ON EDITING GRAPHICS FOR THE BLIND

A manual with examples, and for the interested layman a pictorial overview by Marco Schuffelen formerly of the NLBB,

Netherlands Library for Audio Books and Braille, The Hague, Holland

Copyright © M.L.J. Schuffelen 1989-2002

NLBB, Netherlands Library for Audio Books and Braille (Nederlandse Luister- en Braille-Bibliotheek) Badhuisweg 177 2597 JP The Hague Holland tel: +31 70-338-155-5

Table of Contents

1. PREAMBLE

Quite a number of learned articles have been written on relief representations for the blind, but on the May 1988 Stockholm Conference I gathered no comprehensive shop-floor manual was available. So I figured an accessible translation of the manual I'd written in Dutch might come in useful to the workers in this field. This rewrite into English is the manual's fourth edition: in every edition the general rules expand at the examples' expense, which of course is as it should be in a field as young as this. I guess development still has a long course to run ... This manual is based on the work I've done at the Netherlands Library for Audio Books and Braille, which was almost exclusively on books for secondary schools. I have never occupied myself with mobility maps, and I think they're entirely different from my kind of relief drawings. My graphics are put into relief on the stereo paper produced by Matsumoto, Osaka. As this paper has a finer grain, or is more sensitive than the Swedish product, it allows for stronger contrasts, like fine dots and thin lines next to solid black areas: it is more versatile. It's also more expensive, though, and unfortunately less pleasant to the touch too.

2. INTRODUCTION

In creating graphics for the blind one has to take into account that the fingers' discerning ability is so much less than the eyes', that in most cases magnification will be necessary; and of course text in and around the drawings will have to be put into braille; but I think most graphic material will need more editing to make sense to the blind reader. One might argue that editing is wrong, that the blind ought to be taught reading graphics that are basically the same as in inkprint; maybe there's a point in this, it's paternalistic, but I'm afraid extensive editing is often the only way of rendering a figure meaningful to the vision impaired. Some of the other editing is a choice, because I think it's best to do a drawing this way. For instance, while the seeing person will generally have an overview of a picture at first glance, the blind reader has to go through most of the details in a picture to understand what it's all about: so adding a good title to a drawing is absolutely essential, as a surrogate for this overview-at-first-glance.

Black and white map with King Darius' Heartland in solid back.

Point out King Darius' heartland As another example, look at this historical map. There are no names, but the sighted reader will most likely recognize the area, and that will bring to mind other maps and data of the area that he or she has seen in the past; but to the blind reader it's most likely just a blur with some lines and dots.

I think we have to provide the information that's not obvious to the blind, but that's taken for granted by the mapmakers for the sighted. So I have added a map 'Present-day Countries' in the same outlines, and I have identified some of the surrounding areas in the original map.

King Darius' map in braille with present-day countries outlined with dashed lines and labeled. Nothing is filled in. King Darius' map is in braille with shading for the filled-in areas of the map.

I thank my former and present department heads, Mr Leon Knierum and Mr Herman Philipsen, and my former and present immediate superiors, Mrs Nieuwpoort, Mr Van den Assem and Ms Hélène Vos, for putting and keeping me in this position and allowing me time to think and write about the development of the field; and I thank the members of my staff, especially Marlon Macville, Walter Smekens and Leen Verkijk for their examples and instructive mistakes. One of the ideas on maps I got from from Colin McEvedy's beautiful historical atlases (Penguin); some inkprint graphs etc. were taken from The Economist.

3. BASICS

MINIMUM DISTANCE

As a blind person won't be able to discern two points as separate entities if they're closer together than 2.5mm, this 2.5mm is about the minimum distance between different items in relief drawings.

THE FINGERTIP WINDOW

Also important to keep in mind is the concept of the fingertip 'window', about the size of a Braille cell. Cut a hole about this size in a piece of paper, move that over a drawing to get an idea of a blind reader's perception. Also, if for instance you have to show that a line is interrupted, the break shouldn't exceed this window.

STAINLESS

Keep your drawings clean, free of stains: the blind reader won't recognize smudges for what they are, but will think they're part of the picture.

EXCELLENCE

Strive for excellence in draughting: either make a good drawing or none at all: no halfway house. Understanding graphics will never be easy to the blind, and an unintelligible drawing will put our readers off and is going to amplify the notions about the usefulness of our work. If you are not sure whether a particular drawing makes sense, consult a blind reader, and when still in doubt abort or try a radically different rendering.

THINK FIRST

Ideally one should ask oneself at each figure what its meaning is and how best to represent that to our readers. Of course in many uncomplicated drawings that won't be necessary, but one should be wary of unexpected unclarities and have possible elucidation in mind all the time. One should never unthinkingly copy inkprint, but look for the best way to render the subject to our readers: put things in or leave them out, change, separate, comment, go for a partial or complete description. Consequently the drawings I find hardest to re-create are in the fields that I do not understand the method of, like psychology or economics (I was raised in physical sciences): as I do not understand clearly what their schemes mean I do not know what's important and what isn't, so I don't know which things are to be displayed prominently and which elements might be left out, and I cannot really describe these drawings accurately. So otherwise one has to be careful about editing drawings from subjects one is not familiar with.

ENLARGING, SPACE

Only a few drawings need no magnifying. Sometimes, when recognition of a specific form is asked for, a small figure will do better; but in general draw your graphics as big as possible. If text and key might take up space needed for your graphics, don't hesitate to transfer them to a separate page.

CONTRASTS

Not only should your drawing be large, but also have its elements contrast as much as possible, thin lines and fat lines, no hatchings that look about the same. I think drawings that have a bold, solid look are best.

EXPLAIN, SIMPLIFY

Some drawings contain small real-life parts, unrecognizable to a blind reader: simplify these figures and explain them in key or with an accompanying word.

1. Formalize, Reduce to Essentials

There are two picture answers. C has two large pitchers and 13 small pitchers, and D has three large pitchers and 10 small pitchers. Brailled page of the picture of pitchers. The pitchers are represented with rectangles (large and small) missing the top lined. They are all filled with a dotted pattern. Braille words are in between the tactile diagrams.

True pictures of pitchers will be hard to recognize. Note that the pitchers are all drawn separately, overlapping would make them hard to recognize. Also note that the pitchers are not empty, for those would just look like a crooked line.

2. Simplify, Explain

Professor's head looking at the light shining at a ball casting a shadow on the screen. Simplified braille diagram with the angle from the light point.

Reduce lifelike elements - I wouldn't want my readers having to waste time puzzling over the professor's head. Lightpoint A, 2 meters from screen; ball with center B, radius 30cm; line AB perpendicular to screen, AB=1m.

3. Reduce to Essentials

Map with two homes and another destination off the right side of the map. Several illegible signs are present on the map. Braille version of map with the road represented in the center with vertical lines. Each home/destination is marked with a hatch-filled square. Each route is labeled on the right side of the map.

Would the house shape make more sense than a square?

4. Formalize, reduce to essentials

Picture and illegible text with two beakers, each filled to a different capacity. Braille version of the beaker picture, with braille text at the top and two beakers represented by open-top rectangles, each filled with dots at a different level. The measurements for the beakers are in the middle of the two rectangles.

5. Formalize, Reduce to essentials

Complicated page with 3 figures comparing the height of a giraffe and kangaroo in each figure. Simplified braille replication of the figures from the giraffe page. The giraffe and Kangaroo are represented with horizontal rectangles.

Turn the giraffe and kangaroo into named boxes. The direction has changed from vertical to horizontal to facilitate writing. Also note that a ruler is provided with each drawing, for the blind readers may not have a measuring rod as readily available as the sighted reader.

UNIFORMITY

Graphics being hard for the blind anyway we had best ease the burden by striving for uniformity. If our readers are able to recognize quickly the kind of drawing and its usual items, they only have to touch these lightly, saving time to focus on the particular elements.

TIME

The sighted take in pictures at a glance, but to the blind reader it is always a matter of minutes, a series of maps might take some ten to fifteen minutes; so the draughtsperson should ask himself if this amount of time taken is justified in view of the kind of information provided in these graphics. Imagine a blind student poring over some maps for twenty minutes to answer a petty question in an examination.

4. THREE EXAMPLES

In editing complicated graphics, the draughtsperson should look for the print picture's meaning, and render it in the most simple and/or clearest way to a blind reader.

Example 1:

Take a look at this transverse section through a tree trunk. In print, the different elements have been fanned out: one wonders what kind of impression the faithful copy will make on a blind reader. Do trees look like that? A less complicated, more realistic rendering of the material will make more sense.

transverse section through a tree trunk Braille example of transverse section of the tree

Wrong: can we expect the blind reader to make the leap of imagination to see this as a cut through a tree?

Another simpler braille diagram of the transverse section of a tree trunk

Better, but could use a key. See the image to the left.

The transverse section of a tree trunk is represented as a semi-circle with different texture fills for the center.  The truck is labeled.

In the cell mitosis drawings that go with the tree trunk, I wonder if drawing a cell spatially will be very useful: representing a cell by a rectangle will make the drawing far easier to read. Also note the addition of the word 'mitosis' at the arrows.

Mitosis is represented horizontally with filled rectangles. Key at the top of the rectangles.

Will the spatial drawing with broken lines mean anything to the blind reader?

Each layer of Mitosis is designated by a fill and a label. Mitosis is going vertically down the page.

Also note the addition of the word 'mitosis' in braille.

Two stomach drawings look all right at first glance, but the second one will actually be much clearer to the blind reader.

Simplified, outline drawing of the stomach, filled with a dotted pattern. There are three arrows pointing to different parts of the stomach: one pointing to the entrance at the top (esophagus), one pointing to the middle section, and one pointing to the exit towards the intestines at the bottom left. simplified, outline drawing of the stomach, filled with a finer dotted pattern compared to the first image. Unlike the first image, there are no arrows pointing to different parts of the stomach. Braille labels are present on the different parts of the stomach.

6 mistakes:

1. Spatial elements

The stomach's entrance and exit are drawn spatially, an ellipsis and an arc: will this make sense to the reader? What will the ellipsis mean to him? In the second drawing it is immediately clear what the stomach's openings are.

And besides, the drawing is of a section through: not spatial, not the stomach taken out, so representing entrance and exit as openings makes more sense.

2. Hatching

A hatch is meant to show something's extent. In the first drawing the big dots are so far apart that the reader might easily gather that they are meant to represent something like holes or moles. Ideally a hatch's elements should not be individually discernible.

3. Arrows

What exactly do arrows point at? Isn't there a choice in 2-3A at the arrows indicating the duodenum and oesophagus? Placing one or two characters in the right place is unequivocal, leaves no room for doubt. Sometimes an arrow is the only way of identifying an element, but I think they should be used sparingly.

4. Title

The title is missing. To find out what's in this drawing the reader will have to look it up in the text volume, or he'll have to infer it from the names in the drawing. The small addition 'The stomach' will greatly enhance this drawing's value.

5. Figure number

The figure number is split over two lines, 11.11 in the first line, A in the sixth. Why not simply fig. 11.11-A in the first line?

6. point 6

- There is no need for point 6 in biology.

GRAPHICS VOLUMES

5. GENERAL

In a book of only a few drawings these are added to the text volumes and given 'A' page numbers (89A, 22A, 22B etc.), so as not to be restricted to a fixed number. If the number of drawings exceeds say 15, we dedicate one or more volumes to graphics; these volumes are numbered A, B, C etc. so as again to be at liberty, as I generally find it very hard to guess their number correctly beforehand. The title page of a graphics volume should look like the text volumes' title page. It should state:

TEXT

The rendering of mathematics etc. in a drawing of course has to be uniform with the other text. Formerly most of the text in a drawing, lists of abbreviations etc. were put in the text volumes, but some time ago we have argued at our library that though somewhat more expensive, it is to be preferred to have the graphics volumes stand on their own, so as they can be read without having to look up explanations etc. somewhere else. But we still expect the text volumes to carry the complete titles of graphic material, reference numbers, and besides that the data that are not essential in reading a drawing, like its source or author.

PAGES

In The Hague we are at the moment experimenting on having related pages face each other, but there are some doubts as to the relief rubbing off and pages going to stick to each other. If these objections are met it's of course quite useful, not having to turn the page to get at the key etc.

NUMBERS

The figure or page number is placed at the right-hand upper corner of the page. In general stick to inkprint figure numbers; if missing make them up yourself, preferably relate to chapter and paragraph (fig.3-2 rather than fig.16). Figure numbers are absolutely indispensable for reference in graphics volumes.

TITLE

Never forget to put a title title a drawing, to give the reader an idea what's in store; state also what kind of drawing it is: graph, bar chart, triangle, etc. Do not copy inkprint unthinkingly, but have your title say exactly what your drawing is going to show. Occasionally key or explanation of abbreviations might work as a title, like stating what x and y stand for will introduce a graph. The blind reader will not automatically understand a drawing to be part of a series or an enlargement of a detail, so state those things clearly in your title or at the end of your drawing, 'enlargement detail', 'to be continued on the next page,' etc.

PAGE ROTATION

As we use the A4-format, short side on top, drawings that have more width than heighth will have

to be put on a rotated page; rotate clockwise, or else the reader will have to reach over the facing stack of pages. Use some standard text in cases like this, 'turn page to the right' or 'rotate page clockwise'. (My fonts print this line at one keystroke.) Preferably put key and other text (except number and title) in the direction that the drawing is to be read, also when on seperate pages. It is not a good idea to switch direction within a series, but sometimes it cannot be helped.

MARGINS

Drawings should stay clear of the paper's edges. At the left side a margin of about two centimeters will have to be kept clear for binding; on the other sides a space of about one centimeter is best left open to avoid losses in xeroxing. On a facing left-page the 2cm margin will be at the right of course. Unfortunately our plotter restricts us to a height of 27.2cm anyway.

START

I prefer to begin a drawing by putting down number and title, so as not to encounter a limitation there after having finished the graphic part. When graphics need all available space I limit text to two, or very occasionally one line.

ABBREVIATIONS

Though a complete word will occasionally nicely fill out an area, long words will not point clearly at one element in the drawing, and as they generally take too much space anyway, abbreviations are to be used. We mostly utilize one- or two-character indicators in relief graphics. For ease in reading, try to work out abbreviations that still show something of the original word. Try to use existing abbreviations. List the abbreviations and their explanations in alphabetical order, or, if you really understand what a drawing is about, in the order it should be read. Sometimes part of the inkprint graphics, like numerical values, can be incorporated in this list of explanations. Remember that braille characters a-l cannot stand on their own, but need something like a preceding point 6; and be careful about employing mathematics-code characters in math and physical sciences figures.

LINES

In hand-draughting we utilized pens of .25mm, 1.0mm and 2.0mm width, resulting in three clearly different lines. In plotting Autocad, for technical reasons we only use one pen, 0.5mm width, so we lost the very thin line. In some cases, like grid in graphs, we now use a fine dotted line, preferably about 3.5mm interspaced.

HATCHING

Hatching is what I call filling in areas ... To use in hatching, I've been looking for patterns that are clearly different from each other to the tactile reader. Tests with blind colleagues resulted in this set of eight. I do not object to other types of hatching, but I'm afraid it will be hard to find another clearly different pattern.

A reference chart titled

Some patterns might be used at different angles; but only Line is that clear it can be used to indicate different areas. Choose zigzag's and the dashed lines' angle as will fit your drawing best. Line might look like real lines in a drawing, so use this pattern sparingly to avoid confusion, especially in mathematics. The medium dots ('jan') might look like braille. For larger areas, shading is preferred over filling in with abbreviations. Shading or Abbreviations?

A hand-drawn map titled

(Natural vegetation in Russia)

It isn't wrong, but ...

A simplified, tactile version of the Russian Vegetation Map. The regions are labeled in Braille on the map, and the boundaries between regions are indicated with straight lines. The tactile map simplifies the visual complexity by focusing on the boundaries and the key regions labeled in Braille. The labels match those in Image 1 but are presented in Braille for tactile reading. Another tactile map, similar to Image 2, but with additional hatching patterns and textures to differentiate regions. The patterns include:
Vertical lines for

Shading is preferred over abbreviations for filling in larger areas. Abbreviations are OK for small areas. (This picture was drawn before I developed the hatching-without-borderlines doctrine.

Lines through hatching will not be very clear, so don't follow the original drawing or leave room around the lines. (See also Arrows, below in this chapter.)

Edit your drawing to avoid lines through a hatching

An illustration demonstrating the correct and incorrect ways to edit a drawing to avoid lines passing through hatching.
Original (left): A simple cross-sectional view of a circular object with two measurements indicated. The outer diameter is labeled as 12 cm, and the inner diameter is labeled as 10 cm. The area between the inner and outer circles is hatched with diagonal lines.
Wrong (center): An edited version of the original drawing showing a larger circular object with multiple concentric circles and hatching between them. The measurement lines for the inner and outer diameters pass through the hatched area, making it difficult to interpret the hatching pattern. The measurements are labeled in Braille and standard text, indicating the diameters outside the circles.
Right (right): A corrected version of the drawing showing the same circular object with concentric circles and hatching. The measurement for the inner diameter is placed inside the circle, avoiding any interference with the hatching. The measurement for the outer diameter is placed outside the circle. Both measurements are labeled in Braille and standard text, ensuring the hatching remains clear and unobstructed.
The illustration emphasizes the importance of positioning measurement lines to avoid crossing hatched areas, thereby maintaining clarity in technical drawings.

Counter-highlighting is what I call putting a hatch around the relevant area, leaving the unshaded area standing out (.. blankly). This also allows for writing text or identifying characters in that area. But usually there is so much more blank space on a page that it doesn't work to identify smaller areas.

A tactile graphic demonstrating the concept of counter-highlighting. The image consists of a large area filled with a dot pattern, representing hatching. Within this hatched area, there is an irregularly shaped, unshaded region that stands out prominently. This unshaded area has a thick, wavy line running through it. Above the main graphic, there is a section of Braille text, and the entire image is designed to show how counter-highlighting can be used to leave relevant areas unshaded for writing text or identifying characters. The border of the unshaded area is clearly defined to maintain clarity between different hatched regions.

A borderline in between two hatches impairs clarity, so ask yourself if you can't do without; also don't put lines around the patterns in your keys. Generally I only put in a bordering line when there's hatching only to one side of it.

A tactile map with various regions differentiated by different hatching patterns. Each region uses a unique pattern of lines or dots to distinguish it from neighboring regions. The patterns are spaced sufficiently apart to ensure they are clearly discernible. Two areas are solid black, indicating important landmarks or features. Another version of the tactile map with different hatching patterns. This map emphasizes the use of small dots, vertical lines, and other textures to indicate various types of surface water and other elements. The map includes several areas filled with different patterns to show the minimum distance between hatches. Solid black areas are used sparingly to avoid wasting space and maintain clarity.

Take care your hatches stand at least the minimum distance (2.5mm) clear of each other and other elements, or they won't be clearly discernible. The small-dots pattern feels a bit like the hatch in the plastic Thermoform maps indicating surface water, so I generally use this one for surface water, and also in fluids, cells, living tissue etc., water interpreted broadly.

Solid hatching, a completely black area is only a waste of time and ink, as in relief it will feel the same as a crosshatching like net 15. (In hand-draughting we of course filled in the solid areas using brush and ink.) I think small areas are best hatched in this pattern.

FILLING IN

Sometimes a line in an otherwise clear field in ink print is an edge, an outline: the blind reader on encountering a form like this will only recognize it as a line, not as a form: so I think forms, shapes had best be hatched. Look for example at the Venn-diagrams below. Ink print shows two ellipses, sets of numbers. Imagine a blind person reading a faithful copy, coming across lines and numbers, but what do they mean? "Ah ... here's a line ... I feel a dot ... and a number ... lines crossing ... a dot and a number ..." The ellipses will just be curved lines, and there appear to be some numbers in the drawing. I think sensible editing can make a drawing like this a lot more meaningful: by hatching the sets in different patterns, explaining these patterns in a key and stating 'Venn- diagram, two sets' in the title, of course. Also note that in the braille version there are no dots next to the numbers: the numbers 'represent themselves.'

Filling In To Show Sets (Venn Diagrams)

An ink print Venn diagram with two overlapping ellipses labeled B and C. Each ellipse contains a set of numbers: B contains 2, 4, 6, 8, and 10; C contains 3, 6, 9, and 12. The overlapping section contains the number 6, indicating it is common to both sets. The ellipses and numbers are presented without any hatching. A tactile version of the Venn diagram with two overlapping ellipses. The ellipses are not hatched, and the numbers are presented in Braille within the ellipses. The numbers are positioned similarly to the top left image, but the lack of hatching makes it difficult for a blind reader to discern the sets clearly. An improved tactile version of the Venn diagram with two overlapping ellipses. Each ellipse is filled with a different hatching pattern to differentiate the sets: vertical lines for set B on the left, horizontal lines for set C on the right, and a crosshatch pattern in the overlapping section to indicate the common element. The numbers are presented in Braille within the respective hatched areas. A key above the diagram explains the hatching patterns.

example of the need to fill in spaces because the vision impaired reader does not easily lines as indicating shapes is this ugly picture of the shape of the mouth forming letter 'a'.

Filling In Shapes

A simple line drawing of a side profile of a human head with the mouth forming the letter 'a'. The drawing includes the outline of the mouth and the letter 'a' positioned inside the mouth. The line drawing alone is not easily recognizable as a shape indicating the mouth. A more detailed line drawing of a side profile of a human head showing the mouth forming the letter 'a'. An arrow points to the open mouth. The image includes Braille labels indicating different parts of the mouth and throat. However, the outline alone does not clearly convey the shape of the mouth to a tactile reader. An enhanced version of the previous drawing with various hatching patterns used to fill in different areas of the mouth and throat. The diagram uses vertical lines, horizontal lines, dots, and zigzag patterns to differentiate parts of the mouth and throat. A key above the diagram explains the hatching patterns used. This filled-in version makes it easier for a tactile reader to understand the shape and structure of the mouth, forming the letter 'a'.

Filling in an area shows its extent much better than arrows indicating an outline.

Showing an Outline: Arrows or Filling In?

A rectangular diagram with several sections labeled An enhanced version of the rectangular diagram with the inner rectangle filled with a dot pattern. The surrounding areas are left unfilled, making the filled section stand out clearly. A key above the diagram explains the hatching patterns used. This filled-in version shows the extent of the area much better than arrows, providing a clear and distinguishable shape for a tactile reader.

CLEAR SPACE AROUND BRAILLE CHARACTERS

Braille characters should not be touched by lines and be sufficiently clear of other elements in a drawing.

A diagram illustrating the proper way to clear space around Braille characters to ensure clarity and avoid interference with other elements in a drawing.
A detailed diagram demonstrating the importance of clearing space around Braille characters: Top Section: Includes various Braille characters and patterns with arrows pointing out the required clear space around them. The clear space distances are specified: 4mm above and below, 3mm to the left and right, and 5mm diagonally. Middle Section: Shows examples of correctly and incorrectly spaced Braille characters. The correct examples are labeled "right" and show clear space around the Braille dots, while the incorrect examples are labeled "wrong" and show lines touching or too close to the Braille characters. Bottom Section: Illustrates proper and improper use of surrounding lines and borders around Braille text. The correct examples maintain a clear rectangle of space around each Braille character, while the incorrect examples show lines intersecting or touching the Braille dots. The diagram emphasizes the need for sufficient space around Braille characters to ensure they are distinguishable and not obscured by other graphical elements.

Imagine some lines of braille text. Single out one or two characters. Draw straight lines around the chosen characters at the nearest points in the surrounding braille characters, left and right, above and below. The rectangle shows the amount of exclusive space a braille character needs. Distance to the lines above or below is about 4mm, to the left or right 3mm, diagonal 5mm.

Take care with initial or final characters that don't have a complete row or column of braille dots, like character l or the capital sign: despite the open space the same area should be cleared as around a full character.

The ASCII Braille Alphabet

As well as being the characters used by an embosser, these characters map to the keys needed to produce the Braille character in a word processor, using the Braille font.

A Braille reference chart mapping each Braille cell to its corresponding ASCII character, including letters, numbers, and symbols. Each cell in the chart shows the Braille dot configuration for the character along with the ASCII character it represents. This chart is a reference for converting text to Braille for transcription and printing purposes.

DOTS

Sometimes a graph shows fat dots, points, or in maps cities will be represented by dots or small circles. I prefer to leave out these dots and put the indicating character in its place; except of course when a high degree of precision is called for, but that's rare.

ARROWS

A diagram showing three types of arrows used in tactile graphics:
Right: A solid triangle with a tail. Occasionally: A V-shaped arrow.
Wrong: An arrow lacking the tail.

I try to avoid arrows by placing the indicating phrase in or close to the item, or by using key, but sometimes pointing an arrow is the only way to put a name to an element in a drawing. Employ a solid triangle and don't leave out the tail on the short side, the triangle without it doesn't work; when cramped, a V-shape arrow will do. V-shaped arrows:

A tactile map with various areas and paths marked by V-shaped arrows. The map includes Braille labels indicating different sections and directions. The arrows guide the reader through the map, clearly showing the intended paths and ensuring the map is easily navigable for tactile readers.

In very fat lines (over 5mm), having the line gradually taper to a point is better than adding a big arrow shape at the end. In simple graphs that only have arrows at the axes I leave out these arrows and put in a zero or origin sign. In busy drawings, clear a shaft around the arrow and its tail; sometimes this calls for an accompanying unaddled copy drawing (see figures overleaf).

Clearing Shafts for Arrows

 A detailed cross-section of plant cells without any arrows. The various cell types are depicted using different patterns and outlines. This image serves as the base diagram, illustrating the structure of the plant cells. The same cross-section of plant cells, but with arrows pointing to specific cells. The arrows have clear shafts around them, ensuring that the pointing lines do not interfere with the patterns or the readability of the Braille text. The arrows indicate important features of the cells, with the shafts providing the necessary clear space to maintain clarity and prevent any confusion for tactile readers.

KEY

If a key is needed, put it where it will be read ahead of the drawing proper. If it has to be in another place, notify the reader of this in your title. The columns of a key shouldn't be too far apart. On a page that's to be rotated, the key should preferably be written in the drawing's direction.

STARTING POINT

Some drawings show a sequence of events, a progression or a flow of things. The sighted reader will find the place to start reading in no time; not so the blind reader, so either edit your drawing to have this starting point at the top left of your drawing, where the blind reader starts reading, or indicate its location in your title. Drawing Edited, Starting Point Moved

A tactile diagram showing a sequence of events or a flow. The diagram includes a rectangular structure with various sections, some filled with different hatching patterns. An arrow labeled

1. Starting Point Indicated

An original print graphic showing various fruits scattered across a grid. The fruits include lemons, bananas, pears, and apples, each represented by a distinct shape. The grid lines are clear and distinct, helping to organize the fruits. A small arrow or marker indicates the starting point at the bottom left corner of the grid, guiding the reader on where to begin. A tactile graphic version of the print image with a grid and Braille text. The grid is clear, and a distinct marker (a small circle) is placed at the bottom left corner to indicate the starting point. The Braille text provides a key for the fruits shown in the left image, giving a Braille symbol for each type of fruit (lemons, bananas, pears, and apples). This key helps tactile readers identify the fruits on the grid.

6. GEOMETRY

An inkprint geometrical drawing is a set of dots, lines and shapes: the figure, accompanied by identifiers like characters, and symbols like indicating a 90° angle etc. Inkprint symbols are often graphical, in relief these might easily be mistaken for 'real' parts of the drawing: so I think they had better be replaced by braille code, or their meaning described, to avoid probably confusing images. Take care your identifiers are unambiguous, make sure they point at one item only. For ease in reading, draw lines belonging to different items or of different meaning in different widths, like a triangle fat-lined, the lines inside thin. Take special care of intersecting lines. Basic Editing in Geometry

An inkprint geometric drawing of a triangle and a circle. The triangle is labeled with points A, B, and C. Several identifiers and symbols are included:
Orthogonal sign represented by a small square at the right angle.
Equal angle signs shown as arcs with short lines.
Equal distance signs shown as small parallel lines.
The circle is labeled with a capital letter M.
Parallel lines are marked with arrows.
Various lengths and angles within the triangle are indicated by graphical symbols. A tactile version of the same geometric drawing, adapted for tactile readers with Braille labels and simplified symbols.
The triangle and circle are still present, with the following modifications: Remarks in Braille text replace the orthogonal sign, equal-angle signs, and equal-distance signs due to space limitations. Characters P, Q, and R are added to allow for the replacement of equal-distance signs. Parallel lines and angle signs are described in Braille text rather than shown graphically. The Greek character for 'angle' is preceded by Braille code. Length statements are repeated in Braille text. Different line types and widths are used to distinguish various parts of the drawing.

Basic Editing in Geometry

  1. Orthogonal sign replaced by braille code.
  2. Orthogonal sign replaced by remark in text because there's no fitting palce to put braille code.
  3. Equal-angles signs replaced by remark in text.
  4. Equal-distances signs replaced by remark in text; to allow for that, characters P, Q and R were added.
  5. Parallel-lines signs replaced by remark in text.
  6. Arc not copied, Greek character preceded by braille code for 'angle.'
  7. Length statement replaced by, or at least repeated in text.

Also note that different kinds of lines have been drawn in various line types and widths.

Grids

In general, the grid has to be copied, but don't let it get too fine-meshed, squares with sides smaller than 1½ cm make no sense, preferably go over 2cm. Use very thin or dotted lines for your grid. A very fine grid could either be simplified by rendering only the even lines, have the odd lines represented by a small dash on the axes only, or leave out the lines altogether, and put dots at the (imaginary) intersections.

Two side-by-side diagrams showing examples of grids with geometric shapes, illustrating the correct and incorrect ways to simplify fine-meshed grids for tactile graphics.
Wrong Example: The grid has fine-meshed squares smaller than 1.5 cm, with thick lines making the shapes difficult to discern. The label "wrong" is written below the grid. Right Example: The grid is simplified with only the even lines rendered, using thin lines for better clarity. The odd lines are represented by small dashes on the axes, or lines are left out altogether with dots at imaginary intersections. The label "right" is written below the grid. These images demonstrate the importance of using thin or dotted lines and simplifying fine-meshed grids in tactile graphics to ensure clarity and ease of interpretation for tactile readers.

Some figures carry very small details: if necessary zoom in on a separate drawing. For clarity, or even perceptibility, we sometimes have to make changes, overdoing distances etc.: just as long as we don't change its meaning. Geometry graphics sometimes sport real-life elements: I prefer to edit those parts, as in general they're just there to brighten up the picture. Occasionally a formalized form with an explanation or a description will be necessary.

An inkprint drawing of a geometric scene featuring a small tree and the sun, with detailed surroundings. The tree, sun, and ground form a right-angled triangle. The tree stands vertically on the ground, casting a shadow along the ground towards the right, with the sun positioned at the top left corner of the triangle. The triangle formed by the tree, sun, and ground is an important geometric element in this drawing. The drawing includes elements like grass and a small object on the ground. A tactile version of the geometric scene. The small tree is simplified and represented by a hatched pattern to indicate the foliage. The grass and other small details are omitted for clarity. The triangle representing the geometric shape is clearly defined with thin lines, showing the vertical tree, the horizontal ground, and the hypotenuse formed by the shadow. Important elements are labeled in Braille. The formalized drawing includes measurements and simplified elements to ensure clarity for tactile readers.

Refer also to the formalising examples in earlier chapters.

This also applies to drawings showing tools like scissors, plastic triangles, rulers etc.: in general just mentioning their presence and describing their use makes more sense than trying to reproduce their outline.

A series of four boxes, each containing a geometric diagram with points and angles:
The first box shows two points labeled p and A.
The second box depicts a right-angled triangle with points P, A, and an arc indicating an angle.
The third box shows a right-angled triangle with points P, A, and an arc indicating an angle, with an additional segment intersecting the triangle.
The fourth box features a right-angled triangle with points P and A and an arc indicating an angle, along with a line segment intersecting the triangle to form a smaller triangle within. A tactile graphic representation of two geometric diagrams with points and angles, adapted for tactile readers with Braille labels.
The first diagram shows two points labeled p and A. An arrow points from p to A, indicating movement or direction.
The second diagram depicts an angle formed by two lines meeting at a point labeled P, with an arc indicating the angle between the lines. The points p and 
A are labeled in Braille. A tactile graphic representation of two geometric diagrams with points and angles, adapted for tactile readers with Braille labels.
The first diagram shows a triangle with points P, A, and an arc indicating an angle at the point of intersection, labeled in Braille.
The second diagram features a triangle with points P, A, with lines forming the angle and the points labeled in Braille.

Replace ink print colours by our different hatches or line types; don't forget to have the text changed too. In simple geometry open and filled dots sometimes have a specific meaning, so copy them in a perceptible way.

Spatial geometry, or in fact its two-dimensional renderings, are very hard on the blind student, as a slanting line will not indicate a possible change of plane. I think a cube or pyramid are as far as we can go, and even in these our reader will need help, so I have a figure like these preceded (once in a volume) by a like figure with an explanation as which plane is in front, which on top etc. The Braille text says: "Introduction to the cube. "Plane ABCD is the base, ABFE is in front, etc. "Broken lines are at the figure's back, not visible from the front ... "

A geometric diagram of a cube, showing different planes and lines, adapted for tactile readers with Braille labels. The cube is presented in a perspective view with the following features:
Solid lines represent the edges visible from the front.
Dashed lines represent the edges at the back of the cube, not visible from the front.
The Braille text next to the cube provides an explanation of the different planes and their positions.

7. GRAPHS

A graph consists of axes, and lines or points inside these axes sometimes called functions. Graphs being rather straightforward, they're excellent material for codifying, uniformity. So following the survey of adaptations I have written up a method for graphs. Very simple graphs sometimes have arrows next to the axes: I think arrows don't mean much to our readers, so I put in a zero at the axes' intersection and leave out the arrows altogether. Next to, or below the axes their meaning is often written in full: in particular at the y-axis this is often not a very clear indication (as I explained before) and besides it takes too much space, so I prefer to use an x and y at the axes in any graph, explaining their meaning in a key (years under the x-axis are fine). Only where ink print already has a one- or two-character identifier do I copy those. Basic Graph

A basic print graph showing a curved line representing a function. The graph has an x-axis and a y-axis, both labeled with arrows at their ends. The curved line starts near the origin at the bottom left, rises steadily, and then curves upward more steeply as it moves to the right. The x-axis and y-axis are not numbered, and there is a small circle at the intersection of the axes indicating the origin. The text A tactile version of the basic graph. The graph features an x-axis and a y-axis, labeled in Braille. The curved line represents the same function as in the print graph, starting near the origin and rising steeply as it moves to the right. The small circle at the intersection of the axes is replaced by a Braille number indicating the origin. The x-axis and y-axis are labeled in Braille to explain their meaning. The text below the x-axis in Braille provides the same information as the print version, ensuring tactile readers understand the function being represented.

The small circle at the axes' intersection poses a Braille problem: is it number zero or capital letter O? In mathematics, to be recognized in ink print by x and y at the axes, it's capital letter O; in all other graphs, showing real units at the axes, it's number zero. Preferably put y and y-numbers left of the y-axis, x and x-numbers below the x- axis; but if this should impair the clarity of your drawing put them somewhere else. In mathematics generally only the O and two 1's are shown: if possible, copy; otherwise put in some other number. Sometimes a graph gets clearer by pruning axis numbers, there's often no need for the reader to go over a profusion of numbers.

In my opinion putting an identifying text or word next to a curve or function line is not very clear: you'd better choose different line types and explain their meaning in a key.

Basic Math Graph

 A tactile graphic of a graph with a solid grid. The graph features a line that rises diagonally from the lower left to the upper right. The x-axis and y-axis are marked with numerous numbers. Functions are labeled directly next to the lines within the graph. The grid lines are solid, and there are multiple numbers indicated along both axes.

Wrong:

  1. Too any numbers
  2. Grid is solid line, too similar to other lines
  3. Functions are given next to lines: is that unambiguously clear?
A tactile graphic of a graph with a dotted grid. The graph features a line that rises diagonally from the lower left to the upper right. The x-axis and y-axis are marked with a few essential numbers. Functions are not labeled directly next to the lines but are instead explained in a key. The grid lines are dotted, distinguishing them from the function lines.

Better :

  1. A few numbers suffice (Note #2 on x-axis: there is no room for #1)
  2. Grid is a dotted line, clearly different from other lines
  3. Functions are explained in key

Use A Key

A print graphic of a detailed graph showing the development of stock prices for Texaco and Pennzoil over time. The graph has a detailed grid with lines very close together, making it hard to distinguish between them. The x-axis represents time, marked with months and years, while the y-axis represents stock prices, marked with numerical values.

The grid will make a Braille graph hard to read, and identification next to the lines is not clear

Remove the grid for clarity, and identify the lines in the key;

Note that the line explaining the y is the title; The key might have been placed in line with the graph.

An adapted tactile version of the same graph. The grid has been removed. Two lines represent the stock prices: one solid and one dotted. The axes are clearly marked, with the x-axis labeled with months and years and the y-axis showing stock prices. The lines are separated by a noticeable gap.

The zeroes in the thousands or millions of the units at the axes take unnecessary space: cut down by explaining in the key (e.g. "y - cars manufactured x1000"). In rare cases one of the rows of numbers might be written in a deviant direction. Preferably make a remark about this. Draw the axes in a standard width, for instance 1mm. Don't copy the zigzag indicating an axis interruption: a short break in the axis line (about 7mm, within the fingertip window) is clearer.

A print graphic showing an oil drum with the title An adapted tactile version of the graph. The jagged line from the print version is replaced by a short break in the axis. The y-axis is positioned on the left and the x-axis on the bottom. The graph features a single smooth, solid line representing the data. The y-axis is labeled with Braille text indicating the reserves, and the x-axis is labeled with Braille text indicating the years from 1970 to 2020. The oil drum illustration is not included.

The jagged line has been replaced by a short break in the axis ;

The y explanation is the title; The y-axis has moved to its usual position on the left; and of course no attempt has been made to copy the oil drum.

In rendering the grid, think of the reader who has to go over all these lines to take in your drawing. Ask yourself if grid is really necessary, is that much precision asked for? Sometimes one might just as well only draw lines from important points in the graph to the axes, so these values can be read accurately; in other cases just putting grid below or above the curve will do nicely.

Remove Grid

 print graphic showing a line graph with a dense grid. The graph displays data points connected by a line, indicating fluctuations over time from 1970 to 1983. The y-axis represents numerical values, and the x-axis represents the years. The grid has both horizontal and vertical lines, with broken lines indicating yearly averages, adding visual clutter to the graph.

The blind reader will have to spend a lot of time searching for the curve in a grid like this.

The grid and the broken lines (yearly averages) clutter up the curve too.

Did we really need that grid?

The yearly averages are given in a table. Usually, we draw the curve as a fat line, but in this particular case that would not show the wriggliness well.

An adapted tactile version of the graph with the grid removed. The graph features a single line representing the data points from 1970 to 1983. The y-axis is positioned on the left and the x-axis on the bottom, both labeled with Braille text. The line showing the data is continuous and smooth, without any broken lines or additional grid lines, providing a clearer representation of the data. Two side-by-side diagrams showing examples of grids with geometric shapes, illustrating the correct and incorrect ways to simplify fine-meshed grids for tactile graphics.
Wrong Example: The grid has fine-meshed squares smaller than 1.5 cm, with thick lines making the shapes difficult to discern. The label

Replacing lines of fine grid by dots on the intersections, as already discussed in geometry, may clear up your drawing.

A graph that has more than three or four function lines will generally have to be made into a series of graphs when the lines are too close together. Separate the close lines and try to have one of the lines, preferably a mean or reference line, in each graph of the series. The function lines are the most important part of a graph, so have them stand out, draw them fat so they're easy to find.

If a graph has shadings between the lines we'll have to look for their meaning: sometimes it's just for decoration or sighted clarity and we can leave it out; in other cases the graph is all about the hatches' proportions, the shadings indicate volume, and we had better leave out the lines as they impair clarity. Shading in Graphs

A print graphic displaying a stock market chart titled A tactile version of the stock market graph. The shaded area from the print version has been removed. The graph features two lines: one solid and one dashed, representing the stock's performance. The y-axis is positioned on the left and labeled in Braille, as is the x-axis, which includes the years. A key at the top left of the graph identifies the lines. The reference lines that were previously shaded are now replaced by a standard y-axis.

The shading has no meaning, so it is left out.

Note use of key instead of arrows. Also note that the reference lines have been replaced by a standard y-axis.

A print graphic showing a chart titled  A tactile version of the oil consumption graph. The graph features a key at the top left identifying different hatching patterns used to represent consumption, imports, and domestic production. The y-axis has been moved to the left side of the graph, and the x-axis remains at the bottom. Only one line is present in this version, using a solid line with hatching patterns below it to indicate the volumes. The other line from the print version has been removed for clarity.

The size of the shadings indicates volume

Note the line type used on top; the other line has been removed for clarity. Also note use of key, and y-axis move to standard left.

A print graphic showing a chart titled A tactile version of the import value graph. The graph features a key at the top left identifying different hatching patterns used to represent the various import categories. The y-axis is on the left side of the graph, and the x-axis at the bottom. The hatching patterns fill distinct sections of the graph to represent

The size of the shadings indicates volume.

Note that lines between hatches have been removed for clarity. Also note use of key, and y-axis to standard location on the left. The first year on the x-axis is given in full, after that the '19' is left out.

Except in mathematics there's no reason not to juggle x- and y-scales separately if the lines in your graph are close together. Look out for possibly confusing graphic elements, and simplify or relegate them to text. Estimates into the future are often dashed, in an otherwise continuous-line graph: copying this will unnecessarily complicate your drawing. Reduce unusual graphs to the standard model.

Split Up Complicated Graphs

A print graphic showing a complex chart that illustrates energy production and consumption by type (such as oil, gas, coal, etc.) over time, along with the resulting shortage and surplus. The chart is densely filled with multiple overlapping areas representing different energy sources, with the x-axis showing years and the y-axis displaying values. The graph includes various hatching patterns to distinguish between different types of energy, making it visually complex.

This complicated graph has to be split up, into three standard graphs.

It shows production and consumption of energy by type (oil, gas, coal etc.) and the resulting shortage and surplus.

A tactile version of the first section of the original graph. This graph shows energy production over time, with different hatching patterns used to represent various energy sources. The x-axis shows years, and the y-axis displays values. The graph is simplified by focusing on a single aspect of the original complex graph. A tactile version of the second section of the original graph. This graph focuses on energy consumption over time, using different hatching patterns to represent various energy sources. The x-axis shows years, and the y-axis displays values. This graph also simplifies the original by concentrating on a specific part of the data. A tactile version of the third section of the original graph. This graph illustrates the resulting shortage and surplus of energy over time, with a single line and hatching patterns. The x-axis shows years, and the y-axis displays values. This graph isolates the outcome of the data presented in the first two graphs.

The first two graphs show energy production and consumption over the years by type (coal, oil etc.), the third shows the resulting shortage and surplus.

METHOD

  1. Enlarge your original to desired size; if need be change x:y ratio
  2. Decide on the direction of your drawing: length- or widthwise?
  3. Will the graph leave enough space for your title (including key)? If so, put in page number and title; otherwise draw the graph first.
  4. Draw axes, 1mm width; put in x, y and 0, and dashes and numbers for units.
  5. Put in grid, possibly reduced.
  6. Put in function line or lines, curves. Decide on linetype by expediency (e.g. wriggling line thin, straight line fat).
  7. If so desired, put in referencing lines from important points in your lines to the axes (if no grid was applied).
  8. Reduce confusing elements.

8. CHARTS

PICTURE OR DESCRIPTION?

Charts are a way of representation that's very clear to a sighted person, to take in at a glance, the best way of showing certain data; to a blind reader, however, a list of numbers is far easier to read and understand. So should we transform all charts into tables? Firstly, the blind reader then will never learn how to read charts, so all braille producers should agree on their transformation into text. Secondly, some indescribable charts are left, hard to understand as the reader is not familiar with the basic type. And thirdly, isn't reading charts part of the secondary school's curriculum? We should cut down in drawing charts, especially in non-educational or post-secondary school texts, but that still leaves a lot of charts to be drawn. I am aware of this discussion contradicting my argument in the introduction about editing for the blind. Still waiting for a unified theory. In general, the information in a bar is in its length, width doesn't matter: so go for a comfortable width like 2cm, if space allows. On the other hand, a bar chart intends to compare, so if possible keep it to one page. Sometimes it's best to make a line chart out of a bar chart. A simple bar chart just has some bars in a coordinate system like axes in graphs: in many ways, bar charts are like graphs. Draw axes at 1mm width; draw the bars' outlines in a fat line, like 2.5mm. Now the chart is still just a collection of lines, but filling in the bars with thin lines that also work as reference lines (horizontal in vertical bars, vertical in horizontal bars), and ideally at a distance from each other within the fingertip window is a beautiful solution. It suggests a numerical value. If possible, have an axis-width line at axis-numbers height or width. Don't put grid at the outside.

Filling in the bars with lines that also work as reference lines; note the fine lines that fill in the bars, and the bigger lines referencing to the numbers on the y-axis.

 A print graphic titled A tactile version of the bar chart from the print graphic. The chart features three vertical bars filled with fine lines that also function as reference lines. The first bar is filled with horizontal lines, the second bar with vertical lines, and the third bar with diagonal lines. The y-axis is positioned on the left and is marked with larger lines to reference the numbers, while the x-axis lists the products. Each bar represents one of the product categories:

Charts are often decorated by lifelike elements, or drawn in emblems of their subject matter: to the blind these are not amusing. Again we'd best render them in a uniform way. Edit Fancy Picture to Standard Chart

A print graphic titled A tactile version of the chart from the print graphic. The graph has been standardized, removing the lifelike ears of grain and focusing on a uniform bar chart format. The chart features vertical bars filled with horizontal lines, representing grain imports in million metric tons over different years. The y-axis on the left displays the values, with larger lines marking the reference numbers, and the x-axis at the bottom lists the years. The numbers that were previously in circles are now given in a list format, with fine lines filling the bars to maintain clarity.

The ears of grain would not make sense. The numbers in the circles are given in a list; note the fine lines that fill in the bars, and the bigger lines referencing to the numbers on the y-axis.

Funny Charts for The Sighted (Inkprint Only)

A stylized bar chart titled This collection of four graphics uses playful, metaphorical illustrations to convey statistical information. One graphic compares the sale values of famous paintings using paint tubes as visual metaphors, while another represents top marginal tax rates across different countries as coiled springs atop cartoon characters' heads. A third graphic illustrates the U.S. Department of Defense military spending over time, depicted as a series of stylized bombs or missiles. The final graphic compares oil imports by the United States and Japan, represented as barrels with different fill levels, alongside a comparison to the supply of oil through the Suez Canal. Each graphic integrates whimsical, non-traditional elements to engage sighted viewers.

Of course we're not going to copy the embellishments.

Estimates or projections may not look like the other bars in a chart: for us a uniform rendering is better.

A print graphic showing a bar chart titled A tactile version of the bar chart from the print graphic. The bars are uniformly rendered with no distinction for the estimated 1986 figure. Each bar is filled with horizontal lines, and the y-axis is on the left side, labeled with Braille to indicate the deficit in billions of dollars. The x-axis lists the years, with a Braille note indicating

Do not draw the last bar in a different way – the Braille version has a line: "1986: estimated".

Vertical bars make writing, identification easier, for there is usually only room for two or three Braille characters under a bar, so rotating vertical bars might make the chart easier to read. Move bars from vertical to horizontal

A print graphic titled A tactile version of the bar chart, with the bars rotated from vertical to horizontal for easier identification. Each bar is filled with horizontal lines, representing the number of religious television and radio programs in 1977. The categories are listed vertically on the left, with Braille labels indicating

This chart is a prime candidate for a full description instead of a picture. Nothing would have been lost had this chart been rendered as a simple table. (Where are the axes Eugene?)

Some bar charts have clusters of different bars: try to hatch the largest bar in reference lines. This kind of chart often has half-hidden bars: bring these out in the open like all other bars. Edit to Uniformity

A set of four small bar charts comparing annual percentage changes in employment and labor force among different countries (United States, Japan, West Germany, and Britain). Each chart has clusters of bars representing different metrics, such as employment and labor force changes. The bars are partially hidden and overlap within each chart, and they are filled with different hatching patterns for distinction. The x-axis represents the years, while the y-axis shows percentage changes. A tactile version of the bar charts, consolidated into a single unified bar chart. The bars are evenly spaced and fully visible, with different hatching patterns representing each category. The y-axis is on the left, marked with reference lines, and the x-axis lists the categories. The adapted chart eliminates any overlapping or hidden bars, making each bar distinct and easy to identify.

Bring the half-hidden bars out into the open – also note the standard axes.

Other complicated bar charts have bars divided in sections: choose hatch- type by expediency, like small sections solid black. In this kind of chart it's often better not to have a fat outline, as its top might look like a bar section. Enlarging details on a separate page is a possibility here; mark clearly which part you're going to show in detail. Two-variables bars

A print graphic titled

Would our readers appreciate an artistic rendering of those gas pumps?

A tactile version of the bar chart from the print graphic, presented in a standard bar graph format. The bars are divided into sections representing

Prepare a standard bar graph, axes, key, etc. Key says: "Price minus tax" and "Tax"; the numbers that were written in the pumps are given below the chart in the Braille version.

Again sometimes we'll have to juggle: rotate, mirror etc. to get a clearer picture; sometimes go for a description of a complicated chart, but in those cases it might be nice still to draw a part of the chart and an overview, or a simplified version, so as to give the blind reader a notion of its inkprint graphic representation.. A Complicated Chart

A print graphic showing a complex bar chart with multiple horizontal bars stacked and overlapping. The bars represent various categories, with different hatching patterns to distinguish them. The chart is densely packed with data, making it difficult to distinguish individual elements at a glance. The x-axis represents a numerical scale, while the y-axis lists categories aligned along the center of the chart.

I think it's best to go for a full table description, the basic bars and a few of the full bars as an example.

Part 1

A tactile version of the bar chart's central axis and basic bar structure. The y-axis runs vertically down the center, with horizontal bars extending to the left and right. Each bar is labeled with Braille, and the bars are evenly spaced for clarity.

Part 2

A tactile version that focuses on a few specific bars from the complex chart, showing them in greater detail. The bars are presented with distinct hatching patterns, and the key is provided in Braille above the bars. The x-axis is marked with reference lines, and the bars are aligned horizontally for easier identification.

Maps containing charts are usually for decoration, but occasionally show locations relevant to the bars: in that case we split up in a separate map and chart.

Chart in A Serious Map

Produce Auction Sites in Holland with Volume of Sales

The image is a print map titled

Locations map: Produce Auction Sites in Holland with Volume of Sales Locations, Chart on Next Page

The image is a tactile map of the Netherlands, focusing on the

Also note that braille says: "#6 is in between #1 and #3" for there is no room in the map to print #6.

Produce Auction Sites in Holland with Volume of Sales

The image is a tactile chart titled

Also note that the chart has been rotated to allow writing the twelve identifying numbers that wouldn't have fit below an x-axis.

Pie charts follow the general chart guidelines, but allow for more writing in the sections, which may be useful.

A Pie Chart Example

A print version of a pie chart that consists of two concentric circles, representing two sets of data. The outer circle shows one set of data, and the inner circle shows another. The key, represented by a smaller circle within a circle, explains the data depicted in the pie chart. The chart segments are differentiated by lines and patterns corresponding to the data sets.

I don't think the key in inkprint that explains the two circles is going to work for blind readers.

So draw two separate pie charts, and give the numbers at the key in text.

A tactile version of the pie chart representing the inner circle data from the print version. The sections are differentiated by textures without lines between them. The Braille key is placed above the chart.

Also note that there are no lines between the various shadings.

Braille Part 2.

The second tactile graphic in this series represents the outer circle data from the original print pie chart. This chart has different textures to represent each section, with no lines separating the segments. The key is provided in Braille.

Fractured pies cause unnecessary difficulties in reading

The pie chart is divided into several separate pieces that are not connected, with each segment representing a different portion of the data. The segments are spread out and positioned independently rather than forming a continuous circle. Cylindrical chart with horizontal sections stacked on top of each other, each section labeled with data. The sections are divided by horizontal lines, with text labels on the right side, indicating what each section represents.

I would give a full description of the second chart, maybe the top as a picture.

Population pyramids can't be described satisfactorily, as it will take a lot of imagination to relate a group of numbers to a shape; so we'll have to draw them, and in a standard way. Population Pyramids

A population pyramid graph comparing two populations side by side. The graph features two mirror-image pyramidal shapes representing different population groups. The x-axis represents population, and the y-axis represents age groups. Labels Two graphs are stacked vertically. The top graph shows a bell curve with a grid background representing a population distribution, with the curve extending symmetrically from the center. The bottom graph shows a similar bell curve with a grid background but is narrower, indicating a different population distribution. Both graphs use the same grid format and are intended to represent comparisons between two sets of population data.

The "m" and "v" next to the curves are not ideal.

Two stepped graphs are shown side by side. Each graph has a series of horizontal steps progressing upwards, forming a stair-like pattern. The left graph has a mirror image of the right graph, with each step representing a specific category or data point, tactually emphasizing the difference between two distributions.

A line in text like "men:left, women:right" would have been better than that identification next to the sides.

9. DIAGRAMS

Draw rectangles and connecting lines in different widths, connecting lines must be thick as they are the most important part of your drawing; quite often the rectangles around text might just as well be left out.

Simplify A Diagram

The print diagram is an organizational chart displaying the structure of Ferruzzi Finanziaria and its subsidiaries. The chart consists of multiple rectangular boxes connected by lines, each box containing detailed financial information such as ownership percentages, turnover, and profits for the year 1986. The boxes are arranged in a hierarchical structure, indicating the relationships between the parent company, its wholly-owned subsidiaries, and other related entities.

There's too much text in the boxes, and who needs those boxes anyway?

Tactile diagram with simple lines and arrows to show connections, with essential names and numbers presented in braille.

The braille drawing only gives names and numbers ("numbers in the diagram indicate percentages'); all other information from inkprint is rendered as text, like this:

Figures for 1986 turnover and profits are in billion lire

frf - Ferruzzi Finanziaria Wholly owned by Ferruzzi family mds - Montedison (Chemicals) Turnover 13.000

Do not copy complicated graphical elements in your schemes: just a rectangle and its name will do. A word like 'battery' makes sense to our readers, representing it by a series of straight and curved lines will probably have no meaning. Often abbreviations will have to be used, choose them sensibly; do not change existing codes. In schematic representations like electrical diagrams, the current passes through a wire that should look different from the gauges and apparatus attached, as those might otherwise look like the wire branching out.

Line Widths: Electrical Diagram

electrical diagram with various components represented by circles and rectangles connected by thin, uniform line Tactual depiction of the electrical circuit diagram with uniform line thickness connecting circles and rectangles, no textures applied, braille labels inside circles.

In the 'wrong' rendering, the blind reader tracing the cable, arriving at an object might get the impression it's the wire branching out; different line widths make the picture clearer.

Right

Tactual electrical circuit diagram with thicker lines for main wires, textured rectangles for easy identification.

Keep arrowheads some distance from lines they point at. Take care at intersections: maybe change one of the lines' width for some distance to stay in the clear about which line continues where.

Generally a partial or complete description is to be preferred over copying a complicated diagram. It makes no sense if our readers have to go through a drawing with a lot of lines and abbreviations accompanied by a long list explaining those codes.

Editing A Very Complicated Diagram

Print diagram of the United Nations' organizational structure, featuring interconnected circles and rectangles filled with text and abbreviations. The diagram shows the relationships and hierarchy between various departments and branches using connecting lines. It includes handwritten annotations, adding to its complexity. The overall structure is dense and detailed, intended to represent a structured yet intricate system.

This is a diagram of the United Nations' organisational structure. Imagine the blind reader having to go through the long list of abbreviations. Reading a good description would take about as much time, and make much more sense than the drawings.

wrong, part 1

Tactile diagram of a simplified version of the United Nations' organizational structure. The diagram includes circles and rectangles connected by straight lines, representing different organizational components. Each shape is labeled with braille.

Imagine the blind reader having to go through the long list of abbreviations, and then take on this picture (which is only the first part). Reading a good description would take about as much time, and make much more sense than the drawings.

Wrong, part 2

Tactile diagram of a simplified organizational chart with fewer elements than the original print version. The diagram consists of circles connected by straight, thick lines, each circle labeled with braille to represent various organizational components. The diagram is laid out in a vertical structure instead of a mind map structure.

better

Tactile diagram of an organizational chart, further simplified by displaying only circles connected by thick lines. Each circle is labeled with braille, and the lines connecting the circles are notably thicker to enhance tactile readability. The diagram excludes any additional text or shapes, focusing solely on the connections between the organizational components.

A diagram of the basic structure, most important part, and having the other parts described, makes much more sense, and takes much less time to read.

The data from most complicated diagrams can be given in an easy-to-read descriptions or tables. Even if the blind reader would eventually be able to make sense of these diagrams as pictures that time could be spent much more profitably elsewhere.

Diagrams That Are Better Fully Described

A flowchart titled

It is entirely possible to draw a clear Braille picture of this decision chart, but a description is way easier to read. Number the question boxes. Then make a table like:

Weakness

1. Is the weakness confined to one area of the body?

yes: go to 2.

no: go to 3.

2. Is it present now?

yes: See doctor today

no: Make appointment with doctor

3. Is the weakness associated with flu or cold symptoms?

yes: See: Colds and Flu, page 225.

no: go to 4

4. Is the weakness associated with stress of tension?

yes: See: Stress, Anxiety and Grief, Page 384.

no: Apply home treatment.

The blind people I worked with never liked graphics, the unfamiliarity, and the material is not pleasant to the touch; that's why I would choose to translate this one to text, also taking into account that it will be read under less-than-ideal circumstances.

Numbering the boxes on the left allows for a
description like:
1. Rain?
yes: go to 2
no: go to 3
2. Showers?
yes: Cumulonimbus
No:
A: go to 4
B: Nimbostratus
3. Low clouds?
yes: go to 4
no: go to 5
4. etc. etc.

This is a flowchart used for classifying different cloud types. The chart starts with a question or condition related to cloud observation, such as

"From the top of the distillation column, the lightest fractions, etc. etc."

This image is a detailed print diagram showing the process flow of a distillation column used in refining. The diagram is vertically oriented, with the distillation column on the left and various components and processes branching out to the right. The top of the column is labeled as containing the lightest fractions, while heavier fractions are collected further down. The image includes multiple arrows, text labels, and symbols representing different stages of the distillation process and the movement of various chemical compounds.

Look for original solutions to rendering colors etc. Again the main thing is to understand what the diagram is about.

Diagram Solutions

Row and Column Headers (Periodic Table, first 20 elements)

A partial periodic table showing the first 20 elements. The table is arranged with rows and columns labeled as

Where will you put the "Group" and "Period"?

A tactile diagram showing a portion of the periodic table with braille annotations. The table includes rows and columns, each marked with a tactile 'g' for 'group' and 'p' for 'period' alongside the numbers. The diagram represents the first 20 elements of the periodic table, with the group and period numbers clearly indicated in braille on the table's left and top edges, respectively.

The table column and row headers each have a 'g' for 'group' or a 'p' for 'period' with the number.

This may look like a minor thing, but there is no other way to clearly indicate groups and periods. In a real Braille picture the top left 'p' would be too close to the edge.

Splitting Up (Full Periodic Table)

Periodic table split across two pages

The Periodic Table itself already provides a model for splitting up, which we will take one step further

This Periodic Table gives an electron structure below the atom number and symbol, other Periodic Tables carry other information like atom weight etc.: I would ask the Braille text people to put that in a regular table like this (maybe by now these tables are already on file):

The Periodic Table's elements listed:

A print table listing elements by group and period with corresponding atomic numbers, symbols, and electron structures. The table is organized into columns for group, atom number, symbol, and electron structure.

This table will be a guide to understanding the Periodic Table. Other editions of the Periodic Table may give other data, that also could go in a list like this.

The Periodic Table itself already provides a model for splitting up which we take one step further.

Tactile diagram showing the top portion of the periodic table with a section (elements 22 through 29) removed. Columns 3 and 12 are included to illustrate the table’s structure. Tactile diagram displaying the transition metals section of the periodic table, highlighting the elements typically found in groups 3 to 12. Tactile diagram depicting the Lanthanoids and Actinoids, which are presented separately from the main body of the periodic table.

Change Direction

A print diagram with three rows and three columns of boxes connected by arrows. The top row contains a larger empty rectangle in the middle column. The second row contains three small empty rectangles. The bottom row contains three larger empty rectangles. The arrows indicate a flow from top to bottom and between the columns. A legend in the lower left corner indicates that these rectangles represent

An empty box would be just a square to our readers, so they have been filled in.

A tactile diagram with three rows and three columns of textured rectangles connected by arrows, oriented to flow from left to right. The top row contains a larger textured rectangle in the first column. The second row contains three small textured rectangles. The bottom row contains three larger textured rectangles. The arrows indicate the direction of the flow, moving from the left side to the right side across the diagram.

Line Demarcations

Copying the lines demarcating the teams is going to be messy.

A print diagram depicting a hierarchical structure with multiple levels. The top level has one central box connected by lines to multiple lower-level boxes that branch out to form a pyramid-like structure. Some boxes are connected by curved lines that loop around the diagram, creating an arched layout. A tactile diagram of a hierarchical structure similar to the first image, arranged in a more straightforward layout. The diagram consists of multiple levels with boxes containing Braille characters. The boxes are connected by straight lines, forming a pyramid shape. Each box contains Braille, and the lines indicate relationships between the levels.

The teams are identified by letters.

The boxes around the letters are not necessary, maybe should not have been copied.

Colored Boxes

A print diagram depicting a hierarchical structure using labeled boxes connected by lines. The top section contains three boxes arranged horizontally. Below, three columns extend downward from the top boxes, each containing two or three smaller labeled boxes connected vertically. The boxes are outlined and labeled with text inside, indicating different organizational units or roles. A tactile diagram representing the same hierarchical structure as the print diagram, but with shapes instead of labeled boxes. The top row features a trapezoid, a rectangle, and a circle. Below these, three columns extend downward: the first column has a trapezoid connected to a rectangle, then a circle; the second column has a trapezoid connected to a larger rectangle, then a circle; the third column has a trapezoid connected to two rectangles, followed by a larger circle. Lines connect the shapes to indicate relationships and hierarchy.

Colored Boxes, Replaced by Shapes

Viewing the large number of abbreviations, a diagram like this might as well, maybe better be fully described, instead of offering a picture like this.

10. GEOGRAPHY, MAPS

In maps the main problem is lack of space: the scale we have to work in is so much larger, braille needs more space than inkprint lettering and exclusive space at that, and of course our drawings are limited to A4- size. Basically there are two ways of solving this problem: either enlarge the map and show the parts over several pages, or split up your map into subjects that are treated on different pages. We expect our readers to piece together ("synthesise") the information into a complete map in their mind.

Thematic split-up: (The San Joaquin Valley, California)

A print map of the San Joaquin Valley, California, depicting various geographical features such as mountains, irrigated areas, rivers, dams, canals, and aqueducts. The map uses different patterns and lines to differentiate between these features.

It's not all going to fit on one page. It will be split into:

1

A tactile diagram representing the terrain of the San Joaquin Valley, including mountains and irrigated areas. The terrain is indicated with distinct tactile patterns, and the diagram includes a key.

2

A tactile diagram focused on rivers and dams in the San Joaquin Valley. The rivers are represented with tactile lines, and dams are indicated with tactile symbols. The diagram is part of a series that breaks down the geographical features into manageable sections.

3

A tactile diagram showing canals and aqueducts in the San Joaquin Valley. The canals and aqueducts are represented with tactile lines and symbols, providing a clear understanding of their layout within the valley. This diagram is the third in the series.

If a map is to be enlarged, always have a full area survey first. Indicate the sector map's position clearly, either in your survey, on a map dedicated to this purpose, or on the detailed maps themselves: use compass directions and 'centre'.

Split Up to Enlarge Details (The United States)

Overview, large states identified; the East; the Northeast

Braille map of the US A tactile map of the eastern United States, showing state boundaries and geographic features. The map is outlined with solid lines to indicate the borders of the states. Braille labels are used to mark individual states. The map includes dotted areas to represent certain regions or territories, which are labeled with Braille text. A tactile map focusing on the northeastern United States. The map shows state boundaries with solid lines, and dashed lines are used to indicate other relevant borders or divisions. Arrows are included to point out specific areas on the map, with Braille labels providing additional information about these regions.

When you have a large number of maps an index map may be useful, showing the location of the detailed maps on the overview map.

Use of Index Map (Africa). Overview; index map; North; West; Thematic Map

Unfortunately the other maps in the series are not available.

A tactile map of Africa, highlighting the countries within this region. The map uses dotted lines and Braille labels to distinguish between different countries and borders. A tactile index map of Africa, providing an overview of the continent with marked sections for North and West Africa. This map serves as a reference for the detailed maps provided earlier, with tactile outlines and Braille labels indicating the areas covered by the more detailed maps.

North

A tactile map of Northern Africa, highlighting the countries within this region. The map uses tactile symbols and Braille labels to distinguish between different countries and borders, with a focus on the northern region of Africa.

West

A tactile map of Western Africa, showing the countries in this area with tactile symbols and Braille labels. The map emphasizes the western part of the continent and includes detailed representations of the borders and geographical features.

European Colonies in 1914

Only after the orientation maps can we present a map like this.

A tactile thematic map of the entire African continent, depicting European colonies in 1914. The map uses various tactile patterns to represent different colonial powers, with Braille labels indicating the regions controlled by each colonial power.

In some maps it's better to split up in subjects: start with an orientation map, carry over some orientation points or the outline to the complete series, then put in the various matters on individual maps. Often it's virtually impossible to cram all the information in just one drawing, sometimes clarity is improved by splitting up. On the other hand, drawing comparisons might get harder.

Split Up in Orientation and Thematic Map: (Sea Routes to Rotterdam)

A print map showing sea routes to Rotterdam with labeled locations such as 'Dover,' 'Hook of Holland,' 'Scheveningen,' and others. The map features various lines indicating different routes across the sea, with each route clearly marked and labeled in print.
  1. map
A tactile orientation map of the sea routes to Rotterdam. This map uses dotted texture for water and includes tactile labels for key locations. A tactile thematic map of the sea routes to Rotterdam. It uses varied lines to differentiate between specific themes such as main routes and secondary routes, with tactile labels providing additional information about the routes and locations.

this same vein I will open a book that has a number of maps on a few areas by an introductory of maps on that or those areas, showing important features like main cities, rivers etc., and need be introduces a formalized outline.

A Series of Orientation Maps: (Holland)

  1. realistic outline and waterways
  2. formalized map (Braille says: from now on be using this map)
  3. provinces
  4. main cities
A tactile map representing the realistic outline of Holland along with its waterways. The map includes the coastlines and major water bodies marked in raised lines for tactile exploration. A tactile map of Holland with a formalized outline, marked with raised lines to define the borders. This version simplifies the coastline and other features to provide a clearer and more structured representation of the area. A tactile map showing the provinces of Holland. The map uses dashed lines to denote provincial borders, allowing readers to distinguish between different areas by touch. A tactile map highlighting the main cities within Holland. Cities are indicated with braille letters, with key  at the top of the map.

After the area introduction, later maps will be uncluttered, dedicated solely to the subject in hand. The later, thematic maps have to be in exactly the same outline, of course.

Infant Mortality, Holland 1841-60

A printed map of Holland from 1841-1860, depicting infant mortality rates. The map uses varying shades to indicate mortality rates in different regions: darker areas show higher mortality, and lighter areas indicate lower mortality. A tactile map of Holland from 1841-1860. The map shows infant mortality rates with different textures: solid black areas, dotted areas, and lined areas representing different levels of mortality rates. The dashed line represents the country border, and there is a tactile legend above the map that explains the textures used for different mortality rates.

Average January Temperatures in Holland (°C)

A print map of Holland displays average January temperatures across various regions. Numbers representing temperature values in degrees Celsius are scattered across the map to indicate regional variations. A tactile map of Holland represents average January temperatures. The map includes Braille labels in place of temperature numbers. The coastline and major geographical boundaries are outlined in solid lines.

When a graph or a chart is superimposed over a map these are to be separated in a clean map and a clean chart; unless the map is for decoration only, then it may be left out. See the "Produce in Holland" charts in the Charts chapter.

Three-dimensional drawings have to be edited. The following example is split up in two views (on one page).

Split Up Three dimensional in Two Views

A detailed 3D illustration showing a top-down perspective of a complex structure with multiple sections, pathways, and small ditches. The pathways are narrow, with varied textures representing different materials or water channels.

This is not a very good Braille picture. The ditches are too narrow to show their watery content, there shouldn't be a line on top, and many items are too small for clarity.

A simplified 2D tactile version of the 3D illustration. The diagram is split into two views: the upper portion focuses on the layout of the pathways and ditches, while the lower portion presents a cross-sectional view. The tactile diagram includes a solid outline for the pathways and textures to distinguish different areas.

In drawing a jagged coastline, keep the minimum distance in mind: a number of narrow inlets close together will just be a blur to our readers. It's nice to show a somewhat jagged coastline once, but then its information is spent; our readers had better spend their time on new features. Islands and peninsula of a somewhat larger size also tend to pose a problem: we cannot discernibly hatch a small outlined area. Like in the map of Holland the south-west corner's largish (Dutch-scale) islands and sea-arms leave no room for other information, so in the map I generally use I have reduced the coastline there to one straight line. One might also shift information concerning islands that are small in your map to text, like 'Japan is a first-world country'.

It is rather improbable that the blind reader will recognize an area by its form, so it is essential to put the area's name in the title, or add an orientation map. In case names of neighbouring areas are not given in inkprint, add those in your map, so the reader will be given more clues as to an area's location. For illustration look at the maps of King Darius' Empire in the Introduction.

It's not easy to find text or special items in a hatched area, especially if the hatch is dots; so sometimes what I call counter-highlighting, shading the surroundings of the relevant area, might be useful. For illustration, check the counter-highlighting example in Chapter 5.

Another kind of map shows a recommended walk through an exhibition using V-shaped arrows; check the example in an earlier chapter.

Remember the main points:

11. BIOLOGY

Like in maps, it's most important to have good titles, and we should also help the reader in recognizing and locating the subject by identifying most or all of the items in the drawing, and naming its surroundings.

Identifying might be done by copying the item, or one of its kind in your key. Also remember the clearing of a shaft to the sides of an arrow as described in the General chapter. Keep in mind that an outline is not enough to indicate an area: it has to be hatched too.

A biology picture often has many small items, like cells. These items are generally of a few kinds, but differentiation within a type might be considerable: to a sighted reader this will not pose a problem, but to a blind reader the individual differences will loom large, and I think he will not recognize the types but just discern a lot of different, individual items. So I will draw all cells of one kind in exactly the same manner (which is very easily done in computer-aided draughting, of course). To the sighted this formalized picture may look rather funny, but it will greatly help our readers understand. As I've said before, this kind of editing aks for some knowledge and understanding of the subject matter in hand.

Realistic or Formalized? Cross-section of a leaf:

A tactile diagram of a realistic cross-section of a leaf. The diagram presents various types of cells with individual shapes and details, giving each cell type a distinct identity. The variety in cell depiction makes the diagram intricate and complex.

The individual cells have too much identity of their own, i.e. within a type there is too much variety for the blind reader.

The various types of cells are easy to recognize.

A tactile diagram of a standardized cross-section of a leaf. This diagram simplifies the cell types, ensuring they are easily recognizable by touch. The cells are uniformly shaped, and the diagram focuses on clarity and consistency, making it easier to interpret by touch.

Check also the stomach pictures in an earlier chapter. No Threedimensional Drawings, such as the one of the fanned-out tree or the cell mitosis; and fill in shapes, like in the picture of a mouth saying "a" in an earlier chapter. Also, clear paths for arrows, as in the vascular bundle of a plant picture in an earlier chapter.

12. THE SCIENCES

In physics we often come across apparatus and machinery: represent essentials only, basic principles, try to show how it 'works', simplify or split up in component parts. Pictures are generally three-dimensional: represent by a kind of schematic cross-section; and identify all items in your drawing: to the sighted these may look pretty obvious, but the blind reader generally will not recognize these shapes. Adding explanations or comment will also help.

Schematic Cross-sections; Identify All Parts, Explain

A print diagram of laboratory equipment showing a schematic cross-section. The diagram includes vertical rods or stands, a cylindrical container at the top, and various connected parts and tubes, represented in a detailed and realistic style. A tactile diagram depicting a simplified cross-section of laboratory equipment. The diagram is designed for touch, with clearly defined vertical and horizontal lines representing the equipment's components, focusing on making the structure easily identifiable by touch.

Laboratory equipment and Oscilloscope

A print diagram illustrating an oscilloscope. The diagram shows the internal components. The parts are detailed and labeled. A tactile cross-section of an oscilloscope. The diagram uses textured shapes to represent different components, such as signal paths, connectors, and internal parts, with a simplified design to make it accessible by touch.

Speedometer

A detailed cutaway diagram of a speedometer's internal mechanism, showing components like the rotating magnet, spring, needle, and spindle labeled.
  1. top view: the gauge
  2. the works explained
A tactile diagram showing the top view of a speedometer gauge. It is a simple circle with tactile markings for different speed intervals and a raised arrow in the center pointing to the right. A tactile diagram that explains the workings of a speedometer. It features a simplified representation of a rotating mechanism with an arrow, connected to a rectangular box symbolizing the internal mechanism. This image uses tactile elements to represent movement and the connection between components.

Water Clock (Clepsydra)

A detailed print diagram of a water clock,. The diagram includes various labeled parts, such as the water container, the outlet, and the markings on the container's side to indicate time.

Detail enlarged and explained

 tactile diagram that shows an enlarged and detailed cross-section of the water clock. It includes two main chambers with narrow openings at the top, allowing the water to flow from one chamber to the other. The diagram is simplified, focusing on the shape and flow of water through the clock's mechanism.

complete apparatus (ca 50K)

A tactile diagram representing the complete apparatus of the water clock. The diagram is simplified, showing the general structure and flow of water through the device, with the water levels marked and the directional flow indicated by an arrow. The tactile design makes the diagram accessible to readers using touch.

You have already seen the periodic tables in the Diagrams chapter.