[BlindMath] blindmath tactile graphic example with refreshable braille

[John Miller]

Hello,
This is John Miller.
If you are blind or low vision and have a 40-cell braille display then it is quite likely that you will be able to arrow up and down through the bottom 35 lines of this post and examine the tactile output of a curve.
If you have any comments about what you see in the plot please send them to me at johnmillerphd at hotmail.com.  I welcome any feedback sent to the list as well.
If you are just using speech to review this post you could read the top part but I recommend skipping the end once you reach the line "image data begins here".
The tactile image renders well when using Jaws for Windows 2024 and default settings and pasted into notepad.
I find that the JAWS default settings also work well for reviewing the tactile image right inside Outlook 365.
I found that when I pasted the content of this post into notepad directly the notepad version has a blank line every other line.
I normally review these kind of images in notepad and in that case when I open the text file there are typically no blank lines on alternating lines.
You can learn more about the process of making images like this by contacting me or signing up to a very quiet list blindgraph at googlegroups.com.
I have made a variety of tactile outputs.  This one is example 81.
Here is a summary of the tactile image.
The tactile image is made up of braille characters but there are no braille labels inside the image.
You do not need to know braille to feel the tactile image.
The image is made by a program I authored called tactileGraphic.
The image is a plot of the function of x cubed minus x.
The plot ranges from x equals minus 1.5 to x equals 1.5.
As you arrow down through the image the first 3 rows form a print capital t followed by a print capital l.
The corresponding PNG file would show a TL in the top left corner signifying top left to help with orientation.
The image contains an x-axis and a y-axis that intersect at the origin in the middle of the plot.
The image contains 7 vertical tactile tick marks along the x-axis starting at x equals -1.5 and equally spaced through x equals 1.5.
It also contains 7 horizontal equally spaced tick marks along the y-axis starting at y equals -1.5 and going through y equals 1.5.
In order to best see a tick mark on the x-axis you may find it helpful to up arrow one row above the x-axis and then down arrow 2 times to see the full extent of the vertical tick mark.
The depicted curve starts in the bottom left, crosses the x-axis at the location of the x tick mark with value x equals -1, and then rises a little bit to a local maximum.
The vertical cell spacing is about 0.18.  You should be able to see that the local maximum is about 3 braille cells above the horizontal axis.  The x position of this maximum is near the x tick mark with value x equals -0.5.
>From the local maximum the curve drops down to pass through the origin.  It then reaches a local minimum now about 3 braille rows below the horizontal axis and with a x position near the x tick mark with value x equals 0.5.
The curve then rises up to cross the x-axis at x equals 1 and now takes on positive values as it curves up and to the right to end the section of graph shown.

At the top of what follows is automatically generated text describing the image.
Scroll down about 50 lines or so to get to the "image data begins here:" line to review the tactile image.
When you reach the "bottom of image" line about 35 lines later you have moved out of the tactile image and to the bottom of this post.
Thank you for letting me know what you think.


Example begins here:
the file name is test81_poly4.txt

title: f(x) = x^3-x

min x-value = -1.5000

max x-value = 1.5000

min y-value = -1.8750

max y-value = 1.8750

The min y-value is at (-1.5000, -1.8750)

The max y-value is at (1.5000, 1.8750)

x-value display length = 3.0000

y-value display length = 3.7500

The min display x-value is -1.5000

The max display x-value is 1.5000

The min display y-value is -1.8750

The max display y-value is 1.8750

mean x-value = -0.0000

mean y-value = -0.0000

possible x-intercepts are:

1: x-intercept x-value = -1.0000

2: x-intercept x-value = 0.0000

3: x-intercept x-value = 1.0000

possible y-intercepts are:

1: y-intercept y-value = 0.0000

possible minima are:

1: minima at (-1.5000 -1.8750)

2: minima at (0.5800 -0.3849)

possible maxima are:

1: maxima at (-0.5800 0.3849)

2: maxima at (1.5000 1.8750)

the number of input data samples  is 1001

the number of filtered input data samples  is 301

the number of nonblank symbols is 102

the portion of nonblank symbols to total symbols is 0.0909

horizontal pixel spacing = 0.0448

vertical pixel spacing = 0.0436

horizontal cell spacing = 0.0896

vertical cell spacing = 0.1308

configuration summary follows:

Has axis is 1

Has X tickmarks is 1

Has Y tickmarks is 1

tickmarkXStep = 0.5

tickmarkYStep = 0.5

The 7 X tickmarks are:

X tickmark 1: -1.50

X tickmark 2: -1.00

X tickmark 3: -0.50

X tickmark 4: 0.00

X tickmark 5: 0.50

X tickmark 6: 1.00

X tickmark 7: 1.50

The 7 Y tickmarks are:

Y tickmark 1: -1.50

Y tickmark 2: -1.00

Y tickmark 3: -0.50

Y tickmark 4: 0.00

Y tickmark 5: 0.50

Y tickmark 6: 1.00

Y tickmark 7: 1.50

tile density follows:

1,0.00,0.00,0.00,0.12,0.00,0.11

2,0.00,0.00,0.00,0.12,0.00,0.13

3,0.08,0.36,0.36,0.28,0.08,0.22

4,0.28,0.04,0.04,0.28,0.28,0.16

5,0.24,0.00,0.00,0.12,0.00,0.00

6,0.10,0.00,0.00,0.07,0.00,0.00

image data follows:

c?ca  l

 _    l

 _    v--'

skipping 1 blank rows

                _                ~

                _                s

                _                k

               `?c              _

                _               >

                _               k

               ,#-             ;a

                _              >

                _              l

                _             _

               ,#-            s

        ,034-   _            ;a

       0c   `e8 _            s

2    ;>a   2  `|#     ;     )a   ;

r3333)h3333r3333}73333w33334q3333w

b   ,q     b    _`|'  ~   ,sb    ~

    >           _  d5'   -f

   ,b           _    ch3fa

   >           `?c

   l            _

  _             _

  s             _

 ,b            `?c

 .              _

 s              _

 l             ,#-

.               _

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2               _

bottom of image