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[{[email protected], GeometricTransformation[ Tube[splineCircle[{0, 0, 0}, 1, {0, 3.141592653589}], 1/12], {-1, 1, 1}]}, {1}], Boxed -> False]; g2 = Graphics3D[ Table[{[email protected], GeometricTransformation[ Tube[splineCircle[{0, -1, 0}, 1, {0, 3.141592653589}], 1/12], RotationTransform[Pi, {1, 0, 1}]]}, {1}], Boxed -> False]; g3 = Graphics3D[ Table[{[email protected], GeometricTransformation[ Tube[splineCircle[{0, -1, -2}, 1, {0, 3.141592653589}], 1/12], RotationTransform[Pi, {1, 0, 1}]]}, {1}], Boxed -> False]; g4 = Graphics3D[ Table[{[email protected], 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.
