# Toroidal implicit region looks weird

I have the following toroid surface:

tt = ParametricRegion[{Cos[u] (10 + 0.2 Sin[v]),
Sin[u] (10 + 0.2 Sin[v]), Cos[v]}, {{u, 0, 2 Pi}, {v, 0, 2 Pi}}];
ParametricPlot3D[Evaluate[tt[[1]]], {u, 0, 2 Pi}, {v, 0, 2 Pi},
PlotRange -> {-11, 11}]


I want to build the solid region of the toroid (for the purposes of building a region difference and solving Laplace equation over that boundary)

I proceed by turning the torus

$\{Cos[u](R+r_f Sin[v]), Sin[u](R+r_f Sin[v]), Cos[v]\}$

into the implicit expression

$(\frac{\sqrt{x^2+y^2}-R}{r_f})^2 + z^2 \le 1$

ttSolid =
ImplicitRegion[((Sqrt[x^2 + y^2] - 10.0)/0.2)^2 + z^2 <= 1, {x, y,
z}]
RegionPlot3D[ttSolid]


But the implicit region doesn't look like a torus

Any idea what is the problem, and further, how to properly define a toroid region for NDSolve?

• Could you copy your code into the Question instead of giving an image of it, so that others can copy the code directly into Mathematica? Thanks. Jan 3, 2015 at 18:08
• It should be better now Jan 3, 2015 at 18:13
• Did you want an elliptic section toroid? This gives a thin circular section 0.2 radius ParametricPlot3D[{Cos[u] (10 + 0.2 Sin[v]), Sin[u] (10 + 0.2 Sin[v]), 0.2 Cos[v]}, {u, 0, 2 Pi}, {v, 0, 2 Pi}] Feb 18, 2016 at 16:37

You have too few PlotPoints. Try
RegionPlot3D[((Sqrt[x^2 + y^2] - 10.0)/0.2)^2 + z^2 <= 1,