Add auto_scaling option to threejs plots

[gh-LaisRast]

Up to Sage 9.5.beta4, threejs_template.html can automatically scale down the z-axis if the last entry of aspect_ratio is set to 1 (whether because the user did not specify a value, or because the user specified a value identical to the default value) and the plot extends a lot more in the z direction than in the x and y directions.

For instance, the following example

sage: cubes = sum([cube((0, 0, i)) for i in range(0, 6)])
sage: cubes.show(aspect_ratio=[1, 1, 1])

shows a stack of cubes squeezed along the z-axis, rather than a stack of undistorted cubes.

This behavior is unexpected after explicitly setting the aspect ratio.

In the file threejs_template.html, the lines responsible for this behavior are:

    var autoAspect = 2.5;
    if ( zRange > autoAspect * rRange && a[2] === 1 ) a[2] = autoAspect * rRange / zRange;

That automatic scaling down was introduced in #12402. Quoting from that ticket:

There is already automatic scaling in the z-direction to avoid the tall thin box that appears in the current version on the cell server (and SMC), but that can easily be overridden.

It is worth mentioning that one way to overwrite this behavior is to do:

sage: plot.show(aspect_ratio=[1, 1, 0.99999])

This ticket fixes this behavior and introduces a new threejs-specific plot option.

The new option is called auto_scaling (default: [False, False, False]) and takes a list or a tuple of three booleans; set to True to automatically scale down the corresponding direction if it is too large.

[guenterrote]

This example shows the distortion in a more conspicuous way:

sage: plot = sum([cube((0,0,i)) for i in range(0,10,2)])
....: plot.show(aspect_ratio=[1,1,1])

Apparently this automatic distortion was inserted as a hack to deal with some specific example that looked bad? It should be removed!

[gh-LaisRast]

It turns out this behavior is documented. In the current version of reference/plot3d/threejs.html (see page ​https://doc.sagemath.org/html/en/reference/plot3d/threejs.html) it says

aspect_ratio – (default: [1,1,1]) list or tuple of three numeric values; z-aspect is automatically reduced when large but can be overridden

However, I still believe it should not be the default behavior. Following Günter's suggestion, we can do

    var autoAspect = 2.5;
-    if ( zRange > autoAspect * rRange && a[2] === 1 ) a[2] = autoAspect * rRange / zRange;
+    if ( zRange > autoAspect * rRange && a[2] === "automatic" ) a[2] = autoAspect * rRange / zRange;

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​89f101e

consider the correct diameter

[mkoeppe]

Stalled in needs_review or needs_info; likely won't make it into Sage 9.5.

[mkoeppe]

This is a nice improvement.