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This is rough-and-ready. The Bud Workshop Program is much more sophisticated!

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Adjust the geometric bud-form by dragging white points.

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 on the tip and base of the bud-form.
It is generally rather more difficult to place the lower pole than to place the top pole.

A Beech in Outline, from Aberdeen, Scotland.

The Beech is slightly “bent”, but the geometry applied here is not, so there is a small but unavoidable mismatch of geometry and bud.

The Bud Workshop Program can deal with bent buds.

Please enable Java for an interactive construction (with Cinderella).

Path Curve Geometry also works for real Vortices,

though this picture of a pond-vortex is not the best example, because the the vortex is seen obliquely and in perspective from somewhere nearby, while the geometry is restricted to the architect's beloved "side elevation", namely, a view from infinity through infinitely powerful binoculars!

Thus, these views can't be expected to match very well without appropriate adaptation—but one can form the notion that such adaptation is possible (as, indeed, it is). The exercise also serves to highlight some of the technical difficulties attendant on this work..

Please enable Java for an interactive construction (with Cinderella).

See whether your λ-estimate agrees with that of Lawrence Edwards
on his tracing, made some forty years ago, of a sycamore bud.
He found a λ-value of 1.74.

Please enable Java for an interactive construction (with Cinderella).
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