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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#467886" vlink="#96607D" style='tab-interval:.5in;word-wrap:break-word'><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;mso-ascii-font-family:Aptos;mso-hansi-font-family:Aptos;mso-bidi-font-family:"Times New Roman"'>Have you done much studies on the amount of information that can be done with grey scale.<span style='mso-spacerun:yes'> </span>What I am meaning is how many patterns actually work depending on distances between dots.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;mso-ascii-font-family:Aptos;mso-hansi-font-family:Aptos;mso-bidi-font-family:"Times New Roman"'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman"'>From:</span></b><span style='font-size:11.0pt;font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman"'> Tactile-Talk <tactile-talk-bounces@nfbnet.org> <b>On Behalf Of </b>John Miller via Tactile-Talk<br><b>Sent:</b> Wednesday, January 8, 2025 2:35 PM<br><b>To:</b> David Engebretson via Tactile-Talk <tactile-talk@nfbnet.org><br><b>Cc:</b> John Miller <johnmillerphd@hotmail.com><br><b>Subject:</b> [Tactile-Talk] Tactile Talk Grayscale braille versus position<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>Hello,<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>I have a new idea to share with you.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>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. <o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>I use the method described below at my work to look at intensity versus position images. <o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>Sighted engineers look at intensity vs position images from time to time and find them quite useful.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>I wanted to share with you an example of grayscale braille.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>It sometimes is the case that a blind person wishes to review an analytical 3-D function.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>For visual consumption the grayscale level will often range from 0 through 255.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>With a refreshable braille display or a braille embosser it can be useful to indicate different 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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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'> <o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>I wish to look at the height of a sphere versus position for a sphere that is centered at the origin.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>For z in the range of 0 less than or equal to z less than 0.1, assign "a"<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>for z in the range of 0.1 less than or equal to z less than 0.2, assign "b"<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>...<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>for z in the range of 1.4 less than or equal to z less than 1.5 assign "o"<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>for z in the range of 1.5 less than or equal to z less than 1.6 assign "p"<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>I form a 33 row by 33 column grid of letters ranging from "a" to "o".<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'> <o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>By observation the edges of the plot all evaluate to the "a" symbol or to zero.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>Each row starts at zero and ends at zero and may visit a nonzero value in the middle.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>The same is true for each column.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>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".<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>The image appears to have radial symmetry.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'> <o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>The center of the image evaluates to the "o" symbol or to 1.4.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'> <o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>There are about 6 rows with at most 6 columns in each showing the "o" symbol.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>Surrounding the "o" region is the "n" region evaluating to 1.3.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>There are about 3 "n" symbols adjacent to each other in any row.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>Surrounding the "n" region is the "m" region evaluating to 1.2.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>You can trace a ring through the "n" region, "m" region, and other regions.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'> <o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>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".<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>About half way down the image you can examine a row of letters that includes the peak amplitude letter "o".<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>At the beginning and the end of the row it takes about 5 symbols to go from "a" to "j".<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>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.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>These are observations that are not immediately apparent by just examining a comma delimited CSV file of the data.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>On the other hand, these observations can be made directly by using the grayscale braille image.<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>The grayscale image of a sphere follows:<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaaaaaaaaaaabcdddccaaaaaaaaaaaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaaaaaaaadefgggggggffdbaaaaaaaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaaaaaabcefghhhhhhhggfdcbaaaaaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaaaabefghiijjjjjjjiihggedbaaaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaaabefhhijjkkkkkkkjjiihgfbaaaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaaaefhiijkkkllllllkkjjihgecaaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaabfhijjkkllllllllllkjjihfdbaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaacghijjklllmmmmmmllkkjjigecaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aadehijkkllmmmmmmmmmmlkkjihfeaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaefijkkllmmnnnnnnnmmmllkjigfbaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aafgijkllmmnnnnnnnnnnmllkkihgcaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>abghjkkllmnnnnnnnnnnnmmllkjhhdbaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>acghjkllmmnnnnooonnnnmmmlkjhhecaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>adghjkllmmnnnoooooonnnmmlkjihedaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>adghjkllmmnnnoooooonnnmmlkjihedaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>adghjkllmmnnnoooooonnnmmlkjihedaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>acghjkllmmnnnnoooonnnmmmlkjihecaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>acghjkllmmnnnnooonnnnmmmlkjhhecaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aafgijkllmmnnnnnnnnnnmmllkihgdaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aafgijkllmmnnnnnnnnnmmllkjihgcaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aadfhijkklmmmmnnnmmmmllkkjhgfbaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aabdgijjkkllmmmmmmmmllkkjigedbaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaacghijjklllmmmmmmllkkjjigecaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaabeghijjkkllllllllkkjjihecbaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaaadfghiijkkkkkkkkkjjiihfdaaaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaaabbefghiijjjjjjjiihggedbaaaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaaaaacdefghhhiiiihhhgeecaaaaaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaaaaaabcefghhhhhhhggfdcbaaaaaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaaaaaaaaabcdeeeeeedcbaaaaaaaaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaaaaaaaaaaabcdddccaaaaaaaaaaaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'> <o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>Very best,<o:p></o:p></span></p><p class=MsoNormal><span style='font-family:"Calibri",sans-serif;mso-fareast-font-family:"Times New Roman";color:black'>John<o:p></o:p></span></p></div></body></html>