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«Geometry Expressions Manual TM Saltire Software PO Box 230755 Tigard, OR 97281 0755 © 2013 Saltire Software. All rights reserved. Information in ...»

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(Windows 7 users have no worries.) If you don't see an Annotation Symbol, change the Edit / Preferences / Math / Annotation / Font / Face Name. Try one of the Unicode fonts, e.g. Lucida Sans Unicode. If you are exporting a Metafile, you may have to change the default font in the program to which you are exporting.

System Variables and Animation

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Investigating Variables The Variables toolbox reports all the variables you have used in the diagram and lets you manipulate their values.

© 2013 Saltire Software 144 Geometry Expressions Manual Variables List This list contains the names of all variables used in your diagram.

For every variable name, the system shows:

the current value - these values can be ones that you have explicitly · specified, or just taken from the way you sketched the geometry.

lock status - if the variable is locked (+) its value will not change if · you move the geometry or add additional constraints; the unlocked (-) variable is free to change as the geometry moves or changes.

Functions List When using the Function command to draw a function of the form Y=f(X) +g(X), the Functions tab in the Variables toolbox lists the functions f and g and their values. Use the edit line at the bottom of the box to modify the functions.

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Using the Lock Tool By default, when you drag points in a Geometry Expressions model, it will adjust the numerical sample values used in the various parameters of the model to accommodate the drag, as best it can.

For example, in the model of a 4 bar linkage below, dragging point B will cause lengths a and b and angle q to be adjusted appropriately.

© 2013 Saltire Software 146 Geometry Expressions Manual However, you may want the drag to act as if the members AB and BC were rigid, and only angle theta adjustable. To do this you can lock the

parameters:

The value of a, for example, can still be set from the Variables panel, but it will not change when the model is dragged.

–  –  –

Changing and Locking the Variable Value To make a change to the variable list, first click anyplace in the row of the variable you want to change. That row will be highlighted.

To change the value: highlight the value in the edit window and type the new value.

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Animation Your geometry comes to life with the Animation tools. You simply need to select the parameter that drives the animation, give it a range, then Play.

In the diagram below we select q for the crank of this linkage.

© 2013 Saltire Software 148 Geometry Expressions Manual Click the headings below for details on the animation buttons and

windows:

Animation console - works like a video player.

· Animation modes - indicates how the range for the animation is · stepped through.

Animation values and duration - where you specify the speed and the · range for the driving parameter.

Users of numeric interactive geometry systems may be familiar with the concept of animation based on points animated along line segments or curves. This type of animation can be conveniently modeled in Geometry Expressions using the point proportional along a curve constraint along with parameter based animation.

–  –  –

Animation Console The Animation console works like a standard video console with the Play, Pause, and Stop buttons as well as advance to the Beginning and End buttons.

Animation Modes

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Animation Values and Duration These animation buttons help you adjust the range and speed of the animation.

Click and drag the slider along the bar to manually animate the · drawing.

In the two data entry windows at the bottom right and left of the · toolbox, specify the range of the animation.

The Duration box in the center lets you specify how long the · animation takes to play one time through. Values are between 1 and © 2013 Saltire Software 150 Geometry Expressions Manual

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Animation and the Locus Tool Both the construction of the locus and envelope curves, and the animation of the diagram in Geometry Expressions can be defined in terms of any variable. For example in the model below, we can create a locus over values of the variable t (other variables will be kept constant).

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Many of the menus and icons across the top of the screen duplicate the commands and functions found in the toolboxes.

File Menu The File menu contains the standard Windows file handling operations with options for copying and exporting to other programs. Several of the options are also available from the icon bar.

–  –  –

Importing Files from the Figure Gallery Are there figures which you need to use frequently? The Figure Gallery makes your tasks easier. Browse through the folders to see the many objects, graphs and transformation examples which you can use and tailor to your needs without starting from scratch.

Figure Gallery database file is copied to your computer when you install © 2013 Saltire Software 154 Geometry Expressions Manual Geometry Expressions.





Here are the steps to import a figure:

1. Select File / Import Figure from Figure Gallery

2. Double click a folder or sub-folder (or click and press Select in the lower right corner) to view of the problems in a category. You can also use the search window to find files.

3. Double click a problem (or click and press Select) to see an enlarged view

4. Click the Import button (it replaces the Select button in the lower right corner) to bring the drawing into your drawing window.

Use the Toggle Hidden function from the general context menu to modify constraints in the drawing, or try dragging the geometry to suit your needs. Don't forget to Save.

–  –  –

Use the Search window to find a specific file or types of files. Enter the search word(s) and click Go.

Text at the top center of the dialog tells you which level is displayed. Click Home to return to the top level.

Importing Files from the Geometry Atlas The Geometry Atlas is a huge collection of interesting theorems and problems which are already constructed, waiting for you to discover their mysteries. You just need to have internet access.

© 2013 Saltire Software 156 Geometry Expressions Manual Browse through the atlas, organized in the usual tree structure by

geometry element. Here are the steps:

1. Make sure your computer is on-line.

2. Select File / Import GX File from Geometry Atlas.

3. Double click a folder or sub-folder (or select the folder and press the Select button) to view the problems or sub-folder.

4. Double click a problem (or select the problem and press Select) to see an enlarged view.

5. Click the Import button to bring the drawing into your drawing window.

Browsing the Atlas

–  –  –

Use the Search window to find a specific file or types of files. Enter the search word(s) and click Go.

Text at the top center of the dialog tells you which level is displayed. Click Home to return to the top level.

Exporting a Drawing To export your drawing to another program, choose File / Export. You

can export the drawing in the following formats:

© 2013 Saltire Software 158 Geometry Expressions Manual

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Please note that neither EMF, nor EPS support semi-transparency or transparent images of any kind, thus you will get a warning message if you try to export to either of these formats and you have such an item in the document.

Here are the steps for the export as an Image file, EPS, EMF, SVG or

HTML:

1. For all file types enter the Filename or click the folder icon to select the appropriate folder and file.

2. Image files and HTML files have an extra step at this point as detailed below.

3. Select the region of the drawing with the displayed cursor (click-and-drag opposite corners of the region).

Animation Files and JavaScript Files have a few more details to consider as explained below.

–  –  –

Exporting Image Files When exporting image files, click the down arrow in the Save as type line to select your desired image format.

Next, set the resolution in the File DPI box. Click the down arrow and select the appropriate setting or enter a number in the window.

Exporting HTML Files When you select File / Export / HTML, the HTML Export dialog appears.

Fill in the Html Export Settings with optional Title, Header and Footer text.

The Outputs can be renamed to something less obscure than letters with subscripts. You can give them actual labels using real words. You can also display your output expressions in many popular CAS input formats including Content and Presentation MathML.

© 2013 Saltire Software 160 Geometry Expressions Manual Exporting Animation Files Select File / Export / Animation File to produce an animated gif. This format is supported by many applications and will enable you to embed animations in, for example, PowerPoint slides and Wikipedia pages.

Select the directory and file name of your gif, and you will be presented with a dialog to choose the parameter on which the animation is based, along with various technical aspects of the animation.

–  –  –

File DPI - specify the resolution of the output. The higher number you use, the slower will be the process of creating and loading the animation.

Frames Per Second - if you multiply this number by the animation duration specified in the Variables toolbox, you will get the number of frames captured. For example if you are set at 10 frames per second, and the Variables toolbox specifies the duration of the animation to be 4 seconds, then 40 frames will be captured. The more frames you capture, the slower will be the animation creation process, and the longer the animation will take to load.

Number of iterations - when an animation is played (e.g. when a PowerPoint slide containing the animation is displayed), enter a number to play the animation a specific number of times, or enter 0 to play it continuously.

Variable - choose the variable that controls the animation. (All the variables in the Variables toolbox should be available). The limits of the variable defining the range of the animation should be set in the Variables toolbox.

Exporting JavaScript Files Select File / Export / [HTML5 / JavaScript App] - to export a Geometry Expressions model as a JavaScript application (.html file), within an html page. This can then run within any web browser that supports HTML 5.

Fill out the details in the JavaScript Applet Generator dialog.

© 2013 Saltire Software 162 Geometry Expressions Manual

Output directory - tells Gx where to put the files. It will create a file:

name.html in the specified directory. You should be able to bring name.html up in a browser to see the applet.

Applet Name - is the name of the html file.

Auto-scale - when set to True, the JavaScript applet automatically rescales the drawing when the user changes the value of one of the inputs; when set to False, you click-and-drag a rectangle around the drawing after you click Ok.

Width and Height specify the size of the drawing on the html page.

–  –  –

Note: you can insert html code into the header and footer text, e.g. to

make a word in the footer text bold:

Inputs - lets you choose which variables the user will be able to change, what text Label identifies variable and what type of control to use.

Any variables in your Gx model may be selected as input variables in the JavaScript model. See the topic detailing UI Types below.

Outputs - lets you choose which outputs will appear in the applet, and their text Label.

See the examplesbelow.

© 2013 Saltire Software 164 Geometry Expressions Manual JavaScript Applet Example We’ll use this Gx model, displaying the radius of an incircle to create a JavaScript Applet.

Here are the parameters we entered in the JavaScript Applet Generator

dialog:

Here is the result:

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The exported image can be zoomed in and out using the - and + keys on the keyboard or paned around using the arrow keys. If displayed on a touch sensitive device, the app supports multi-touch features.

© 2013 Saltire Software 166 Geometry Expressions Manual JavaScript Animated Applet In this applet, we'll draw a general function, f(x) and then create its derivative at t (using the Point proportional constraint). Here is the

Gx drawing:

Here are the parameters we entered in the JavaScript Applet Generator

dialog:

–  –  –

Selecting slider for the UI Type of variable t we now have the Go/Stop button to control the animation of t between the ranges defined in the Variables panel above.

© 2013 Saltire Software 168 Geometry Expressions Manual

–  –  –

To modify the function, simply type a new one in the edit field. A multiline function allows more options.

Creating Lua Applets If you have a TI-NspireÔ calculator, you can put your Geometry Expressions model on it by creating an interactive Lua app.

Variables can be adjusted from a text box or with a slider. Any points in the Geometry Expressions model constrained by variable Coordinates or a variable parameter for the Point Proportional constraint can be set as draggable points in the Lua app.

After you create your Gx model select File / Export /Lua App. Fill out the details in the Lua App Generator dialog.

© 2013 Saltire Software 170 Geometry Expressions Manual

Output directory - tells Gx where to put the file. It will create a file:

name.tns in the specified directory.



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