acer

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It is possible to thicken the axes of 2D plots by adjusting the underlying data structure, since the appropriately placed THICKNESS() call within the PLOT() data structure is recognized by the Standard GUI. This does not seem to be recognized for PLOT3D structures, however.

The issue of obtaining thicker axes for 2D plots can then be resolved by first creating a plot, and then subsequently modifying the PLOT structure.

The same techniques could be used to thin...

I was recently looking at rotating a 3D plot, using plottools:-rotate, and noticed something inefficient.

In the past few releases of Maple, efficient float[8] datatype rtables (Arrays or hfarrays) can be used inside the plot data structure. This can save time and memory, both in terms of the users' creation and manipulation of them as well as in terms of the GUI's ability to use them for graphic rendering.

What I noticed is that, if one starts with a 3D plot data structure containing a float[8] Array in the MESH portion, then following application of plottools:-rotate a much less efficient list-of-lists is produced in the resulting structure.

Likewise, an effiecient float[8] Array or hfarray in the GRID portion of a 3D plot structure gets transformed by plottools:-rotate into an inefficient list-of-lists object in the MESH portion of the result. For example,

restart:

p:=plot3d(sin(x),x=-6..6,y=-6..6,numpoints=5000,style=patchnogrid,
          axes=box,labels=[x,y,z],view=[-6..6,-6..6,-6..6]):

seq(whattype(op(3,zz)), zz in indets(p,specfunc(anything,GRID)));
                            hfarray

pnew:=plottools:-rotate(p,Pi/3,0,0):

seq(whattype(op(1,zz)), zz in indets(pnew,specfunc(anything,MESH)));
                              list

The efficiency concern is not just a matter of the occupying space in memory. It also relates to the optimal attainable methods for subsequent manipulation of the data.

It may be nice and convenient for plottools to get as much mileage as it can out of plottools:-transform, internally. But it's suboptimal. And plotting is a topic where dedicated, optimized helper routines for some particular data format is justified and of merit. If we want plot manipulation to be fast, then both Library-side as well as GUI-side operations need more case-by-case-optimizated.

Here's an illustrative worksheet, using and comparing memory performance with a (new, alternative) procedure that does inplace rotation of a 3D MESH. plot3drotate.mw

The goal here is to produce plots for inclusion inside Worksheets or Documents of the Standard GUI at specific sizes.

[update: Maple 18 has this as a new feature for 2D plots. See the `size` option described on ?plot,options]

When manually resizing an existing plot, using the mouse pointer, there is no visual cue as to what pixel size has been attained. Hence any worksheet author who wishes to produce a plot of size 600x600 is presented with two barriers. The first is that resizing must be done manually, and the second is that there is no convenient mechanism showing the actual size attained.

The `Resize` package attempts to address these barriers by allowing construction of a plot, inside a worksheet, with programmatically specified width and height in pixels.

The default behaviour of the package is to produce the plot inside a new Worksheet, from whence it may be selected and copied. An optional behaviour is to show the constructed plot inside a Task Template (a form of help-page), where it may be previewed for correctness and inserted into the current Worksheet or Document at the press of a single button.

It appears to function for both 2D and 3D single plots.

It won't work for so-called Array plots, which are collections of multiple plots displayed side-by-side inside a worksheet table.

This first version is a bit rough. The plot is currently being inserted as input, which is why it isn't centered on the page. I suspect that it would be best to insert the first argument (eg. a `plot` call) as input to an execution group, and then have the plot be the output. That would look, and hopefully act, just as usual. And with the plot call inserted as input, the original `Resize` call could be neatly deleted if desired.

To install this thing, use the File->Open from the Standard GUI's menubar. Choose this .mla file as the thing to open. (You may have to slide a scrollbar, and select a view of "All Files", in order to see it in the pop-up File Manager.) Double-clicking on the file, to launch it, should ideally also open it but it looks like that functionality broke for Maple 15.

Resize_installer.mla

Alternatively, you could run the command,

march( 'open', "...full...path...to...Resize_installer.mla");

The attached .mla archive is a (graphically) self-unpacking installer, when opened in this way.

The bundled materials include a pre_built .mla containing the package itself, the source code and a worksheet that rebuilds it from source if desired, a short example worksheet, and a worksheet that rebuilds the whole installer (and re-bundles all those files into it). I used the `InstallerBuilder` to make the self-unpacking .mla installer, as I think it's a handy tool that is under-appreciated (and, alas, under documented!).

It's supposed to work without the usual hassle of having to set `libname`. This is an automatic consequence of the place in which it gets installed.

It seems to work in Maple 12, 14, and 15, on Windows 7. Let me know if you have problems with it.

acer

I saw an image yesterday of some math done similar to how one can write on paper, with each new reformulation shown on the next line, with a down-arrow between each such line. In other words, operations and output moving down the sheet rather than along it to the right.

The first thing that came to mind was: can this be done in Maple with context-menus?

Here is an attempt,

    cm_downwards.mw

Most programs will not produce and assign to a large number of global "top-level" names. But it is interesting that the cost associated with such global name assignment is related to the number of entries in libname.

A possible cause of this cost is the need to check whether the name is protected, before assigning.

The following timings were made on 32bit Maple 15 running on Windows 7, on an Intel i7. The set of four timings is...

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