how to project a perfect circle from a plane to a curved shape?

Ofcourse when a circle is projected on an eggshape it becomes an ellipse.

What I want is an translation of the  perfect circle from Top Plane onto  an eggshaped bowl.

The purpose is to cut perfect circles perpendicular through an eggshape.

And if that is possible these perfect circle holes should be patterned..not in a square of cirlce, but along a curved line.

It seems simple, but how?

Mathilde

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