The “trick” for all these instances (except the vortex)
is to place point C on the profile
at the height of the maximum width of the bud-form,
but to do this after the “poles” have been placed.

Place white point A on the tip of the bud-form,
Then set the axis using white point E.
Finally, using white point D,
Set white point B on that axis
at the base of the bud-form.

It is generally rather more difficult to place the lower pole than to place the top pole.

The Tulip is composite, and so its flanks differ.
One can fit an excellent path curve to each, but independently.

Often, especially as the time of a bud's opening nears,
it becomes impossible to match the whole bud, as here.
Typically, the inside of the bud begins to thrust out,
and pushes the outer parts at the base out of its way.
The bud in effect acquires a “waist,”
so that a fit can be obtained either to the top, or to the bottom, of the bud,
but not to both at the same time.
The start of the bud's opening can be detected by the geometry long before it is obvious to the eye.