Nested Path Curve Hierarchy
As we see on the page concerning how to fit a path curve to a bud profile, we may use the semi-imaginary invariant tetrahedron as a coordinate system.
Embedded ("nested") in these NULL coordinates is a further invariant "path" triangle, X'Y'Z', with vertex Z' "local", and both vertices X' and Y' at infinity. This is the "subNULL" InVariant Triangle (IVT).
This IVT is used as a further, 'nested' coordinate system.
If the point (F,G) lies in a path curve passing from vertex X', at infinity, to vertex Y', at infinity, then points F and G lie in geometric series on their respective triangle sides.
Finally, if the logarithms of the ordinates of these path-points F and G are plotted against each other, they lie in a straight line—the SubNULL Path Profile.
On the right, the method is applied to the right profile of a suspended water drip.
A water drip on a twig of a rose bush. Its right profile is a very good path curve at NULL level.
