[Tactile-Talk] Tactile Talk Grayscale braille versus position

[John Miller]

Hello,
I have a new idea to share with you.
I thought this list was going to be used primarily for how to use a Graphiti or a Monarch or a multi-line braille display to look at tactile position information.
It is true that looking at the output of a 3D printer or looking at a tactile image generated by a traditional braille embosser or reviewing a text file sent to a traditional braille embosser all have merit for showing tactile information versus position.
I use the method described below at my work to look at intensity versus position images.
Sighted engineers look at intensity vs position images from time to time and find them quite useful.
Intensity vs position often shows up as a rainbow of colors from Red to Blue, or also can be different levels of gray when reviewed visually.

I wanted to share with you an example of grayscale braille.
It sometimes is the case that a blind person wishes to review an analytical 3-D function.
Visually these functions are often displayed in grayscale with different locations in a 2-D region having a gray level ranging from black to white.
For visual consumption the grayscale level will often range from 0 through 255.
Using letters of the alphabet results in coarser intensity resolution than 256 levels but allows for one braille symbol to be placed in one braille cell position rather than having to use 3 braille cells for a 3-digit number.
With a refreshable braille display or a braille embosser it can be useful to indicate different amplitudes of the image with different letters of the alphabet.
For example, the letters "a" through "t" can be used to indicate level 0 through level 19. This leaves letters "u" through "z" for special emphasis such as using "u" to mark the locations of a route through a topology map showing various altitudes of the land.
With 8-dot braille it is possible to use "a" through "z" followed by "A" followed by "Z" to display 52 levels. Additional symbols such as "1" through "0" can be extended to give 62 different levels of change but in this example only the symbols "a" through "t" are assigned.

I wish to look at the height of a sphere versus position for a sphere that is centered at the origin.
In this case the radius of the sphere is 1.5 and I examine the grid of x ranging from -1.6 through 1.6 and y ranging from -1.6 to 1.6 both with steps of 0.1.
For each (x, y) pair I evaluate the expression z equals the square root of the quantity r squared minus the sum of x squared plus y squared end quantity.
For z in the range of 0 less than or equal to z less than 0.1, assign "a"
for z in the range of 0.1 less than or equal to z less than 0.2, assign "b"
...
for z in the range of 1.4 less than or equal to z less than 1.5 assign "o"
for z in the range of 1.5 less than or equal to z less than 1.6 assign "p"
I form a 33 row by 33 column grid of letters ranging from "a" to "o".
The plot shows the top hemisphere of the sphere. Note that for the equation of the sphere for each (x, y) there is both a positive z value and a negative  z value with the same amplitude.

By observation the edges of the plot all evaluate to the "a" symbol or to zero.
Each row starts at zero and ends at zero and may visit a nonzero value in the middle.
The same is true for each column.
The letters in each row start with "a" and ascend with some jumps and some duplicates to a high letter and then descend in similar fashion back to "a".
The image appears to have radial symmetry.

The center of the image evaluates to the "o" symbol or to 1.4.

There are about 6 rows with at most 6 columns in each showing the "o" symbol.
Surrounding the "o" region is the "n" region evaluating to 1.3.
There are about 3 "n" symbols adjacent to each other in any row.
Surrounding the "n" region is the "m" region evaluating to 1.2.
You can trace a ring through the "n" region, "m" region, and other regions.

Returning your attention to the "n" region you can see that the band is at most 3 symbols wide or that the band has a width of at most 0.2.
The "g" region evaluating to 0.6 is only 1 symbol wide and on some rows has to be inferred by following the boundary between a letter earlier in the alphabet than "g" such as "f" followed by a letter later in the alphabet than "g" such as "h".
About half way down the image you can examine a row of letters that includes the peak amplitude letter "o".
At the middle of the row of letters the gradient from a "o" to a "j" is very gradual taking about 11 symbols to go from one to the other.
At the beginning and the end of the row it takes about 5 symbols to go from "a" to "j".
This means that an object with some decent traction placed near the middle of this row on the sphere would stay put but if it was placed on the left or the right edge of the sphere it would slide off.
In other words, the left and right sections of this row have a large change in altitude for a small change in horizontal position whereas the middle of the row has a small change in altitude for a small change in horizontal position.
These are observations that are not immediately apparent by just examining a comma delimited CSV file of the data.
On the other hand, these observations can be made directly by using the grayscale braille image.
The grayscale image of a sphere follows:
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
aaaaaaaaaaaabcdddccaaaaaaaaaaaaaa
aaaaaaaaadefgggggggffdbaaaaaaaaaa
aaaaaaabcefghhhhhhhggfdcbaaaaaaaa
aaaaabefghiijjjjjjjiihggedbaaaaaa
aaaabefhhijjkkkkkkkjjiihgfbaaaaaa
aaaaefhiijkkkllllllkkjjihgecaaaaa
aaabfhijjkkllllllllllkjjihfdbaaaa
aaacghijjklllmmmmmmllkkjjigecaaaa
aadehijkkllmmmmmmmmmmlkkjihfeaaaa
aaefijkkllmmnnnnnnnmmmllkjigfbaaa
aafgijkllmmnnnnnnnnnnmllkkihgcaaa
abghjkkllmnnnnnnnnnnnmmllkjhhdbaa
acghjkllmmnnnnooonnnnmmmlkjhhecaa
adghjkllmmnnnoooooonnnmmlkjihedaa
adghjkllmmnnnoooooonnnmmlkjihedaa
adghjkllmmnnnoooooonnnmmlkjihedaa
acghjkllmmnnnnoooonnnmmmlkjihecaa
acghjkllmmnnnnooonnnnmmmlkjhhecaa
aafgijkllmmnnnnnnnnnnmmllkihgdaaa
aafgijkllmmnnnnnnnnnmmllkjihgcaaa
aadfhijkklmmmmnnnmmmmllkkjhgfbaaa
aabdgijjkkllmmmmmmmmllkkjigedbaaa
aaacghijjklllmmmmmmllkkjjigecaaaa
aaabeghijjkkllllllllkkjjihecbaaaa
aaaadfghiijkkkkkkkkkjjiihfdaaaaaa
aaaabbefghiijjjjjjjiihggedbaaaaaa
aaaaaacdefghhhiiiihhhgeecaaaaaaaa
aaaaaaabcefghhhhhhhggfdcbaaaaaaaa
aaaaaaaaaabcdeeeeeedcbaaaaaaaaaaa
aaaaaaaaaaaabcdddccaaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Very best,
John
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