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New Polar Axes

Posted on 2008-05-27 23:06 By pchin (Maple Rating 2 163)
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It's been a while since I've updated my blog, but the recent Maple 12 release gives me a good opportunity to talk about some of the features I'd been working on for the past months. A few people on MaplePrimes had asked for more details about Maple 12, so I'll start by saying a bit about the new polar axes. A lot of this work was done by my colleagues in the GUI Group and they may have additional interesting things to say about the feature.

In previous versions of Maple, you could draw polar plots using the plots[polarplot] command or with the coords=polar option, but these were always displayed with Cartesian axes. In Maple 12, polar axes are displayed by default, as seen here.

plots[polarplot](1+cos(theta), theta=0..2*Pi, axis[radial]=[tickmarks=5])

 A number of new options were added to the polarplot command so that you can customize the axes.  The most useful ones are the axis[radial] and axis[angular] options. These work like the axis[1], axis[2] and axis[3] options available for general plots, and you can use them to control color, tickmarks and other properties of the radial and angular axes.

Typeset math on plots had been introduced in Maple 11, and now we can take advantage of this with nice axis labels, in multiples of Pi, on the angular axis. These labels appear by default, but of course, they can be customized with the axis options. The plot/typesetting help page provides information on how to add typeset math to plots through the command line. There are also interactive ways to do this, using the context menu.

You can add polar axes to plots created by commands other than plots[polarplot], by using the axiscoordinates=polar option. However, not all the options offered by plots[polarplot] are available generally. Here is an example using plots[implicitplot].

plots[implicitplot]([x^2+2*y^2 = 1, x^2+1.5*y^2 = 1], color = ["Blue", "Green"], x = -1 .. 1, y = -1 .. 1, axiscoordinates = polar);

It is also possible to get the pre-Maple 12 Cartesian axes back with polar plots, by adding the axiscoordinates=cartesian option.

There are many more options available with the plots[polarplot] command, and there are other ways to create and manipulate polar plots without having to use the command-line. As it's rather late in the day (Waterloo time), I'll leave this information for a future blog post.

Comments

Polar axes?

Comment on 2008-05-28 17:17 from jakubi (Maple Rating 4 925)

I wonder whether English speaking mathematicians do use the expression "polar axes" to denote coordinate lines in a curved coordinate system like the polar coordinates.

Not being an English speaker, the use of "axes" for "curves" sounds to me as an oxymoron, because an axis normally meant something rectilinear. Even more together with "polar" that means itself a direction.

Indeed, some googling has shown me that this strange usage is somewhat commonplace within the computing community. But I doubt whether this is a reason to endorse this usage.

contours

Comment on 2008-05-28 16:36 from Mariner (Maple Rating 4 562)

In my world, an axis is a straight line, so it might be better to refer to constant r and theta contours. A bit clumsy, perhaps...

J. Tarr

on the 'Polar' Axes

Comment on 2008-06-02 13:44 from dawgit (4)

 The term "Polar" as used in this description of a view is refering to the "Z" Axes. As for the term "Polar", it would be in reference to the Earth Axes, as in the one that runs (S) Pole to (N) Pole. The view then is as if one where looking down on the Earth onto either the 'N' or 'S' Pole.  In 3D type depictions (or graphs) one would be looking into the 'Z' Axes. (with X¹ to X², your left to right, and of course, Y¹ to Y², your up and down.)

 

(an old dawg) Still Learning.

a further clearification

Comment on 2008-06-02 13:55 from dawgit (4)

I left a bit out on the model above:

 

¹ to X² would normally be Left to Right, in a Polar view it would be also West to East.¹ to Y² then again normally Up and Down, but also refering to North and South as one would be from an Equaterial view.

(an old dawg) Still Learning.

 

And the Y

And the "Polar" view is than just that.

The X

My Keyboard (Fingers) Need to be Calibrated

Comment on 2008-06-02 13:58 from dawgit (4)

or, I'm getting old. Again, the part left out:

(an old dawg) Still Learning.

 

And the Y¹ to Y² then again normally Up and Down, but also refering to North and South as one would be from an Equaterial view.

Global view

Comment on 2008-06-02 14:54 from Mariner (Maple Rating 4 562)

David,

Try looking at a globe in the way described in your first post .i.e. along the spin axis, and see if you can point to the East-West and North-South axes.

J. Tarr

What I see... (I'm coming

Comment on 2008-06-03 06:59 from dawgit (4)

What I see... (I'm coming from 3D CAD mentality here, and GIS as well)
For this to be a true "Polar" view, Eye-balling the "Z" Axes then,
the "X" Axes is appearing to be the concentric circles around the center point. (point Ø on the Z axes) The Y Axes will then appear as the "Cross Hairs" ( —, again with the center point being on that axes as well, to the left a '-' distance, to the right a '+' distance.) Wither to the North or South will depend on wither it is a "North Polar" View then to the South) or a "South Polar" View (then to the North) The Outer Circle, or Ring, the Equator in a Polar view is usually the Ø on the X Axes (with ± descending towards the Pole or center point, here being X±90°).
A Polar View (Z axes) is when rotated 90°, you'll have the 'normal' X-Y axes 2D view. (with the Z axes vectoring out from the center point).
Ok, That's what I see in a “Polar View”. Very usefull in 3D CAD or GIS data (or 3D Graphing for that mater). Just MHO. -d

(an old dawg) Still Learning.

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