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, also shown to the right. 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.
