How to find the centre of a non-planar closed curve

Hi All

Would anyone know how to locate the centre point of a non-planar closed curve? (pls see attached file).
I know the Polygon Centre might work but not in my case of a degree 3 curve. I have tried to change degree to 1 for the curve which works, but this would be a compromise of the form.

Most graceful for any help at all!

Yutakacentre for non-planar periodic (3.6 KB)

centre for non-planar periodic curve_2019Dec15a
centre for non-planar periodic (4.5 KB)

Same as average of mid-point of lines connecting opposite points:

centre for non-planar periodic (10.4 KB)

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Thank you Joseph and Jakinta, for the inspirational replies. Shows how we break away from ready made components to work round problems!
Thank you so much!!