A math teacher came to us with the question: ‘Can you create a 30/60/90 degree version of a triangle tool for the TactiPad’? He wants his students to draw 3D shapes such as cubes, prisms and pyramids. Being interested to improve/extend the Thinkable products we have taken up this challenge.
After describing the details of the tool, we present some of the decisions we made during the design process. You will also find information on some of the aspects of the creation of ‘3D space’ using the TactiPad.
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In late summer 2021, Thinkable CEO Jaap Breider was visited by journalist Eskandar Abadi and film maker Shahab Kermani. They produced a video for Deutsche Welle TV (Persian department). Jaap was accompanied and interviewed during one day in his house and company headquarters in Huissen (NL).
Besides receiving his guest, talking about himself and Thinkable, Jaap explains the basics of tactile graphics to the interviewer. Being a blind man himself, he is obviously experiencing something completely new: Jaap draws or plots graphics for him while he also explains the “codes” behind certain ways of drawing from the seeing world.
It is these kinds of moments that keep Jaap inspired since decades. With Thinkable, he constantly works on innovations to give ever more VIPs access to tactile graphic information.
However, in order to use a software version of this generation in full mode, your software license needs to be eligible. You can check here if you already have such a license. (You need your software product code (SPC) for this. You can find it in the menu ‘Help’ > ‘About TactileView’.)
If your license is already eligible:
First, check the TactileView version you have installed already. Go to the menu ‘Help’ > ‘About TactileView’ and check if the version number starts with 2.5 . In this case, there is nothing you need to do.
If you have a lower version, go to the menu ‘Help’ > ‘Check for New Updates and Release Notes’.
Alternatively, you can download the latest software installation file and start the installation process by opening it.
If your license is not yet eligible:
Option 1: Use our webshop
Purchase an SPC upgrade in our webshop. You will receive and email with instructions and a key (code) which can make your SPC eligible to use TactileView generation 2.5 .
After making your SPC eligible, you can either go to the TactileView menu and select ‘Settings’ > ‘Update TactileView Components’ and choose ‘Check for new software updates’.
Alternatively, you can download the latest software installation file and start the installation process by opening it.
Option 2: Ask your distributor
Contact your distributor and request a license upgrade for your SPC. When your request has been processed, you will receive an email to inform you that your SPC is now valid for the upgrade to TactileView generation 2.5 . In this email you will find a download link to the latest version.
Photo: Spur wheel with 12 teeth (prototype 3D-print)
Detailed description of the spur wheel template
There are different types of spur wheels. This shape represents the mechanical properties with which the force can be maximised. When you interlink two wheels of this type, their teeth always have a point of contact under an angle of 90 degrees when rotating. Although it looks like an arbitrary number of teeth can be placed in a circle, this is not the case.
The wheels in the set have 12 or 15 teeth respectively. The spaces between them – their negative counterparts – are placed on the inside of the round template, so that the drawing result will have its teeth on the outside. The body of the spur wheel has finger fitters in eight positions along the outside for easy lifting or extra grip. You find pushpin markers in the top surface of the body.
Utilising the spur wheel template
The spur wheel is a relative complex tool to use / shape to create. We recommend to use one to two push pins to fixate to tool on the TactiPad. Draw the inner contour of the spur wheel and you have created the first step into the mechanical domain or flower design.
Once you have interlinked two spur wheels, you will experience a complex issue: finding the perfect position for one tooth on the one and two teeth on the other wheel to “bite each other”. This gives you an impression of how delicate spur wheel systems are in mechanics.
Detailed description of the regular polygon template
The set contains templates for regular polygons with five, six, seven, eight and nine corners referred to as pentagon, hexagon, heptagon, octagon and nonagon respectively. The radius of the polygons ranges from two to eight centimetres.
In a regular polygon all corners have the same angle. The corners are interconnected with lines that have all the same length. Another way to describe a polygon: A polygon consists of a number of equal leg triangles where the top corners of all equal legged triangles are at the same position. So they are arranged in a circle like slices of a pie. The distance from all corners to the centre point is the same.
The body of the tool is two centimetres wide. It is shaped as a triangle where one side is not present. It could be described as a jaw hook. The angle between the two sides is less than 90 degrees. Near to the rounded outside corner and near to the tips you find pushpin markers. One side of the polygon tool contains a number of wholes, indicating the number of corners of the particular polygon.
The side with the wholes is referred to as ‘radius side’. This radius side has a centimetre indication in the top surface and indents every half centimetre. The inner side of the side with the finger fitter to the far right is referred to as ‘drawing side’. The drawing side has the same number of indents as found on the radius side.
To construct the polygon, the pen position in the radius side has to correspond with the one in the drawing side, measured starting at the inner corner. As an example, a groove as a visual tactile clue ending at the four centimetre radius indication shows the direction to look for the corresponding indent in the drawing side and/or the respective bisectrix position. The value for the radius is measured starting at the inner sharp corner and increases towards the tip. The once selected position at the radius side is going to be the centre of the polygon.
At the outer side of the drawing side you find indents as well. They indicate the position for the bisectrix of the equal leg triangle. The outside corner in between the radius side and the drawing side is rounded to allow for alignment with the ruler; the distance from the sharp hook to the ruler remains the same when you move/rotate the polygon tool.
Utilising the regular polygon template
The regular polygon tools are mainly used to create these shapes. You can also create mandalas. You have to use at least one pushpin to mark the centre of the polygon. A second pushpin is handy to mark the position to draw to along the drawing side.
Detailed description of the rectangular hook template
The two sides of the rectangular hook are under an angle of 90 degrees and are 10 centimetres long. The body of the tool is two centimetres wide. The corner between the sides is rounded at the outer side. The sides are ending with a 90 degree hook. Near the rounded corner and near to the tips, you find push pin markers.
You find indents for 30, 45 and 90 degrees at the rounded corner for alignment with the ruler. There are centimetre indicators along the inner side on the top surface. The inner sides have indents every half centimetre. At the outer side you find indents to perform a 30 or 45 degree rotation in reference to the inside angle. On the outer sides, near to the tips you find a finger fitter for easy lifting or extra grip.
Utilising the rectangular hook template
When you drawing along the two sides towards the inner corner you create two lines with a 90 degree angle. When you connect the two endings of the previously created lines you will get an irregular triangle on the TactiPad. By rotating and/or mirroring a triangle, you can create shapes such as diamond or kite.
Photo: The six centimetre equal sided triangle of the set (prototype 3D-print)
Detailed description of the triangle template
The templates for the triangles are of the type equal sided triangle. The length of the sides ranges from three to eight centimetres respectively. One outer corner is rounded, the other two are sharp. Along the outside you find indents at every centimetre. They correspond with the corners at the beginning/ending of the inner sides. The body of the triangle is about 12 millimetres wide. On the top surface, you find pushpin markers.
The inner sides have an indent at their halfway position.
On one of the outer sides you find a finger fitter for easy lifting or extra grip.
Utilising the triangle template
When you place the triangle template somewhere on the TactiPad in any orientation and then draw along the inner contour, you create your first triangle.
With the equal sided triangle you can create other shapes: a rectangular triangle of 30, 60 or 90 degrees, a diamond and star.
Photo: The four centimetre square of the set (prototype 3D-print)
Detailed description of the square template
The sizes of the squares ranges from two to ten centimetres. The frame that forms the square is one centimetre wide. So a four centimetre squared template has the inner dimension of four centimetres. The outside is six centimetres in square.
Two diagonal opposite outside corners are sharp, there you can find the pushpin. The other two corners are rounded. Along the outside a small indent is provided at every centimetre. The inner side has an indent at the halfway position of each of the four sides. In two of the opposing outer sides you find finger fitters for easy lifting or extra grip.
Utilising the square template
When you position the square somewhere on the TactiPad in any orientation and then draw along the inner contour, you create your first square. With the square template you can create many more shapes such as diamond, parallelogram, trapezium, and also 3D shapes such as pyramid or cube.
Learn how to create mathematical graphs with coordinate systems and grids that are suitable for tactile graphics
Introduction: Graph and Grid
The TactileView drawing tool ‘Draw graph’ has a large number of examples for grids. A complete grid consists of the axis setup, formula(s) and tactile appearance settings. Selecting an example and modifying this will get you in a few steps to a tactile usable graph that can be produced on swell paper, a braille embosser or on the motorised drawing arm (MDA).
Produced in braille or on swell paper, it also will present the text labels for the formula in different mathematical braille notations.
External math software such as MathType that uses MathML file format can be used to import a formula to have this plotted in a graph
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‘Graphs’ menu: Many options to chose from
The item in the main menu ‘Graphs’ and the icon in the vertical tool bar ‘Draw graph’ both bring up the same range of features to create a graph with ease. Ease is still a relative concept; to obtain a tactile usable graph quite a number of aspects has to be thought through. Over 30 parameters can be set to design the axes, graph(s) and overall appearance.
Chicken–egg dilemma in tactile drawing with software
When you know what kind of formula you need to have plotted in a graph, you have aspects like the type of the scale, the range and texts for the axis etc. already in mind as well. In other words, do you want to compose the axis setup first (as you would do on paper) so you can add the formula in a second step? Or do you want to enter the formula first (what you can actually do in software) and afterwards adapt the axes fitting the produced graph? With this latter approach you have to be concerned about all the aspects that make the grid a tactile usable diagram.
Solve the dilemma: Grid examples as a starting point
The TactileView software has a number of examples with preset values available for graphs of various types. There are examples for coordinate systems (grids with just the axis settings) and also a number of examples that contain a single formula or even multiple formulas.
A modified example grid can be stored as a ‘MyGrid’ for future use.
Learn how to create three different axis types in this tutorial
The following three worksheets will show you step by step how to create a grid with a linear axis scale, a logarithmic one or using degrees and radians as units.
Worksheet 1: Linear scale
When we set our first steps in math, we begin with linear functions. A Function like plus (+), minus (-), multiply (*) or division (/) can be used for any value of x. Also square, square root and power are common.
In most cases they are plotted on a linear scale from a negative (when allowed) to a positive value. For a linear scale the distance from one value to the next is always the same.
You can apply all the known constants like Pi, E and Fi in the formula. The available functions and constants can be selected from a list or the formula can be entered in a text box.
Detailed instructions
Open the ‘Graphs’ item from the main menu or click the ‘Draw graph’ icon in the vertical toolbar. Select the ‘formulas and graphs’ option.
In the dialogue box, select ‘linear’ scale type. Browse the list and select the example grid with the formula x to the power of 2 (x^2).
To check/set the range for X and/or Y axis, use the ‘change coordinate system’ button. The dialogue box “Grid Properties” will show you the horizontal (X) and vertical (Y) axis. Open the respective option to change. Exit with ‘OK’.
To enter a second formula, which will produce a second graph in the same grid, use the ‘Multiple Formulas’ button. The dialogue box “Grid Properties” will now show you a list of (filled and empty) formulas. Open ‘Formula 2’ and insert 0.5*x-1 in the field behind “y=”. Exit with ‘OK’.
To finalize, choose either the ‘Insert in new document’ or ‘Insert in current document’ button.
Once you have the grid inserted in the document you can produce the image on swellpaper, emboss it on a braille embosser or sketch it with the MDA.
Screenshot: TactileView creating a linear axis grid with graphs of two formulas (x^2 and 0.5*x-1).
Worksheet 2: Logarithmic Y scale to represent the Covid19 infection cases
The range for the X axis for this graph is in days. We want to see what the absolute effect of the virus is after a number of days, given a known reproduction rate and a number of infected cases. This axis is linear: the distance from one day to the next is always the same.
The Y axis has a logarithmic scale to indicate the number of infections. The higher the values and the more upwards the axis goes, the same distance between two points on the axis contains ever larger numbers.
For example: If the first centimeter on a logarithmic scale goes from 0 to 10, the second centimeter could already go from 10 to 100 and the third centimeter from 100 to 1000. As a result, compared to linear scales, quickly rising numbers with very steep and sharply pointed graphs can be “pressed together”. Having a logarithmic scale thus allows to have a large range in a small and compact graphical representation.
Detailed instructions
Open the ‘Graphs’ item from the main menu or click the ‘Draw graph’ icon in the vertical toolbar. Select the ‘formulas and graphs’ option.
In the dialogue box, select ‘logarithmic’ scale type. Browse the list and select the example grid with the formula y=1.3^x*1000.
To check/set the range for X and/or Y axis, use the ‘change coordinate system’ button. The dialogue box “Grid Properties” will show you a list with items. The horizontal (X) and vertical (Y) axes are two of them. Open them to make your preferred changes. For example: Open ‘Horizontal (X) Axis’ and change the number of days on the axis from 28 to something else in the field ‘Highest value on X Axis’. Exit with ‘OK’ each time.
To change the formula, use the ‘Change Formula’ button. Change the numeric values in the field behind “y=”. (Note: The symbol for ‘power of’ is ^. The default values of this grid example are: 1.3 as reproduction rate, 1000 as number of infections on day 1. The value for x is taken from the x axis and represents each day on that scale). You can either select ‘Renew Preview’ or directly exit with ‘OK’.
To finalize, choose either the ‘Insert in new document’ or ‘Insert in current document’ button.
Once you have the grid inserted in the document you can produce the image on swelllpaper, emboss it on a braille embosser or sketch it with the MDA.
Screenshot: TactileView creating a grid with logarithmic Y axis and one graph (formula: 1.3^x*1000 [a possible Covid-19 reproduction rate]).
Worksheet 3: Scale in degrees or radians for goniometrical functions
Sine or cosine graphs (or combinations of both) are applied in many domains. To understand the basics, they can be plotted with two different scale types. One way is to have the variable for the X axis in degrees. The range is in many cases from 0 to 360 degrees or maybe more to show the cyclic effect.
Alternatively, the X axis can be set to radians.
Selecting radians for the X axis will state ‘pi’ for the name for the X axis.
Set the range from zero (0) to two (2) for a full cycle. In case of Pi, the X parameter may have a negative value.
A sine graph with the X axis 0 to 360 degrees or 0 to 2 Pi will have the same shape, assuming the same amount of distance in centimeters or inches from the lowest to the highest value is set for both.
Detailed instructions
Open the ‘Graphs’ item from the main menu or click the ‘Draw graph’ icon in the vertical toolbar. Select the ‘formulas and graphs’ option.
In the dialogue box, select ‘degrees’ or ‘radians’ scale type. Browse the list and select an example grid with sine or cosine.
To change the X axis’ scale type from ‘degree’ to ‘radians’ or vice-versa, use the ‘change coordinate system’ button. Open the horizontal (X) axis properties to switch ‘type’ between ‘degrees’ or ‘radians’. Exit with ‘OK’ each time.
To finalize, choose either the ‘Insert in new document’ or ‘Insert in current document’ button.
Once you have the grid inserted in the document you can produce the image on swelllpaper, emboss it on a braille embosser or sketch it with the MDA.
Screenshot: TactileView creating a grid with an X axis in degrees and one graph (sine formula; wave shape).
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