# How to Discretize the Following Region Using Reasonable Bounds?

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?

• {{x, -5, 5}, {y, -5, 5}} – David G. Stork Dec 27 '17 at 20:04
• @DavidG.Stork How come this works but the others don't. – Arbuja Dec 27 '17 at 20:12
• (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? – No don't shown my real name Dec 28 '17 at 1:55
• @Nodon'tshownmyrealname Because I'm careless! I edited the question. – Arbuja Dec 28 '17 at 2:04

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}}
]


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

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 )

• I tried your code but I doesn't give the full picture. – Arbuja Dec 27 '17 at 20:56
• For some reason only entering {x,-5,5} and {y,-5,-5} works. – Arbuja Dec 27 '17 at 21:00
• there seems to be a version issue. Works for me with 10.1 , not with 11.1. – george2079 Dec 27 '17 at 21:15
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]


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