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Re: Re: Clever Tricky Solutions

• To: mathgroup at smc.vnet.net
• Subject: [mg94252] Re: [mg94219] Re: Clever Tricky Solutions
• From: Brett Champion <brettc at wolfram.com>
• Date: Tue, 9 Dec 2008 06:57:21 -0500 (EST)
• References: <27271771.1228394784179.JavaMail.root@m02> <ghavpg$o9j$1@smc.vnet.net> <200812081122.GAA15823@smc.vnet.net>

On Dec 8, 2008, at 5:22 AM , congruentialuminaire at yahoo.com wrote:

> Hello MathGroup:
>
> Thanks to Helen, et.al. for helping me to understand more about this.
>
> I submitted a summarizing post [to MathGroup] about this simple,
> common problem. Maybe it can help a new user past this simple problem.
>
> But reading Brett Champion's explanation about the behavioral change
> baffles me. He explains that new options like Filling->Bottom
> motivated the change to the PlotRange semantic.
>

[I haven't looked up my afore-mentioned response, but some  
clarification...]

This behaves the same in both V5 and V7:

g1 = Graphics[Disk[{0, 0}, 1], PlotRange -> {{-2, 2}, {-2, 2}}, Axes - 
 > True,
    Background -> Hue[0.2]];
g2 = Graphics[Disk[{3, 3}, 1], PlotRange -> {{2, 4}, {2, 4}}, Frame ->  
True,
    Background -> Hue[0.8]];
Show[g1, g2]

so I don't think Show has changed much if at all.

The thing that has changed is that starting with V6, the frontend is  
responsible for rendering graphics.  Previously this was handled by  
the kernel during the generation of postscript (and then the frontend  
rendered postscript, but this was at a very low level.)

The frontend is capable of deriving explicit settings for PlotRange- 
 >Automatic, but usually the kernel functions (Plot etc...) can do a  
better job because either the kernel function has to make an  
assumption about what the setting will be (Filling/ClippingStyle  
etc..) or because the kernel knows additional information about the  
resulting graphic.

For example, the default setting of PlotRange for Plot[] is actually  
{Full,Automatic} in V6+.  The Full indicates that Plot should generate  
a plot range corresponding to the specified range of the variable.  So  
Plot[Sqrt[x], {x, -1, 1}], will use an x-range of {-1,1}, even though  
there isn't really any interesting content for x<0.

I agree that it would be nice if Show[] could do something better by  
default, and hopefully it will in a future version.

Brett Champion
Wolfram Research

• References:
  • Re: Clever Tricky Solutions
    • From: congruentialuminaire@yahoo.com