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Re: Reordering limits for Plot3D


On 6/13/06 at 1:07 AM, djmp at earthlink.net (David Park) wrote:
>From: Ken Levasseur [mailto:klevasseur at mac.com] To:
To: mathgroup at smc.vnet.net

>>One of my students just noticed that the plots generated from

>>Plot3D[x y^2, {x, 4, 1}, {y, 8, 0}] and Plot3D[x y^2, {x, 1, 4}, {y,
>>0, 8}]

>>are identical.  In general, how does Plot3D handle the iterators that
>>define the plotting domain?

>Yes, Mathematica orders the plot iterator limits so they always go
>from minimum to maximum.

Hmm... I wonder if that is literally true. Possibly the mechanism is somewhat different. Suppose Mathematica simply samples the function over the range given by the iterators using something akin to 

Sort@Range[Sequence@@iterators, -Subtract@@iterators/n]

Then the initial points for sampling the function would be independent of the order of the iterators and the resulting plot would be identical.

Given the observed behavior, i.e. Plot[f[x],{x,0,8}] creates the same Plot as Plot[f[x],{x,8,0}] I don't know that the details of what Mathematica does is important. And without access to the source code there is no way to know for certain how Mathematica implements a particular feature.
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