November 27, 1994
Greetings from Dr. Nemeth to all us plotters:
This file will contain a few miscellaneous thoughts.
1. Graphics and Braille Embossers: I have personally concluded
that a braille embosser is the wrong device with which to prouce
graphs. The first impulse is to attribute this failure to the
coarseness of the resolution. Upon closer reflection, however,
I find that the principal difficulty is the inability to place a
dot on the curve. I believe that Emerson called attention to this
matter. It is this inability to place dots on the curve that
gives an embosser-produced graph its stair-step effect and thus
makes it unsatisfactory. If you carefully examine the numbers in
the table that I sent in connection with the circle with a 3-inch
radius, you will see what happens. As we proceed from row to row,
y changes at the uniform rate of 0.09 inches per row (the dot
pitch of an embosser in graphics mode.) Near the top of the
circle, x changes so quickly with respect to y that as we proceed
from row 24 (the top of the circle) to row 25 (one row down), x
changes from 45 to 37, (a gap of 8 dots). As we go down another
row, x changes from 37 to 34, (a gap of 3 dots), etc. As we
approach the part of the circle near the x-axis, x changes so
slowly with respect to y that, for many rows in the neighborhood
of the x-axis, the circle appears to have straight sides rather
than being curved.
2. How Important Is Resolution? In print, a graphic is much
more than the curve that represents the graph of an equation. It
is a picture, a three-dimensional drawing with an incredible amount
of detail, a drawing in which the shades of gray or of color
intensity change in an analog fashion (that is, imperceptably and
gradually) as the eye sweeps across the landscape. Furthermore,
the two-point threshold of discrimination for the eye is much finer
than the two-point thrsheold of discrimination for the sense of
touch. Lloyd Rasmussen correctly remarked that once you
attain a dot pitch of 16 or 20 dots per inch, you have reached the
point of no return, that is, a resolution that is finer than that
cannot provide greater detail, although it might be useful for the
purpose of conveying a different texture. When we feel a line
produced by a spur wheel, we have the sensation that such a line
is formed from dots, but our perception is that of a continuous
curve that no amount of increased resulution would alter.
3. The Dot Matrix Printer: When I first proposed the dot
matrix printer in this forum, I had in mind a printer dedicated
to the task of producing tactile graphics. Once the soft platten
was installed, it would become a permanent part of the printer and
that printer would be used solely for the purpose of producing
graphics. The initial problem is that of finding a platten made
from a suitable matthial. Mike thought that the impact of a dot
matrix printer might not be strong enough to produce a tactile
graphic. But as I previously commented, its impact is sufficient
to produce legible copies through a ribbon and four-ply forms with
three sheets of carbon paper in between. I am not even sure that
four-ply is the upper limit. Can we produce braille with a dot
matoix printer? If we can froduce any graphs at all, the answer
is yes. Just as bit-mapped graphics can be used to produce
graphics in the shape of print letters and other characters on the
screen or on paper, bit-mapped graphics can also be used to produce
graphics that represent braille dots which are spaced and positioned
to form braille characters of the kind with which we are familiar.
In graphics mode, periods are placed at the ends of sentences, a
dot is placed above a lowercase i, and dots are created to form the
parts of a semicolon or colon. The dot matrix printer can then
print out this "braille" in the same way that it prints out any
other graphics. I can hardly wait for the day that we license
MicroSoft to use our braille "Windows 1.0" that we have created
to let a dot matrix printer put braille graphics to represent braille
characters on a piece of paper. That would be poetic justice for a
braille-impaired company!
4. Supplies: Every so often the specialists at NBA or at
CTEVH who deal with raised-line drawings publish a list of
supplies together with sources where they can be bought in their
respective journals or bulletins. I recall seeing a description
of a spur wheel in which every fourth tooth was filed down
to produce a dashed line. There are spur wheels which can produce
a double line. When my father operated a factory in the garment
district of New York, he used a spur wheel which can be bought in
a store that sells sewing notions. He would place a paper pattern
which contained an embroidery design over a piece of material.
He would trace the embroidery design with the spur wheel so as
to make holes in the paper. He would then apply a special powder
to the paper that would fall through the holes made by the spur
wheel, thereby transferring the embroidery design to the material.
He would then take the piece of material to the embroidery machine
and trace the design to produce the actual embroidery stitching.
The powder could be easily removed from the material afterwords.
I once owned such a spur wheel. Its teeth were more coarsely
spaced than the teeth on a Perkins spur wheel, and could be used
when a different texture was desired.
5. Conclusion: In his latest posting, Tim poses a problem which
goes far beyond that of producing a simple line drawing. I will
give that matter some thought and record those thoughts in a
future posting. Meanwhile, I will direct my attention to other
aspects of the calculator. When we arrive at a suitable
technology for producing graphs and its feasability demonstrated,
I know that John and I can write the software that will produce the
desired graph using that technology and incorporate that software
into the rest of the calculator. We know that the range of
tactile graphs that are meaningful is a very small subset of the
graphs that can be produced for the sighted world using the various
currently available technologies. Therefore, I suggest that we
first draw up a laundry list of the kinds of graphs that we deem
suitable for tactile implementation, together with some features
that we feel can be usefully incorporated into such graphs.
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