A quite arbitrarily closed curve k[φ]
(on the sphere) defines two parts of a sphere. How can I mesh for example the smaller surface part? I intend to use the mesh topology for further calculation (area or something like this)
For example
k[φ_] := {Cos[φ] Sin[π/10 - 1/20 π Sin[4 φ]],
Sin[φ] Sin[π/10 - 1/20 π Sin[4 φ]], Cos[π/10 - 1/20 π Sin[4 φ]]}
defines a surface part which I would like to mesh(triangle)?
My first attempt considering only the boundray
ParametricRegion[k[φ], {{φ, 0, 2 Pi}}]
DiscretizeRegion[%]
(* DiscretizeRegion did not find any sample points *)
fails.
Is there an easy way to create such a surface mesh? Thanks!