Re: Cool example with ContourPlot+EvaluationMonitor

• To: mathgroup at smc.vnet.net
• Subject: [mg125584] Re: Cool example with ContourPlot+EvaluationMonitor
• From: David Kahle <david.kahle at gmail.com>
• Date: Tue, 20 Mar 2012 02:19:29 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <jk1fpb\$4v0\$1@smc.vnet.net> <201203191001.FAA01040@smc.vnet.net>

```Yea, really nice work.    Adding to Ralph's question - is there a particular method that Mathematica (predominantly) follows for this?  Can you refer me to a good source? (Text, paper, etc?)

Cheers
david.

On Mar 19, 2012, at 5:01 AM, Ralph Dratman wrote:

> Could one of you please explain a little more? I think I get the
> general idea about putting together the plot of an implicit function
> by a sort of scanning process, but I don't understand the details.
> Thank you.
>
> Ralph
>
> On Sun, Mar 18, 2012 at 3:43 AM, Murta <rodrigomurtax at gmail.com> wrote:
>> Nice!.. I played with the code and made it shorter.
>> It's the same thing.
>>
>> Dynamic[
>> ListPlot[data, Frame -> True, AspectRatio -> 1, PlotStyle -> Blue,
>> PlotRange -> {{-1.6, 1.6}, {-1.6, 1.6}}, Epilog -> Circle[{0, 0}]]]
>> data = {}; freeze = 0.01
>>
>> ContourPlot[x^2 + y^2 == 1, {x, -1.5, 1.5}, {y, -1.5, 1.5},
>> EvaluationMonitor :> (AppendTo[data, {x, y}]; Pause[freeze])]
>>
>> []'s
>> Murta
>> On Mar 17, 4:51 am, psycho_dad <s.nesse... at gmail.com> wrote:
>>> The following example shows in real-time (sort of) how ContourPlot calculates a contour (in this example a unit circle):
>>>
>>> f[x_, y_, freeze_] := (Pause[freeze]; (x^2 + y^2))
>>> data = {}; freeze = 0.04;
>>> Dynamic[ListPlot[data, Frame -> True, AspectRatio -> 1,
>>>  PlotStyle -> Blue, PlotRange -> {{-1.6, 1.6}, {-1.6, 1.6}},
>>>  Epilog -> Circle[{0, 0}]]]
>>> ContourPlot[f[x, y, freeze] == 1, {x, -1.5, 1.5}, {y, -1.5, 1.5},
>>>  EvaluationMonitor :> AppendTo[data, {x, y}]];
>>>
>>> Initially I just wanted to get all the points from ContourPlot, but then it dawned on me that using Dynamic I could do that in real time! I hope you like it :D
>>>
>>> Cheers
>>>
>>> PS Change the parameter freeze (set to 0.04 secs) to make the animation slower or faster.
>>> PPS This is so cool, I just knew I had to share it!
>>
>>
>

```

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