How to Discretize the Following Region Using Reasonable Bounds?

Question

I want to accurately discretize the implicit equation $x^2+x+y^2+\sin(4xy)+\sin(3xy)=3.9$.

To get the whole discretized shape, I'm forced to use oversized bounds {x,-70,80} and {y,-70,80}

curve = DiscretizeRegion[
  ImplicitRegion[
   x^2 + x + y^2 + Sin[4*x*y] + Sin[3*x* y] == 
    3.9, {{x, -80, 70}, {y, -80, 70}}]]

If I reasonable bounds such as {x,-3,3} and {y,-3,3}, I get the following.

What adjustments can be made and how will this improve the accuracy?

(I'm new to Mathematica; sorry if this is a silly question.) Why do you have x^2 + x + y^2 in your code but just $x^2 + y^2$ in the equation at the top of your answer? Why the extra x term? — IridescenceDeep, Dec 28 '17 at 1:55
@Nodon'tshownmyrealname Because I'm careless! I edited the question. — Arbuja, Dec 28 '17 at 2:04

Carl Woll · Accepted Answer · 2017-12-27 21:54:54Z

5

Give DiscretizeRegion a second argument specifying bounds:

DiscretizeRegion[
    ImplicitRegion[
        x^2+x+y^2+Sin[4*x*y]+Sin[3*x*y]==3.9,
        {{x,-3,3},{y,-3,3}}
    ],
    {{-3,3},{-3,3}}
]

answered Dec 27 '17 at 21:54

Carl Woll

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$\begingroup$ ah.. note if you do RegionBounds on the intermediate ImplicitRegion it returns an incorrect result. $\endgroup$ – george2079 Dec 27 '17 at 22:02

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george2079 · Accepted Answer · 2017-12-27 20:16:16Z

5

making that parameter exact seems to fix things:

curve = DiscretizeRegion[
  ImplicitRegion[
   x^2 + x + y^2 + Sin[4*x*y] + Sin[3*x*y] == 
    39/10, {{x, -3, 3}, {y, -3, 3}}]]

note with the exact parameter and your origial "oversize" bounds you get a poor discretisation:

( remedied with MaxElementSize , etc )

answered Dec 27 '17 at 20:16

george2079

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$\begingroup$ I tried your code but I doesn't give the full picture. $\endgroup$ – Arbuja Dec 27 '17 at 20:56
$\begingroup$ For some reason only entering {x,-5,5} and {y,-5,-5} works. $\endgroup$ – Arbuja Dec 27 '17 at 21:00
1

$\begingroup$ there seems to be a version issue. Works for me with 10.1 , not with 11.1. $\endgroup$ – george2079 Dec 27 '17 at 21:15

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David G. Stork · Accepted Answer · 2017-12-27 20:06:08Z

3

DiscretizeRegion[
  ImplicitRegion[
  x^2 + x + y^2 + Sin[4 x y] + Sin[3 x y] == 3.9, 
  {{x, -5, 5}, {y, -5, 5}}],
  AccuracyGoal -> 8]

answered Dec 27 '17 at 20:06

David G. Stork

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$\begingroup$ How come {x,-5,5} and {x,-5,5} works but not {-4,3} and {-3,3} does not work. $\endgroup$ – Arbuja Dec 27 '17 at 20:11

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3 Answers 3