The “trick” is to place point C on the profile
at the height of the maximum width of the bud-form,
after the “poles” have been placed on the tip and base of the bud-form.

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.