may wish to write the entire document
    in raw SVG form, or alternatively, to use software that generates
    SVG either directly, or indirectly).
    The problems are, in all cases scale and location on "the page"
    as well as all issues of page-size and orientation, etc.
    Then the problem is getting these into tactile form.  The Viewplus
    hardware can generate Braille dot pictures from SVG, as can other
    hard/software.
    Another solution, is to "proof" the image onto special (but
    expensive) "bubble paper" and then to fuse ("toast") this using
    relatively cheap hardware (I call it "toasting").
    Most systems come with fonts (& other means) to convert any text
    into Braille or Moon fonts which you put into "invisible" boxes
    and move above in the same way as the labeled boxes above.
    If you are partially sighted, there are a number of alternative
    software tools that allow interactive screen based diagram
    production.  These are then converted into tactiles in the ways
    described. However, none of this is particularly satisfactory.
    So the answer to you first question is "yes ... but ...."!

    Recently, there is software that will "sonify" (i.e. convert images
    into a sound representation).  The reverse process also works,
    that is, you can (it's not very good!) sing a note (I assume you
    have pitch perfect!!!), this places two dots somewhere on a 2D
    screen.  Sing another note, and two more dots are put on the
    screen.  Rising notes appear as a series of rising dots, falling
    notes as falling dots.  It may be (the work needs to be done) that
    some such noises (a sung chord perhaps?) will allow us to draw a
    particular kind of image, and a limited number of these "chords"
    (patterns perhaps?) will generate a "trend graph", say ...
    (Did I imply this was blue sky research, sorry, I should have
    done ...)

2. Ah! A vexed issue. "Are raised dot images good at conveying
    diagrams?". Well it depends on what you mean and what you and
    your students have learned.  And yes, the answer to your question
    is "training is definitely necessary".  It is not inuitively obvious
    that left to right is an usual assumption, or that top to bottom
    is used to convey notions of gravity.  In computer science "a tree"
    often has it's root at the top of the page, when for someone
    feeling the diagram, it may be much much better to put it flowing
    from left to right, or from the centre outwards.
    (I understand from medics that have researched this sort of
    thing that this may be because of the nature of left to right
    [learned or trained] proprio-detection in fingers, have I
    spelled that right?).
    It is the case that if you have a model in your head (how you
    acquire such a model is an interesting question) of what the
    diagram might be, then you approach the problem differently
    and perhaps "accurately"?  Clearly, you and your students will need
    the same language for all this, and sing from the same model set.
    We sighted are limited by our acquired notions of left/right
    up/down, 2D paper diagram presentation.  If you seek to
    duplicate that then, yes, there are languages that help in
    explaining how to describe a diagram in words that will preserve
    and act within that model, and that can be translated into diagrams
    and then into raised dot and/or bubble paper tactiles.

    All this, it seems from many conversations, can best describe up
    to 2D geometry (say 2.5D, if we allow any single x,y location to
    be represented by (say) 8 dot heights [can all eight be used, can
    they be side by side to give notions of rising surfaces ... mmm].
    What it seems they cannot do, is capture the "3D depth cueing" that
    the two eye sighted manage using learned "stereopsis". Thus, for
    any geometry rendition that is of 3D subjects, it may be better
    to think up other methods.  This begs the question, might it be
    better in a more perfect world to start there when teaching geometry
    and to abandon 2D.  I wonder if impressed plastic sheet, direct
    or reversed might be better at conveying 3D haptically (tactually)
    mmm ... And, for your wiki-stick preferring student, stix can
    point right out, to give pyramids (Euler formulae appreciation;
    Schlaafli notation for polytopes and then the algebra ... and
    higher dimensions. Other polygonal structures - notional
    flattening them onto the plane - teaches orthogonal projection;
    my guess, you have a budding geometrician there, firmly to be
    encouraged :-)

My best wishes - Bernard Diaz

(I have some recipes that might help with geometry generation of
  tactiles, contact me off list at b.m.diaz at liv.ac.uk)

Roni Mathew wrote:
> Hi, I am a blind teacher of visually impaired children, and have a
> two-pronged question:
> 
> 1.	Is anyone aware of software which may be used in creating geometric
> drawings, which may then be output to a Braille embosser?
> 2.	One of my student's issues is confusion about raised images in the
> Geometry text. Her classroom teacher finds she works better when figures are
> produced with Wicki Sticks and  glue. However, this method is extremely
> labor intensive and time-consuming for the teacher, and I have been trying
> to explain that such material will not necessarily be offered to her
> following High School. So I ask, are there software-driven means of
> producing lines/figures of varying thickness and height to provide greater
> contrast  of angles, shapes  etc, but also for differentiation of properties
> within a figure?
> 
>  
> 
> Thank you very much for assistance.
> 
> Sincerely,
> 
> Roni Mathew
> 
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