{"id":2091,"date":"2009-12-27T11:43:52","date_gmt":"2009-12-27T10:43:52","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=2091"},"modified":"2009-12-29T10:31:42","modified_gmt":"2009-12-29T09:31:42","slug":"walking-randomly-sage-bounty-hunt-1","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=2091","title":{"rendered":"Walking Randomly Sage bounty hunt #1"},"content":{"rendered":"

Regular readers of Walking Randomly will know that I am a big fan of the Manipulate<\/a> function in Mathematica.\u00a0 Manipulate allows you to easily create interactive mathematical demonstrations for teaching, research or just plain fun and is the basis of the incredibly popular Wolfram Demonstrations Project<\/a>.<\/p>\n

Sage<\/a>, probably the best open source mathematics software available right now, has a similar function called interact<\/a> and I have been playing with it a bit recently (see here<\/a> and here<\/a>) along with some other math bloggers<\/a>.\u00a0 The Sage team have done a fantastic job with the interact function but it is missing a major piece of functionality in my humble opinion – a Locator control.<\/p>\n

In Mathematica the default control for Manipulate is a slider:<\/p>\n

Manipulate[Plot[Sin[n x], {x, -Pi, Pi}], {n, 1, 10}]<\/pre>\n
\"Manipulate<\/p>\n
The slider is also the default control for Sage’s interact:<\/p>\n
@interact\r\ndef _(n=(1,10)):\r\n    plt=plot(sin(n*x),(x,-pi,pi))\r\n    show(plt)<\/pre>\n
\"Interact<\/p>\n
Both systems allow the user to use other controls such as text boxes, checkboxes and dropdown menus but Mathematica has a control called a Locator<\/a> that Sage is missing.\u00a0 Locator controls allow you to directly interact with a plot or graphic.\u00a0 For example, the following Mathematica code (taken from its help system) draws a polygon and allows the user to click and drag the control points to change its shape.<\/p>\n
Manipulate[Graphics[Polygon[pts], PlotRange -> 1],\r\n {{pts, {{0, 0}, {.5, 0}, {0, .5}}}, Locator}]<\/pre>\n
\"Mathematica<\/p>\n
The Locator control has several useful options that allow you to customise your demonstration even further.  For example, perhaps you want to allow the user to move the vertices of the polygon but you don’t want them to be able to actually see the control points.  No problem, just add Appearance -> None<\/strong> to your code and you’ll get what you want.<\/p>\n
Manipulate[Graphics[Polygon[pts], PlotRange -> 1],\r\n {{pts, {{0, 0}, {.5, 0}, {0, .5}}}, Locator, Appearance -> None}]<\/pre>\n
Another useful option is LocatorAutoCreate -> True<\/strong> which allows the user to create extra control points by holding down CTRL and ALT (or just ALT – it depends on your system it seems) as they click in the active area.<\/p>\n
Manipulate[Graphics[Polygon[pts], PlotRange -> 1],\r\n {{pts, {{0, 0}, {.5, 0}, {0, .5}}}, Locator,\r\n  LocatorAutoCreate -> True}]<\/pre>\n
When you add all of this functionality together you can do some very cool stuff with just a few lines of code.  Theodore Gray’s curve fitting code<\/a> on the Wolfram Demonstrations project is a perfect example.<\/p>\n
All of these features are demonstrated in the video below<\/p>\n
<\/object><\/p>\n
So, onto the bounty hunt.\u00a0 I am offering 25 pounds worth (about 40 American Dollars) of books from Amazon to anyone who writes the code to implement a Locator control for Sage’s interact function.\u00a0 To get the prize your code must fulfil the following spec<\/p>\n