# 4 circular arcs, how plot the minimal surface?

By using Sjoerd de Vries code for circular arcs:

ClearAll[splineCircle];
splineCircle[m_List, r_, angles_List: {0, 2 π}] :=
Module[{seg, ϕ, start, end, pts, w, k}, {start, end} =
Mod[angles // N, 2 π]; If[end <= start, end += 2 π];
seg = Quotient[end - start // N, π/2]; ϕ =
Mod[end - start // N, π/2];
If[seg == 4, seg = 3; ϕ = π/2];
pts = r RotationMatrix[start].# & /@
Join[Take[{{1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1,
0}, {-1, -1}, {0, -1}}, 2 seg + 1],
RotationMatrix[seg π/2].# & /@ {{1,
Tan[ϕ/2]}, {Cos[ϕ], Sin[ϕ]}}];
If[Length[m] == 2, pts = m + # & /@ pts,
pts = m + # & /@
Transpose[
Append[Transpose[pts], ConstantArray[0, Length[pts]]]]];
w = Join[
Take[{1, 1/Sqrt[2], 1, 1/Sqrt[2], 1, 1/Sqrt[2], 1},
2 seg + 1], {Cos[ϕ/2], 1}];
k = Join[{0, 0, 0}, Riffle[#, #] &@Range[seg + 1], {seg + 1}];
BSplineCurve[pts, SplineDegree -> 2, SplineKnots -> k,
SplineWeights -> w]] /; Length[m] == 2 || Length[m] == 3

g1 = Graphics3D[
Table[{Hue@0.1,
GeometricTransformation[
Tube[splineCircle[{0, 0, 0}, 1, {0, 3.141592653589}],
1/12], {-1, 1, 1}]}, {1}], Boxed -> False];
g2 = Graphics3D[
Table[{Hue@0.1,
GeometricTransformation[
Tube[splineCircle[{0, -1, 0}, 1, {0, 3.141592653589}], 1/12],
RotationTransform[Pi, {1, 0, 1}]]}, {1}], Boxed -> False];
g3 = Graphics3D[
Table[{Hue@0.1,
GeometricTransformation[
Tube[splineCircle[{0, -1, -2}, 1, {0, 3.141592653589}], 1/12],
RotationTransform[Pi, {1, 0, 1}]]}, {1}], Boxed -> False];
g4 = Graphics3D[
Table[{Hue@0.1,
GeometricTransformation[
Tube[splineCircle[{0, 0, -2}, 1, {0, 3.141592653589}],
1/12], {-1, 1, 1}]}, {1}], Boxed -> False];
g4 = Show[g1, g2, g3, g4]


I plotted these four circular arcs:

How can I make a minimal surface that describes both the space inside it, and outside it stretching out to infinity? The minimal surface should describe the object as a whole and not the four arcs individually.

-
Have you seen this? indiana.edu/~minimal/archive/web/mathematica.html – Dr. belisarius Jan 17 '14 at 15:24
No I have not seen it before. – Mats Granvik Jan 17 '14 at 15:27
It's linked in the page you referenced – Dr. belisarius Jan 17 '14 at 15:28
There is now a solution at the generalized question Can Mathematica solve Plateau's problem (finding a minimal surface with specified boundary)? – Rahul Jan 23 '15 at 9:11
Sorry, I would like to retract my close vote. This question asks for the minimal surface to extend beyond the boundary too. – Rahul Jan 23 '15 at 9:13