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Re: [Maxima-discuss] Problem with draw2d(implicit(...))
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From: Richard F. <fa...@be...> - 2020-03-22 21:07:58
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This is probably not going to solve this particular problem,
but the general problem of making sure that plots don't lie
because of numerical errors can be addressed by interval
arithmetic, at least sometimes. google search for "honest plotting".
Not that Maxima has any seriously implemented interval arithmetic.
RJF
On 3/22/2020 12:56 PM, Leo Butler wrote:
> Here are two other ways to get implicit to do the right thing, besides
> using f^(1/3) as I posted earlier. Using the form
>
> unit_step(f-c)
>
> guarantees that the fudge factor epsilon is side-stepped altogether.
>
>
>
> (%o41) feq0(x,y):=unit_step(2*y^5-x*y^3+2*x^2*y^2-x^3*y+2*x^5)
> (%i42) draw2d(grid = true,ip_grid=[100,100],ip_grid_in=[10,10],implicit(feq0,x,-0.1,0.1,y,-0.1,0.1),terminal=dumb);
>
> 0.1 +------------------------------------------+
> | : : : |
> | : : : |
> | : : : |
> | : : : |
> | : : : |
> | : : *** : |
> | : : ** * : |
> | : : ** * : |
> | : : * * : |
> | : :** * : |
> 0.05 |-+........:..........:*....*...:..........|
> | : :* ** : |
> | : ** * : |
> | : * * : |
> | : * ** : |
> | : * * ****** |
> | : * ** *** * |
> | : * * *** : * |
> | : * ***** : ** |
> |**** : ***** : *** |
> | ***** : *** *** |
> | ******* ** ***** |
> 0 |-+........:..***************...:..........|
> | : * : |
> | : * : |
> | : * : |
> | : * : |
> | : * : |
> | : * : |
> | : * : |
> | : * : |
> | : * : |
> | : * : |
> -0.05 |-+........:..........*.........:..........|
> | : ** : |
> | : :* : |
> | : :* : |
> | : :* : |
> | : :* : |
> | : :* : |
> | : :** : |
> | : : * : |
> | : : * : |
> | : : * : |
> | + + ** + |
> -0.1 +------------------------------------------+
> -0.1 -0.05 0 0.05 0.1
>
>
> (%o42) [gr2d(implicit)]
>
> (%i43) feq0(x,y) := if is(''f>0) then true else -1;
>
> (%o43) feq0(x,y):=if is(2*y^5-x*y^3+2*x^2*y^2-x^3*y+2*x^5 > 0) then true else -1
>
> (%i44) draw2d(grid = true,ip_grid=[100,100],ip_grid_in=[10,10],implicit(feq0,x,-0.1,0.1,y,-0.1,0.1),terminal=dumb);
>
> 0.1 +------------------------------------------+
> | : : : |
> | : : : |
> | : : : |
> | : : : |
> | : : : |
> | : : *** : |
> | : : ** * : |
> | : : ** * : |
> | : : * * : |
> | : :** * : |
> 0.05 |-+........:..........:*....*...:..........|
> | : :* ** : |
> | : ** * : |
> | : * * : |
> | : * ** : |
> | : * * ****** |
> | : * ** *** * |
> | : * * *** : * |
> | : * ***** : ** |
> |**** : ***** : *** |
> | ***** : *** *** |
> | ******* ** ***** |
> 0 |-+........:..***************...:..........|
> | : * : |
> | : * : |
> | : * : |
> | : * : |
> | : * : |
> | : * : |
> | : * : |
> | : * : |
> | : * : |
> | : * : |
> -0.05 |-+........:..........*.........:..........|
> | : ** : |
> | : :* : |
> | : :* : |
> | : :* : |
> | : :* : |
> | : :* : |
> | : :** : |
> | : : * : |
> | : : * : |
> | : : * : |
> | + + ** + |
> -0.1 +------------------------------------------+
> -0.1 -0.05 0 0.05 0.1
>
>
> (%o44) [gr2d(implicit)]
>
>
> Gunter Königsmann <gu...@pe...> writes:
>
>> ********************************************************
>> Caution: This message was sent from outside the University of Manitoba.
>> ********************************************************
>>
>> I am still convinced that I have overlooked something important: In all
>> examples I could fild the line from the "implicit" graphics object was
>> at plus epsilon, never at 0 and I don't really understand why. But for
>> all problems I found the attached patch seems to resolve the problem -
>> even if epsilon for problems with really big numbers should be outside
>> the dynamic range of the floats and for problems that use small numbers
>> it feels way too high. What do we do with problems that include both big
>> and small floats?
>>
>> Kind regards,
>>
>> Gunter.
>>
>>
>> _______________________________________________
>> Maxima-discuss mailing list
>> Max...@li...
>> https://lists.sourceforge.net/lists/listinfo/maxima-discuss
>
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